Political Capital

Gratton, Gabriele; Holden, Richard; Lee, Barton E

doi:10.1093/jleo/ewab027

Abstract

An organization must make a binary choice in each of the two periods. The optimal choice depends on an unknown state of nature. The leader of the organization has a stock of political capital and observes a private signal of the state. The leader faces an intertemporal choice problem. She may choose to spend (some of) her political capital to increase the probability that the choice is not the one that would otherwise be made. Her political capital increases if the decision is correct ex post. We characterize the optimal use of political capital by the leader and how it evolves over time. We identify different leadership styles that depend on the initial stock of capital of the leader, the precision of her information, and the importance of the issue to her. We study how different leadership styles determine the evolution of power within the organization. Finally, we consider issues of optimal organizational design that structures the allocation of power to a leader. (JEL D21, D23, D71, D72).

1. Introduction

“I earned $\dots$ political capital, and now I intend to spend it. It is my style.”
George W. Bush

Most organizations—in business, politics, and academia—feature leaders who can sway collective decisions. In business, a CEO may persuade her firm’s board to approve a project the board is initially skeptical about. She may do so by appealing to personal friendships with members of the board, or even by threatening to resign. In politics, US presidents may coax Congress into passing legislation that does not have the initial support of the majority of members. They may, for example, claim a popular mandate for policies on which they campaigned, or appeal to party unity. Similarly, in academia, a senior faculty member may push to hire a job candidate the recruiting committee is initially inclined to reject, perhaps by exerting influence over junior colleagues.

That leaders have the power to influence decisions is not controversial. Yet, power to influence is not an easy concept to define, as it includes both formal and informal components. For example, in Hollander’s (1958, 1960, 1978, 2009) theory of “idiosyncrasy credit,” leaders have an account of credit with group members they can spend to deviate from group norms and assert influence (see also Bass 1990: Ch. 17).¹ These credits are “given and received as rewards” from a leader’s social exchange with her followers (Hollander 1978). Therefore, power to influence derives from the leader’s network of friends and allies within the organization, the organization’s informal system of favor exchanges, and even the organization’s culture (March 1981: 216–219).

All these elements contribute to the leader’s power to sway collective decisions² and determine whether and when the leader may choose to exercise this power. In fact, forcing the hand of others on one issue today may have consequences for the leader’s future influence. For example, the leader may lose future influence because she makes enemies among those who are strongly opposed to the alternative she advocates, or because she loses the support of those who feel they owed her just one more favor. But the leader may also increase her future influence if the alternative she advocated turns out to benefit many in the organization. Just as she may be held accountable for supporting the wrong alternative, so may she be rewarded for advocating the right one. As pointed out by Hollander, a leader’s stock of credit evolves dynamically: it “increase[s] or decrease[s] as a function of the group’s perception of the individual’s task performance” (Hollander 1958). The extent of these effects may depend on a “culture of reward” or “culture of blame” within the organization.

In this article, we take an economic approach to defining informal power by focusing on a class of leader-specific assets: the leader’s political capital. This concept is meant to encompass any intangible asset of the leader that (i) affords the leader greater power to influence decisions; (ii) is immediately reduced when the leader chooses to exercise this power;³ and (iii) dynamically increases if the leader advocates in favor of an alternative that benefited many in the organization.⁴ Our objective is two-fold: first, we study the leader’s problem of whether and when to use her power to influence decisions; second, we study this problem’s implications for the design of organizations that induce leaders to use their power effectively.

We analyze a model in which a leader can gain or lose political capital by voicing dissent against a default alternative chosen by other members of her organization. In the model (i) a leader with greater political capital has more power, in the sense that she has a greater chance to affect the decision; (ii) voicing dissent immediately reduces the leader’s political capital—we say that the leader spends her political capital; but (iii) it may either increase or decrease her future capital, depending on whether her dissenting opinion turns out to be correct for the organization as a whole.

We study whether the leader chooses to spend her capital on today’s decision or save it for a future decision. The leader’s optimal choice depends on her stock of capital, the precision of her information, and whether the issue at stake is more or less important for her. For example, the President of the United States may choose to spend her political capital only on issues that were central to her campaign. Similarly, senior faculty may choose to spend their political capital only on job candidates in their own fields.

We show that the leader optimally chooses one of three leadership styles and that the chosen style affects the dynamics of power within the organization. Leaders with sufficient political capital but poor information choose to be patient: they save their capital and spend it only on issues that are important to them. Although patient leaders spend their capital sparingly, when they spend it they are unlikely to regain it, and therefore their power declines over time. Leaders with intermediate precision of information choose to be loud: they spend their capital on all issues and their power declines over time. Finally, the most informed leaders choose to be strong: they spend their capital on all issues and their power grows over time.

For a given stock of political capital, leaders with the least precise information are more likely to be patient. Therefore, conditional on disagreeing with the default choice of the organization, leaders are more likely to spend political capital when their information is more precise. But the unconditional probability of spending political capital on any given issue is nonmonotonic in the precision of the leader’s information—while loud leaders have less precise information than strong leaders, they are more likely to voice their dissent on any given issue.

More political capital does not necessarily induce the leader to voice dissent more often. To put it another way: some patient leaders have more political capital and power than some loud leaders.⁵ How more capital affects the leader’s decision hinges on the marginal power of political capital and therefore on the shape of the mapping of political capital into power. Intuitively, when the marginal power of capital is greater after the leader’s preferred alternative is revealed to be better (respectively, worse) than the default, then a larger initial stock of political capital translates into a greater return (respectively, smaller loss) to voicing dissent. We give a concrete example within a linear framework and show how our results naturally relate to the leader’s power “career concerns.”

Our model formalizes aspects of social psychology theories by Homans, Hollander, and Alvarez, and derives their implications for the design of organizations. Our flexible, reduced-form approach permits our framework to speak to a range of issues, including the institutional and cultural design of organizations. The leader’s initial stock of political capital, and therefore her power, is, in many ways and in many instances, an organizational-design choice (Cyert and March 1963; Milgrom and Roberts 1988) reflecting issues such as the political legitimacy of the leader’s office or the composition of a firm’s board.⁶ The experimental literature that builds off Hollander’s (1958, 1960) theory of idiosyncrasy credits shows that an organization can affect a leader’s stock of political capital by changing their job title and by constructing artificial tasks that show the leader excelling in front of group members (see e.g., Hollander 1960; Alvarez 1968). We show that the optimal allocation of power depends on the leader’s precision of information and how her power career concerns affect her behavior. Because a leader concerned about her future power may optimally choose to save her political capital for future issues, the organization may need to optimally tradeoff a more active, but less powerful leader with a less active, but more powerful one. For a leader with sufficiently precise information, the second option dominates, whereas the first option dominates when the leader’s information is imprecise. Therefore, it may be optimal to allocate more power to leaders with less precise information.

How changes in political capital map into changes in power to influence decisions also largely depends on institutional details. We show how this mapping can be used to affect how “junior” leaders optimally spend political capital. Finally, we discuss how organizations can induce a more or less active leadership style by promoting organizational cultures that differently reward the leader’s contribution—an idea echoed by General Electric’s former CEO Jack Welch’s remark that “we reward failure” since doing otherwise would only discourage the daring (Farson and Keyes 2002).

In their seminal work, Cyert and March (1963) observe that side payments within organizations are often nonmonetary and, instead, take the form of policy commitments or promises over future decisions (see also Gibbons 2019). Our power career concerns capture precisely such nonmonetary incentives, and our results show how political capital, appropriately allocated and controlled, can complement monetary incentives for leaders.⁷ For example, because of the multitasking nature of a CEO’s job, the optimal contract naturally creates issues that are more or less important for her. In this case, the CEO’s desire to accumulate political capital for future issues that the contract makes important to her may induce her to exert effort to persuade the board also on issues that the contract cannot cover or does not reward.

More broadly, we model a multitasking environment. In such environments, incentives can lead to crowding out—the agent exerts greater effort on incentivized tasks at the expense of unincentivized tasks (Holmström and Milgrom 1991). However, the empirical evidence on this crowding out effect is mixed, suggesting that incentivized tasks may have positive spillovers on unincentivized tasks (Lazear 2000; Belot and Schröder 2016; Kuang et al. 2019). Kuang et al. (2019) argue that positive spillovers can result from complementarities between unincentivized and incentivized tasks.⁸^,⁹ Our model captures a particular form of complementarity—which we call political capital—that stems from interpersonal relationships within organizations. In particular, we show that positive spillovers (respectively, crowding out) is more likely to occur when a leader holds a lower (respectively, higher) stock of political capital.

Related approaches are taken in Li et al. (2017) and Campbell (2017). Li et al. (2017) study relational contracts where the principal allocates “power” to an agent, and then dynamically adjust this allocation depending on the agent’s performance. Campbell (2017) considers mechanisms that elicit information from an agent by restricting participation in future decision making. We also study a feature of organizations that dynamically determines a leader’s power to affect decisions—political capital. In contrast to the scope of the mechanisms studied in these papers, in our context, the organization can only partially control how political capital and power interact.

The comparison between our patient and loud/strong leadership styles naturally connects to two commonly discussed leaderships styles in the Full Range Leadership Model (Burns 1978; Bass 1985, 1988), namely active and passive management-by-exception (MBE). Active MBE leaders regularly “intervene to correct problems and pointing out mistakes”; passive MBE leaders “intervene only when it is absolutely necessary” (Atwater and Yammarino 1996). Our nonmonotonic comparative static results may offer an explanation for Singh’s (2009), Yang’s (2015), and Yang and Li’s (2017) mixed evidence on the relationship between these leadership styles, a leader’s power, and organization performance (see also Atwater and Yammarino 1996; Bass 1985, 1990).

There is a large body of work on “leadership”—particularly those papers which consider signaling by leaders as a means of persuasion.¹⁰^,¹¹ Notable examples include Prendergast and Stole (1996), Hermalin (1998), and Majumdar and Mukand (2004).¹² We take a more reduced-form approach to persuasion by the leader, but focus on how and when the leader chooses to exert influence—that is, her “style.” Rotemberg and Saloner (1993, 2000) connect leadership style and organizations, which relates to our Section 5, below. Bertrand and Schoar (2003) show that a significant amount of the heterogeneity in managerial practices can be explained by “style.” We suggest a channel in addition to the one(s) they identify and our analysis implies that such styles are not immutable managerial characteristics.¹³

Our framework bears some similarity to Aghion and Tirole’s (1997) notion of “real versus formal authority” in that decision rights are noncontractible so that power and authority are determined within the organization rather than by it. Our concept of spending political capital partially embodies the idea that communication in organizations is costly. We share this idea with the now large literature on communication in organizations initiated by Dessein (2002), although we do not consider strategic information transmission à la Crawford and Sobel (1982).

In our model, political capital affords limited veto power to the leader. In a recent article, Bouton et al. (2018) emphasize that majority voting with veto power combines positive elements of both majority voting and unanimity. In practice most organizations do not allocate “hard” veto power “forever” to any of their members. Our concept of political capital may therefore be thought of as a more flexible, informal, and dynamic allocation of veto power. We take the perspective that such a flexible structure is naturally present in most organizations and focus on how institutions should be designed to take full advantage of it and incentivize an efficient use of a leader’s political capital.

The remainder of the article is organized as follows. Section 2 introduces our model and discusses some of our modeling choices. Section 3 characterizes the leader’s optimal strategy. Armed with this, Section 4 analyzes the relationship between leadership and power—specifically how power evolves, and different leadership styles. Section 5 takes an optimal organization design perspective in light of leadership styles and political capital. Section 6 offers some concluding remarks.

2. The Model

Consider an organization which operates for two periods. In each period

t \in {1, 2}

⁠, the organization chooses an alternative a_t from the set

{0, 1}

⁠. Which alternative is best for the organization depends on an unknown state,

θ_{t} \in {0, 1}

⁠. In particular, the value

v_{t} (a_{t} | θ_{t})

of choosing alternative a_t when the state is θ_t is given by

v_{t} (a_{t} | θ_{t}) = {\begin{matrix} 1 & if a_{t} = θ_{t}; \\ 0 & otherwise . \end{matrix}

In each period t, the organization’s default choice is optimal (⁠ $a_{t} = θ_{t}$ ⁠) with probability $π > 1 / 2$ ⁠. Without loss of generality, we can relabel the alternatives in ${0, 1}$ such that, for each period t, the default choice is a_t = 0. Notice that this implies $\Pr (θ_{t} = 0) = π$ ⁠. Deviations from the default choice are possible only if the organization’s leader spends some of her political capital in favor of alternative a_t = 1.

The leader’s initial stock of political capital is k₁. At the beginning of each period t, the state $θ_{t} \in {0, 1}$ is realized, and then the leader privately observes a signal $s_{t} \in {0, 1}$ such that $s_{t} = θ_{t}$ with probability $σ > π$ ⁠. Upon observing the signal $s_{t},$ the leader can choose to spend c > 0 units of her political capital in favor of alternative a_t = 1. If the leader chooses to spend capital, then a_t = 1 with probability $P (k_{t})$ ⁠. Hence $P (k_{t})$ is the leader’s power to sway the organization’s choice. We assume that $P : ℝ \to [0, 1]$ is increasing and we say that the leader is irrelevant whenever $P (k_{t}) = 0$ ⁠.¹⁴ For simplicity, we assume that irrelevant leaders cannot spend political capital.

Spending political capital also affects the leader’s future stock of capital once the state is revealed. In particular, her capital in period 2 is given by¹⁵

k_{2} = {\begin{matrix} k_{1} + B (θ_{1}) - c & if she spends capital at t = 1; \\ k_{1} & otherwise, \end{matrix}

where

B (1) > 0 > B (0)

⁠. Our law of motion of political capital captures the idea that spending political capital is a risky gamble for the leader, as it entails assuming responsibility for her intervention. In contrast, not spending political capital—not voicing dissent—has no effect on the leader’s future power.¹⁶ For the remainder of the analysis, we focus on the case

B (1) > c

so that it is possible for the leader’s political capital (and therefore power) to increase.

Within each period, the leader’s preferences are aligned with those of the organization. Nevertheless, some issues may matter to the leader more than others. In particular, at the beginning of each period t, the leader observes the importance

α_{t} \in {α^{L}, α^{H}}

of the period-t issue to her, such that the value

u_{t} (a_{t} | θ_{t}, α_{t})

for the leader of choosing alternative a_t when the state is θ_t is given by

u_{t} (a_{t} | θ_{t}, α_{t}) = {\begin{matrix} α_{t} & if a_{t} = θ_{t}; \\ 0 & otherwise, \end{matrix}

where

0 < α^{L} < α^{H}

⁠.¹⁷ The prior probability that the period-t issue is of high importance to the leader is

\Pr (α^{H}) \in (0, 1)

⁠.

2.1 Discussion of the Model

Our reduced-form approach allows us to delineate three channels in which organizational design can affect how leaders use their political capital. These different channels naturally map into the elements described in the social psychology literature we discussed in the introduction. First, the initial stock of political capital k₁ is meant to capture the leader’s legitimacy and credit at the time she is appointed as “leader.” Second, the function P is meant to capture institutional details that determine how political capital maps into power to influence decisions. Third, the law of motion of capital B captures aspects of the organization’s culture that differently reward the leader’s contribution. We will return to each of these three elements and discuss how they can be optimally designed in Section 5.

The state-independent cost of spending capital, c, aligns with Hollander’s (1958) view that a leader “loses credits” for deviating from group norms. Whether the value of c depends on k_t is a key distinction between Hollander’s theory and Homans’s related theory of social exchange. However, the empirical literature has failed to provide conclusive evidence either way (Alvarez 1968).

In the next section, we study the optimal strategy for the leader of a given organization. We do so under one regularity assumption about the organization itself. For some values of the model’s parameters, the leader may prefer to spend capital in favor of an alternative that she does not believe to be optimal for the organization, that is, she spends capital in favor of a_t = 1 when she believes that $θ_{t} = 0$ with probability greater than 1/2. In fact, if the current decision is of low importance to her (⁠ $α_{t} = α^{L}$ ⁠), she may choose to spend political capital in favor of alternative a_t = 1 solely in the hope of accumulating more capital, and therefore power, in the future (if $θ_{t} = 1$ ⁠). Because our focus is on the intertemporal decision of when to spend political capital, rather than in favor of which alternative, we rule out this perverse incentive for the leader. We thus impose some structure on the function P. Assumption 1 says that the organization is designed in such a way that the leader does not spend her capital in favor of alternatives she does not believe in (when she prefers alternative a_t = 0).¹⁸

Assumption 1. Spending political capital in period 1 when $s_{1} = 0$ results in an expected decline of the leader’s power.¹⁹

3. The Leader’s Optimal Strategy

We now study the leader’s optimal strategy. We proceed backward, starting from period t = 2. Lemma 1 says that in period 2 the leader optimally spends political capital if and only if she prefers alternative $a_{2} = 1$ and she is not irrelevant.

Lemma 1

(The leader’s optimal strategy in period 2). In period 2, a nonirrelevant leader spends political capital if and only if she prefers alternative $a_{2} = 1$ ⁠.

Proof. In Appendix A. □

Intuitively, in period 2, the leader only needs to choose whether to influence the decision on the period-2 issue, without any consideration to the future trajectory of her political capital. Therefore, she spends capital in favor of alternative $a_{2} = 1$ if and only if she believes it to be optimal for the organization.

The leader’s optimal strategy in period 2 does not depend on the amount of capital accumulated, k₂, or on the relative importance to her of the period-2 issue, α₂. In contrast, her optimal strategy in period 1 depends on both her initial stock of capital, k₁, and the relative importance of the period-1 issue, α₁. This is because the leader trades off the chance of influencing the period-1 decision with the possibility of increasing or decreasing her power to influence the period-2 decision.

To study this tradeoff, we express the leader’s expected payoff from the period-2 decision as a function V of her political capital in period 2. Using Lemma 1:

V (k_{2}) = \bar{α} π + \bar{α} (2 \Pr (θ_{2} = 1 | s_{2} = 1) - 1) \Pr (s_{2} = 1) P (k_{2})

(1)

where

\bar{α}

is the expected importance to the leader of the period-2 issue.²⁰ The first term is the leader’s expected payoff if she does not spend capital in period 2. The second term is the additional value for her of having political capital to optimally spend in period 2.

If the leader does not spend capital in period 1, then the organization takes the default choice and the leader retains all her initial stock of capital. Therefore, the leader’s expected payoff is given by

α_{1} (1 - \Pr (θ_{1} = 1 | s_{1})) + V (k_{1}) .

(2)

If instead she chooses to spend capital in favor of alternative

a_{1} = 1

⁠, then the organization chooses that alternative with probability

P (k_{1})

and the default choice with the remaining probability. Furthermore, her capital will evolve stochastically. With probability

\Pr (θ_{1} = 1 | s_{1})

⁠, k₂ equals

k_{1} + B (1) - c

⁠; otherwise, k₂ equals

k_{1} + B (0) - c

⁠. Therefore, the leader’s expected payoff is given by

\begin{matrix} α_{1} [(1 - \Pr (θ_{1} = 1 | s_{1})) + P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1}) - 1)] + \\ + \Pr (θ_{1} = 1 | s_{1}) V (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1})) V (k_{1} + B (0) - c) . \end{matrix}

(3)

The optimal choice for the leader depends on the comparison of the values in (2) and (3). Proposition 1 says that a non-irrelevant leader spends political capital in favor of alternative $a_{1} = 1$ whenever the issue is of high importance to her or her information is sufficiently precise.²¹

Proposition 1

(The leader’s optimal strategy in period 1). There exists a cutoff $σ^{*} (k_{1})$ such that a non-irrelevant leader spends political capital in period 1 if and only if she prefers alternative $a_{1} = 1$ and either $α_{1} = α^{H}$ or $σ > σ^{*} (k_{1})$ ⁠.

Proof. In Appendix A. □

Intuitively, when the period-1 issue is of high importance to the leader, she optimally spends her capital to influence the period-1 decision, rather than saving her capital for a future issue which, in expectation, is of lower importance. Instead, when the period-1 issue is of low importance, the leader needs to choose between the chance of influencing the period-1 decision and the possibility to save more capital for a future issue which, in expectation, is of greater importance. Since the leader loses political capital only when she spends it in favor of an alternative that turns out to be wrong, a leader with sufficiently precise information prefers to spend political capital also when the period-1 issue is less important to her. In contrast, a leader with very imprecise information faces a great risk of seeing her political capital reduced if she spends it in period 1. Hence, she prefers to save her capital for future issues if the period-1 issue is of low importance to her.

4. Leadership and Power

4.1 The Evolution of Power

The leader’s political capital increases whenever she spends it in favor of alternative

a_{1} = 1

and this alternative turns out to be optimal for the organization, that is,

θ_{1} = 1

⁠. By Proposition 1, the leader spends political capital only if she prefers alternative

a_{1} = 1

⁠. If the leader prefers alternative

a_{1} = 1

⁠, then this alternative a₁ is indeed optimal with probability

\Pr (θ_{1} = 1 | s_{1} = 1) = {[1 + \frac{1 - σ}{σ} \frac{π}{1 - π}]}^{- 1},

which is increasing in σ. Therefore, leaders with better private information are more likely to see their capital increase when they spend it. But capital matters for the leader, as well as for the organization, only insofar as it translates into power to affect decisions. Proposition 2 says that, when the leader optimally spends her political capital, she expects her power to grow if and only if her information is more precise than a threshold, which depends on her initial stock of capital.²²^,²³

Proposition 2

(The evolution of power). There exists a cutoff $\bar{σ} (k_{1}) \in (σ^{*} (k_{1}), 1]$ such that if the leader optimally chooses to spend her political capital, then

if $σ > \bar{σ} (k_{1})$ ⁠, the leader’s power is expected to grow over time;
if $σ < \bar{σ} (k_{1})$ ⁠, the leader’s power is expected to decline over time.

Proof. In Appendix A. □

A leader who expects her power to grow whenever she optimally spends her capital will spend capital on all issues, even those of low importance, that is, $\bar{σ} (k_{1}) > σ^{*} (k_{1})$ ⁠. Intuitively, spending capital improves the period-1 decision but may cost future power. However, when the leader expects her power to grow, there is no such tradeoff: spending capital both improves the period-1 decision and, in expectation, increases the leader’s power.

Proposition 2 says that small differences in either the quality of a leader or her initial stock of political capital may lead to different outcomes in terms of the evolution of power within the organization. Consider two organizations with leaders with information and capital $(σ, k_{1}) : σ^{*} (k_{1}) < σ < \bar{σ} (k_{1})$ and $(σ^{'}, k_{1}) : \bar{σ} (k_{1}) < σ^{'}$ ⁠, respectively. In period 1, both organizations have the same function P and culture, and leaders with the same initial stock of capital, and therefore power. Furthermore, the two leaders behave identically: they both spend their political capital whenever they dislike the default choice of their respective organizations. Therefore, the two organizations, as well as the leaders, may appear to be identical and following the same leadership style, to an observer that cannot directly measure a leader’s precision of information.²⁴ Yet, in expectation, the leader with precision $σ'$ will have greater power in period 2. In contrast, the leader with precision $σ < σ'$ will see her power decline. Hence, the first organization develops a more concentrated decision-making process; the second develops a more diffused decision-making process.

4.2 Leadership Styles

Propositions 1 and 2 together reveal three possible leadership styles:²⁵

Patient. A patient leader spends political capital only on issues that are of high importance to her. Her power is expected to decline over time.
Loud. A loud leader spends political capital on all issues. Her power is expected to decline over time.
Strong. A strong leader spends political capital on all issues. Her power is expected to grow over time.

A leadership style simultaneously determines the role that a leader chooses to play within the organization and how power evolves within the organization. In particular, only organizations that feature a strong leader are likely to develop concentrated power structures where a single person takes most decisions. In our model, this translates in the leader having greater power in period 2, and therefore a greater probability that the organization will choose alternative $a_{2} = 1$ ⁠. Thus, while a loud and a strong leader with the same initial stock of political capital k₁ will produce identical outcomes in period 1, they are likely to produce different outcomes in period 2, when their stock of political capital is expected to differ.

We now study what induces a leader to choose one of the three styles.

Proposition 3

(Optimal leadership styles). A non-irrelevant leader is patient if $σ < σ^{*} (k_{1})$ ⁠, loud if $σ \in [σ^{*} (k_{1}), \bar{σ} (k_{1}))$ ⁠, and strong if $σ ⩾ \bar{σ} (k_{1})$ ⁠.

Proof. In Appendix A. □

Proposition 3 connects with both theoretical and empirical findings in the management science literature. The distinction between patient and “active” (i.e., loud or strong) leadership styles that we identify finds a natural parallel in the distinction between passive and active MBE leadership styles in the Full Range Leadership Model (Burns 1978; Bass 1985, 1988). Furthermore, our analytical characterization of active-MBE leaders having more precise information (e.g., greater expertise) than passive-MBE leaders is consistent with empirical findings in Atwater and Yammarino (1996).²⁶

Figure 1 shows the optimal leadership style in the

(σ, k_{1})

space. The figure is drawn for a simple case we shall return to at several stages when building intuition for our results. In this special case, the leader’s capital evolves with law of motion

B (θ)

such that

B (1) = - B (0) \equiv b > c

⁠, capital translates into power (piece-wise) linearly, and the leader is irrelevant whenever she has less than c units of capital²⁷:

P (k_{t}) = P_{L} (k_{t}) = {\begin{matrix} 0 & if k_{t} < c; \\ \max {k_{t}, 1} & if k_{t} ⩾ c . \end{matrix}

Figure 2 depicts this function.

In this special case, if the leader has less than c units of political capital, she cannot influence the organization’s decision and is therefore irrelevant. However, if her capital is greater than c, but her information is sufficiently imprecise, she prefers to use her power sparingly, only spending political capital when more important issues arise. Such a patient leader eventually loses the little power she has, as her political capital tends to decrease over time. In contrast, when her information is very precise, the leader optimally chooses a strong style. Such a leader is so sure of herself that she spends political capital on any issue on which she disagrees with the default choice. She does so at no expected cost, because her information is so precise that spending political capital results in an expected growth in power. Between these two extremes lies a leadership style that we call loud. A loud leader is sufficiently sure of herself to spend capital on all issues on which she disagrees with the default choice. But her information is not precise enough to avoid frequent mistakes. In fact, her probability of making mistakes is large enough that her power will decline.

Conditional on preferring alternative $a_{1} = 1$ to the default choice, both a loud and a strong leader will voice their dissent. Nevertheless, we now show that loud leaders are indeed “louder” in the sense that they have a higher probability of voicing their dissent on any given issue. Proposition 4 states this result. Figure 3 provides an illustration for the special case when P = P_L, $B (1) = - B (0)$ ⁠, and the leader has an initial stock of political capital $k_{1} = 0.4$ ⁠.

Figure 1.

Leadership Styles in the $(σ, k_{1})$ Space for P = P_L and Parameter Values $c = 0.2, B (1) = - B (0) = 0.3, π = 0.55, α^{L} = 1, α^{H} = 30, \Pr (α^{H}) = 0.95$ ⁠.

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Figure 2.

The Piece-Wise Linear Function P = P_L.

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Figure 3.

The Leader’s Probability of Spending Political Capital in Period 1 for P = P_L and Parameter Values $k_{1} = 0.4, c = 0.2, B (1) = - B (0) = 0.3, π = 0.55, α^{L} = 1, α^{H} = 30, \Pr (α^{H}) = 0.95$ ⁠.

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Proposition 4

(Loud means loud). The probability that a nonirrelevant leader spends political capital in period 1 has local maxima at $σ = π$ and $σ = σ^{*} (k_{1})$ ⁠, and is strictly decreasing in σ for $σ < σ^{*} (k_{1})$ and $σ > σ^{*} (k_{1})$ ⁠.

Proof. In Appendix A. □

To gain some intuition, consider a loud and a strong leader. Both leaders voice dissent whenever they disagree with the default choice. But a loud leader’s information is less precise than that of a strong leader. Since the default choice is right more than half of the time, a loud leader is more likely to disagree with it than a strong leader in the first place. Thus, leaders who choose a loud style are those with the highest probability of voicing disagreement with the default choice on any given issue.

4.3 Political Capital and Leadership Styles

We now explore how political capital affects the leader’s choice of a style. By spending political capital in period 1, the leader suffers an expected loss of capital of

c - \Pr (θ_{1} = 1 | s_{1} = 1) B (1) + [1 - \Pr (θ_{1} = 1 | s_{1} = 1)] B (0)

but may also benefit from influencing the period-1 decision. In particular, the expected period-1 benefit of spending capital is

α_{1} [2 \Pr (θ_{1} = 1 | s_{1} = 1) - 1] P (k_{1}) .

An increase in political capital increases the benefit from voicing dissent while not changing the expected loss of capital. However, the leader does not care about political capital per se. Rather, she cares about political capital only in the measure in which this translates into power to influence future decisions.

To illustrate this distinction, consider a thought experiment in which capital and power coincide (i.e., $P (k_{t}) = k_{t}$ and $k_{1} \in (0, 1), k_{1} - c - B (0) ⩾ 0, k_{1} - c + B (1) ⩽ 1$ ⁠). In this case, more political capital increases the prosperity of the leader to spend capital. However, in the real world, not all marginal increases in capital translate to the same marginal increase in power. In our model, this is captured by the fact that the function P maps political capital into a probability in $[0, 1]$ ⁠. Therefore, the function P is necessarily concave (or convex) for some values of k_t, so that the marginal power of capital $P^{'}$ is decreasing (increasing). For example, a leader who is initially very powerful but short of being able to dictate decisions (i.e., $P (k_{1}) = 1 - ε$ for $ε > 0$ small) has little to gain from capital accumulation but faces a (relatively) large downside risk if she spends capital on the wrong alternative. Therefore, if the period-1 decision is of sufficiently low importance she will prefer to be patient.

To characterize the relationship between political capital and leadership styles, and how this is mediated by the manner in which capital translates into power, we first build intuition by analyzing the simple (piece-wise) linear function P_L and $B (1) = - B (0) \equiv b > c$ ⁠.

Suppose $P = P_{L}, B (1) = - B (0) \equiv b > c$ ⁠, and consider a nonirrelevant leader who initially holds little capital: $c ⩽ k_{1} < 2 c + b$ ⁠. The second inequality implies that if the leader chooses to spend capital, she faces the risk of becoming irrelevant. In fact, if the state is later revealed to be $θ_{1} = 0$ ⁠, the leader will remain with capital $k_{2} < c$ ⁠, and therefore $P (k_{2}) = 0$ ⁠. This potential cost of spending capital—losing the status of powerful leader—is increasing in the initial stock of capital. Therefore, a leader with marginally more capital (and therefore power) has a greater incentive to be patient and save her capital for the future. Now consider a leader who initially holds much power, but short of what would be enough to dictate decisions whenever she spends capital: $1 - (b - c) < k_{1} ⩽ 1$ ⁠. The first inequality implies that if the leader chooses to spend capital, she may be in the future able to dictate decisions. If she spends capital and the state is later revealed to be $θ_{1} = 1$ ⁠, her capital will increase by a quantity $b - c > 0$ ⁠. Yet, the leader will only experience an increase of power equal to $1 - P (k_{1}) < b - c$ ⁠. This increase in power is decreasing in the initial stock of capital. Therefore, a leader with marginally more capital (and therefore power) has a greater incentive to be patient and save her capital for the future. Proposition 5 formalizes this intuition and says that the effect of political capital on the leader’s style is nonmonotonic: more capital may increase or decrease the propensity of the leader to spend capital (see also Figure 1).²⁸

Proposition 5

(The effect of capital on leadership styles when

P = P_{L}

⁠). Suppose

B (1) = - B (0) \equiv b

⁠. Let

P = P_{L}

and let

Σ^{P} (k_{1}) \equiv {σ \in (π, 1] : σ < σ^{*} (k_{1})}

be the interval of leader’s information precisions that induce her to optimally choose to be patient. If

Σ^{P} (k_{1})

is nonempty for some

k_{1} ⩾ c

⁠, then the length of

Σ^{P} (k_{1})

increases with k₁ when

k_{1} \in [c, 2 c + b)

and when

k_{1} \in [1 - (b - c), 1)

⁠. Otherwise, it decreases with k₁.²⁹

Proof. In Appendix A. □

This example illustrates how the shape of the function P affects the relationship between political capital and leadership styles. Intuitively, the function P transforms the potential gains and losses in political capital into gains and losses in the leader’s expected payoff from the period-2 decision according to $V (k_{2})$ in (1). When spending political capital, the potential gain is proportional to $P (k_{1} + B (1) - c) - P (k_{1})$ ⁠; the potential loss is proportional to $P (k_{1}) - P (k_{1} + B (0) - c)$ ⁠. Therefore, a marginal increase in the initial stock of political capital is more likely to induce the leader to voice her dissent when the marginal power of capital $P'$ is large at $k_{1} + B (1) - c$ and at $k_{1} + B (0) - c$ compared to what it is at k₁. Proposition 6 makes this intuition more precise.³⁰

Proposition 6

(The effect of capital on leadership styles). Let

Σ^{P} (k_{1}) \equiv {σ \in (π, 1] : σ < σ^{*} (k_{1})}

be the interval of leader’s information precisions that induce her to optimally choose to be patient. If

Σ^{P} (k_{1})

is nonempty for some

k_{1} \in ℝ

⁠, then the length of

Σ^{P} (k_{1})

increases with k₁ if

\begin{matrix} (1 - π) σ^{*} (k_{1}) P' (k_{1} + B (1) - c) + π (1 - σ^{*} (k_{1})) P' (k_{1} + B (0) - c) < \\ [(1 - π) σ^{*} (k_{1}) + π (1 - σ^{*} (k_{1})) - \frac{α^{L}}{\bar{α}}] P' (k_{1}) . \end{matrix}

(4)

Otherwise, it decreases with k₁.

Proof. In Appendix A. □

5. Organization Design

5.1 Optimal Allocation of Political Capital

Organizations have limited ability to determine the initial stock of political capital of a leader. For example, in politics, different electoral systems may give more or less legitimacy to the president, or even guarantee that a majority of the legislature supports her platform. Therefore, while the legislature maintains its independence, the president’s initial stock of political capital is in part determined by institutional choices. Similarly, board of directors may delegate more or less authority to a CEO, and shareholders may choose board members that are personally close to the CEO. Therefore, while the board has the ultimate control over the CEO, the CEO’s initial stock of capital is in part determined by the composition of the board itself. In both cases, the organization may allocate more or less political capital, and therefore power, to the leader, but only within limits.

We now study the optimal allocation of political capital to the leader when the organization operates with an exogenously given function, P.³¹ The organization can choose any initial stock of political capital³²

k_{1} ⩽ \bar{k}

to maximize

E [\sum_{t = 1}^{2} v_{t} (a_{t} | θ_{t}) | k_{1}] .

The optimal allocation of political capital

k^{*} (σ)

obviously depends on the precision of the leader’s information σ and uniquely identifies the optimal allocation of power

P^{*} (σ) : = P (k^{*} (σ)) .

Our main result is that the functions $P^{*}$ and $k^{*}$ are not necessarily monotonic. That is, the optimal allocation of political capital (and therefore of power) may give more capital (and hence power) to a less informed leader.

Proposition 7

(The optimal allocation of political capital). The optimal allocation of political capital

k^{*} (σ)

⁠, and therefore power

P^{*} (σ)

⁠, is not necessarily monotonic in σ. It is equal to

\bar{k}

for all

σ \in (π, 1)

if

(1 - π) π [(P (k_{1}) - P (k_{1} + B (0) - c)) - (P (k_{1} + B (1) - c) - P (k_{1}))] ⩽ \frac{α^{L}}{\bar{α}} P (k_{1})

(5)

holds when

k_{1} = \bar{k}

⁠. It is U-shaped if (5) does not hold for all

k_{1} ⩽ \bar{k}

and the length of

Σ^{P} (k_{1})

increases with k₁ at

k_{1} = \bar{k}

(see Proposition 6).

Proof. In Appendix A. □

Figure 4 depicts a case when the optimal allocation of power is U-shaped. Intuitively, the organization values the leader’s interventions in the decision process. Yet, while for each issue taken individually the organization’s incentives are perfectly aligned with those of the leader, the leader’s choice of whether to spend her political capital on a given issue depends on its relative importance to her. Since the organization views all issues as equally important, it faces a tradeoff. On the one hand, if the leader spends her political capital often enough, the organization wishes to make her interventions as effective as possible, and hence prefers to allocate more power to the leader. On the other hand, as we discussed in Section 4.3, more power may induce the leader to embrace a patient leadership style, therefore saving her political capital when the issue at stake is of low importance to her.³³ Said otherwise, for a given leadership style, the organization wishes to maximize the leader’s initial stock of political capital; for a given stock of political capital, the organization strictly prefers a more active (loud or strong) leader to a patient one. Therefore, depending on the leader’s information, the organization may need to trade off a more active but less powerful leader with a less active but more powerful one.

Obviously, this tradeoff is not present if the leader optimally chooses an active leadership style whenever she is allocated an initial stock of political capital equal to the maximal stock

\bar{k}

⁠. In this case, the organization prefers to allocate as much power as possible to the leader, no matter how precise her information is—a “flat” allocation of power:

σ^{*} (\bar{k}) = π \Rightarrow P^{*} (σ) = P (\bar{k}) for all σ \in (π, 1) .

This corresponds to condition (5) in Proposition 7 holding for $k_{1} = \bar{k}$ ⁠. By Assumption 1, the left hand side of (5) is strictly between 0 and 1. Therefore, a flat allocation of power is optimal when the leader values low-importance issues almost as much as high-importance ones (α_L close to $\bar{α}$ ⁠) so that her incentives almost perfectly align with those of the organization. On the contrary, a flat allocation of power is less likely to be optimal when some issues are much less important than others to the leader, when the loss in power for spending capital on the wrong alternative is much greater than the gain for spending capital on the right alternative, or when the default choice is less likely to be correct.

Since sufficiently well-informed (and nonirrelevant) leaders always choose to be active (i.e., $σ^{*} (\bar{k}) < 1$ ⁠), when the leader is sufficiently well-informed, the organization can afford to maximize the effectiveness (power) of the leader’s interventions without inducing a patient leader. However, for leaders with less precise information (⁠ $σ < σ^{*} (\bar{k})$ ⁠) the organization needs to choose between maximizing the leader’s power and inducing an active leader. We now show that this tradeoff may induce the organization to optimally allocate more power to a less informed leader.

Suppose that for low values of σ the leader optimally chooses to be patient for any

k_{1} ⩽ \bar{k}

⁠. This corresponds to condition (5) in Proposition 7 not holding for all

k_{1} ⩽ \bar{k}

⁠. Then if the leader is sufficiently uninformed, the organization prefers to give the leader all the power that it can, as to make the leader as effective as possible when she chooses to spend her political capital. Yet, for higher values of σ, the leader may optimally choose to be loud (or strong), and therefore to be active more often, but only if the organization gives her less power. Now suppose that the organization’s function P is such that, for a leader with initial stock of political capital equal to

\bar{k}

and information

σ = σ^{*} (\bar{k})

⁠, a marginal increase in the initial stock of political capital induces the leader to be patient. By Proposition 6, this corresponds to

\begin{matrix} (1 - π) σ^{*} (k_{1}) P' (k_{1} + B (1) - c) + π (1 - σ^{*} (k_{1})) P' (k_{1} + B (0) - c) < \\ [(1 - π) σ^{*} (k_{1}) + π (1 - σ^{*} (k_{1})) - \frac{α^{L}}{\bar{α}}] P' (k_{1}) . \end{matrix}

(6)

Then for a leader with information just short of $σ^{*} (\bar{k})$ ⁠, the organization can afford an active leader by giving up only a very small amount of the leader’s power. Therefore, the organization strictly prefers an active, yet less powerful leader. This means that there exists a level of σ at which the organization optimally switches from a very effective but patient leader to a less effective but more active one. Figure 4 depicts such a situation when P = P_L and $B (1) = - B (0)$ ⁠. In this case, a nonmonotonic allocation of power is more likely to be optimal when the maximum amount of power $P (\bar{k})$ that the organization can allocate to the leader is close to 1 or c so that, by Proposition 5, a marginal increase in the initial stock of political capital induces the leader to be patient.³⁴

The actual value of $\hat{σ}$ at which the organization optimally switches from a very effective but patient leader to a less effective but more active one, naturally depends on how much the organization values having a more active leader. Since the cost of having a patient leader is proportional to the likelihood that the leader will save her political capital for future issues, $\hat{σ}$ is, all else equal, decreasing in $\Pr (α^{L})$ ⁠.

The Optimal Allocation of Power When k¯=1 and P = PL with Parameter Values c=0.2,B(1)=−B(0)=0.3,π=0.55,αL=1,αH=30,Pr⁡(αH)=0.95.

Figure 4.

The Optimal Allocation of Power When $\bar{k} = 1$ and P = P_L with Parameter Values $c = 0.2, B (1) = - B (0) = 0.3, π = 0.55, α^{L} = 1, α^{H} = 30, \Pr (α^{H}) = 0.95$ ⁠.

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5.2 Institutional Design

Our reduced-form model affords us to take a flexible approach as to how political capital maps into power to influence decisions. In fact, power to influence is distinct from political capital—in particular, organizational details, such as procedural norms, institutions, and rights to veto, induce different mappings from political capital into power. In our model, this implies that the function P is in part determined by institutional design. For example, if decisions are taken by majority voting, such as in a parliament or in a committee, the support of the pivotal median voter has very different consequences on the leader’s ability to influence decisions than the support of any other member of the organization. In this case, the function P has an “S” shape. The requirement of a broader consensus, such as supermajorities, would shift the vertical section of the S-shaped function to the right. Furthermore, the inclusion in a committee of other powerful personalities with effective veto powers may limit the amount of power afforded to the leader for any stock of political capital.

In practice, institutional design variables such as voting rules or the presence of veto players are typically “sticky”—often, as is the case for political institutions, to control the behavior of future leaders. We therefore take a long-term view and ask what type of institutions are more conducive to organizational welfare behind a veil of ignorance, that is, given a possible distribution F of future leaders with precision of information σ and initial stock of political capital k₁.

Our previous results highlight the importance of providing incentives for the leader to spend her political capital often enough in the interest of the organization. This is particularly important for leaders who, while not irrelevant, hold a small stock of initial political capital and are at risk of becoming irrelevant if they lose too much political capital. As we have seen, the incentives for such leaders depend on the shape of the function P which translates political capital into power to affect decisions. It is therefore natural to ask what type of institutions favors a more active role of junior leaders. To make more precise our analysis of this scenario, in this section we make the assumption that there exists a level of political capital $\underline{k}$ such that $P (k_{t}) = 0$ for all $k_{t} < \underline{k}$ ⁠. (In the case of our linear function P_L, $\underline{k} = c$ ⁠, that is, the cost of spending capital in favor of alternative a_t = 1).

Essentially, the institutional designer has two levers. First, he can choose the maximum amount of power $\bar{P} ⩽ 1$ to give to leaders with sufficient political capital. Second, he can choose how fast junior leaders can climb the power ladder, by choosing institutional details that make the function P raise more or less steeply from $P (\underline{k})$ to $\bar{P}$ ⁠.

One possible option is to give all leaders who are not irrelevant a constant amount of power: $P (k) = \bar{P}$ for all $k_{t} ⩾ \underline{k}$ ⁠. Such a design has the virtue of making all leaders, even those with little capital, very effective. Proposition 8 says that such a constant function is not always optimal.

Proposition 8

(Optimal institutions). There exist parameters c and b and distribution F such that the optimal function P is strictly increasing for some $k_{t} ⩾ \underline{k}$ ⁠.

Proof. In Appendix A. □

Intuitively, a constant function P does not leverage any career concern of the leader to induce her to be active and spend capital on issues that are not very important to her. Thus, junior leaders with little capital will be patient. Since this design aims to maximize the effectiveness of leaders, then it serves best this objective when $\bar{P} = 1$ ⁠. Furthermore, since career concerns incentives are relevant only for leaders who optimally choose to be patient, this design is optimal when most leaders are expected to hold large initial stocks of political capital.

Otherwise, the optimal function needs to leverage the career concerns of the leader, and so P must be strictly increasing for some k_t. On the one hand, this design makes leaders with little capital more valuable for the organization, as they will use their power more often. On the other hand, this design has two drawbacks. First, leaders with little capital are less effective when they choose to spend it. Second, some leaders that, under the design with constant power, would optimally choose to be active are now induced to be patient, as they fear that spending political capital may decrease their future power. Therefore, a design that leverages the leader’s career concerns is optimal only when most leaders have either very little or very large initial stocks of political capital.

5.3 Organizational Culture

Organizations vary as much in culture as they do in structure.³⁵ For example, an organization may embody a culture of reward, where success draws more attention than failure or, conversely, a culture of blame, where failure draws more attention.

The culture of an organization has a clear effect on leadership styles. As put by Groysberg et al. (2018), “for better and worse, culture and leadership are inextricably linked.” Entrepreneurs often underlined that innovation relies on encouraging experimentation and even failure. In the words of IBM’s Thomas Watson Sr., “the fastest way to succeed is to double your failure rate” (Farson and Keyes 2002). Therefore, organizations may adopt cultures that place relatively greater emphasis on leaders’ positive contributions to incentivize more active leadership styles. We focus on the effect of organizational culture on leader’s accumulation of political capital.³⁶ A leader in an organization with a greater culture of reward is expected to accumulate more political capital when the alternative she spends her capital on is revealed to be correct, and to lose less political capital when the alternative is revealed to be incorrect. Thus, a greater culture of reward is expected to increase the propensity of the leader to spend her political capital and is conducive to a patient leader becoming loud, and a loud leader becoming strong. The reverse can be concluded for a leader in an organization with a greater culture of blame.

To formally analyze the relationship between organizational culture and its effect on leadership styles we consider variations of the law of motion of political capital. Recall that a leader with an initial stock of political capital k₁ has period-2 capital given by

k_{2} = {\begin{matrix} k_{1} + B (θ_{1}) - c & if she spends capital; \\ k_{1} & otherwise, \end{matrix}

where

B (1) > 0 > B (0)

and

B (1) > c

⁠. We measure the relative importance of reward and blame by the values of B(1) and B(0). When the alternative that the leader spends her capital on is revealed to be correct her capital increases from k_t to

k_{t} + B (1) - c

⁠, otherwise it decreases to

k_{t} + B (0) - c

⁠. Thus, a greater B(1) provides the leader with more reward, and a greater B(0) provides the leader with less blame. We say that an organization with

B (θ_{1})

has a greater culture of reward than

\hat{B} (θ_{1})

if

B (1) ⩾ \hat{B} (1)

and

B (0) ⩾ \hat{B} (0)

⁠. Proposition 9 says that a greater culture of reward increases the propensity of the leader to spend political capital and is conducive to patient leaders becoming loud, and loud leaders becoming strong.

Proposition 9

(Culture of reward or blame). Let $Σ^{P} (k_{1}) \equiv {σ \in (π, 1] : σ < σ^{*} (k_{1})}$ and $Σ^{S} (k_{1}) \equiv {σ \in (π, 1] : σ ⩾ \bar{σ} (k_{1})}$ be the intervals of leader’s information precisions that induce her to optimally choose to be patient and strong, respectively. An increase in the culture of reward decreases the length of $Σ^{P} (k_{1})$ ⁠, and increases the length of $Σ^{S} (k_{1})$ ⁠.

Proof. In Appendix A. □

The intuition for Proposition 9 can be understood most clearly by returning to the tradeoff faced by a leader who faces a low-importance period 1 issue,

α_{1} = α^{L}

⁠, and receives the signal

s_{1} = 1

⁠. The expected payoff of spending political capital in period 1 is then

\begin{array}{l} α^{L} [(1 - \Pr (θ_{1} = 1 | s_{1} = 1)) + P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1} = 1) - 1)] \\ + \Pr (θ_{1} = 1 | s_{1} = 1) V (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \\ V (k_{1} + B (0) - c) . \end{array}

Her expected payoff of not spending political capital in period 1 is instead given by

α^{L} (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) + V (k_{1}) .

Recall that the future value of capital V is increasing in the level of period-2 capital. Therefore, a greater culture of reward increases the benefits of spending capital in period 1 via an increase in the expected stock of period-2 capital. On the other hand, changes in the culture (i.e., B(1) or B(0)) do not affect the expected payoff of not spending capital. A similar logic shows that the expected period-2 power is weakly increasing as B(1) increases and/or B(0) decreases. Thus, the threshold required for a leader to accumulate power over time, $\bar{σ} (k_{1})$ ⁠, is decreasing as the culture of reward increases.

Given Proposition 9, it may be tempting to view a greater culture of reward as analogous to an increase in the leader’s power or an upward shift in the function P.³⁷ However, this is not the case. As we discussed in Section 5.2, an increase in power or upward shift of the function P can create incentives for both loud and patient leadership styles; that is, there is an ambiguous effect on the leader’s propensity to spend political capital. For example, a leader with a high level of capital, say $P (k_{1}) = 1 - 2 ε$ for some sufficiently small $ε > 0,$ facing a low importance period-1 issue, $α_{1} = α^{L}$ ⁠, has little incentive to spend capital—at most, she may attain an additional $2 ε$ units of power. An upward shift in the function to $\hat{P}$ such that $\hat{P} (k_{1}) = 1 - ε$ would further reduce this incentive, since now the leader can attain at most additional ε units of power. In contrast, a greater culture of reward has an unambiguous effect: it increases the leader’s propensity to spend capital.

The key difference between an increase in the culture of reward and an increase in power is the timing of the effects they produce. An increase in power affects the leader’s period-1 power and hence her ambitions to accumulate power for the following period. A greater culture of reward does not affect a leader’s period-1 power. Instead, it only increases the expected future power returns of spending capital today.

6. Concluding Remarks

We have offered a simple framework for thinking about how collective decisions in an organization are influenced by a leader’s political capital. This framework is rich enough to capture issues like managerial “style” and the endogenous evolution of political capital, yet simple enough to permit a complete characterization of the leader’s optimal strategy and to analyze issues of organizational design and the allocation of power. Perhaps our most striking result is that the optimal allocation of power is nonmonotonic in the precision of the leader’s information.

Since at least Crawford and Sobel (1982) economists have been interested in how an expert with superior information to, but different preferences from, a decision maker can convey information and thus affect decisions. In a sense, cheap-talk models are about how information filters up a hierarchy. In contrast, we are concerned with how information flows down and how it is mediated by power. In our model, power stems from political capital.³⁸

Future leaders themselves have the ability to invest in their initial stock of political capital. In fact, alliances and friendships may be built well before the leader assumes her position, often at significant costs. In our model, from the point of view of the leader, political capital (and therefore power) and her own precision of information (or “talent”) are complements. Thus, the leader’s optimal investment in political capital (weakly) increases with the precision of her information.

Organizations and their leaders may also invest in the quality of the information they possess (via training, workshops, further education, investments in technology, etc.). Should this investment be concentrated on the organization’s leader or spread across all decision makers? Investing in the leader’s information may not be optimal from the organization’s perspective if the leader is patient and avoids making decisions in an attempt to preserve her political capital. But investing in other decision makers may also be wasteful if their decisions are likely to be revised by the leader. In our model, the value the organization attains from a marginal increase in the precision of the leader’s information is increasing in the leader’s political capital, whilst the relationship is reversed for the accuracy of the default choice—a measure of the precision of the information spread across all decision makers. Intuitively, the organization is better off when a more informed decision is made. When the leader has a higher level of political capital, her opinion is more likely to be decisive. Therefore, the organization relies heavily on the leader’s information and experience, and thus places greater value on marginal increases in the precision of her information. In contrast, a leader with a lower level of political capital is less likely to take the final decision. Therefore, the organization relies more heavily upon the collective wisdom of its members, and thus places greater value on marginal increases in the precision of the information spread across all decision makers.

There is now a sizable literature on “persistent performance differences” in organizations.³⁹ A striking empirical finding due to Bertrand and Schoar (2003) is that individual (top) managers have a significant impact on both firm behavior and performance. Remarkably, these are related to certain observable characteristics of managers such as their educational background or age. Our theory suggests that one potentially important unobservable characteristic of a CEO is her political capital. Moreover, since the realizations of decisions are stochastic this capital evolves over time. Finally, organizational design can affect managerial style in this regard.

We can also think of regulatory reforms as having an impact on the allocation of power. The Sarbanes-Oxley Act (2002) introduced a number of measures, one of which was aimed at increasing independence in the Board of Directors, ostensibly by requiring a majority of independent directors (Linck et al. 2009). This presumably limits the power of the CEO which, in the context of our results, may lead to a better alignment of the incentives of the leader/CEO and the organization.

Finally, as we have stressed, within an organization who is “the leader” may depend on context. In firms it is perhaps natural to think of the CEO as the unitary leader. In contrast, in an academic department, the role of leader may depend on the topic of the decision to be made—such as the subfield of a hiring decision. It may also be the case that in some circumstances it is better to think of the leader as a group of members in the organization rather than a single individual. This immediately raises questions of how such groups form, their stability, and other issues. Such questions may be an interesting prospect for future work.

We are grateful to Daniel Barron, Steven Callander, Juan Carlos Carbajal, and Andrea Mattozzi for helpful discussions, and to seminar participants at the Australian National University, Chicago Booth, Chicago Harris, University of Cagliari, University of Geneva, HEC Lausanne, Innsbruck, LSE, Warwick, the 37th Australasian Economic Theory Workshop, and the 13th Annual Organizational Economics Workshop. The authors acknowledge financial support from the Australian Research Council.

Footnotes

1

Similar ideas are present in Homans’s (1961) theory of social exchange; for an in-depth discussion that compares Hollander’s and Homans’s theories see Alvarez (1968).

2

In this sense, power captures the effectiveness of a leader’s “influence activities” (Milgrom and Roberts 1988).

3

Property (ii) is what distinguishes political capital from the concept of “social capital,” which, as argued by Arrow (1999), cannot be spent or invested.

4

As put by Karl Rove, “the president understands that if we are successful in the prosecution of the war, that will create political capital that can be used to expand on other things whether international or domestic” (Richard L. Berke, New York Times, December 12, 2001).

5

While discussing Homans’s theory of social exchange, Alvarez (1968) notes that a leader’s stock of credit may be a determinant of a leader’s propensity to dissent. However, this relationship need not be monotonic: “high-status persons initially have so much esteem that they can afford to risk the relatively small loss incurred by taking a deviant course; low-status persons have so little esteem that the threat of a relatively large loss is ineffectual […]; and, finally, middle- status persons do not have sufficient esteem that they can ‘write off’ some losses, but they do have enough esteem to make the threat of losing ‘their precious all’ painful. These may be the reasons why people deviate differentially.”

6

As stated in Hollander (1978): “The effectiveness of leadership also depends upon a leader’s legitimacy and authority. Legitimacy may come from appointment, election, or from the willing support of followers. […] A leader’s authority also is related to the nature of the rules governing the activity.”

7

In settings where monetary rewards are not possible or are customarily very low, such as in voluntary associations, clubs, or political parties, the informal incentive schemes we describe are likely to be the most important form of incentives for leaders, if not the only one.

8

This is also discussed briefly in Section 2.3 of Holmström and Milgrom (1991).

9

Building off Bénabou and Tirole’s (2003) single-task model, Al-Ubaydli et al. (2015) provide an alternative explanation for positive spillovers that derives from both the agent and principal having hidden information.

10

The dynamic nature of our analysis and our concern with the stock of political capital suggests a natural connection to work on reputation-effects (Kreps and Wilson, 1982; Kreps et al., 1982; Milgrom and Roberts, 1982; Fudenberg and Levine, 1983, 1986): in long-lived interactions, players have an incentive to give up something today in terms of their payoff to gain a reputation for playing in a certain fashion, which may benefit them down-the-track. In our model, the leader is conscious of the cost of using her influence today in terms of her ability to influence decisions in the future. Unlike the reputation-effects literature, our setup does not require considerations of (sequential) equilibrium as it involves a control problem for the leader. Moreover, our notion of political capital is not synonymous with reputation. For instance, it can be determined in part by organizational design choices. We further discuss the relation between our concept of political capital and reputation in Footnote 16.

11

The rapidly growing body of work on “Bayesian persuasion” initiated by Kamenica and Gentzkow (2011) shares some similarities with our approach. Such models emphasize how the choice of signal structure can influence a decision maker, whereas we are concerned with the use of power—stemming from political capital—to influence collective decisions.

12

Caillaud and Tirole (2007) consider leaders creating cascades to influence followers.

13

Dessein and Prat (2017) take a broad view of organizational capability, introducing the notion of “organizational capital.” Our concept of political capital might be thought of as a subset of organizational capital.

14

In Hollander’s theory, the leader is irrelevant when k_t = 0: “affiliation with the group—as perceived by the group—ceases when the individual’s credit balance reaches zero” (Hollander 1958).

15

In our model, political capital does not depreciate in time. As put by Karl Rove, “if you don’t spend it, it’s not like treasures stuck away in a storehouse someplace; it is perishable.” (Richard L. Berke, New York Times, December 12, 2001). The depreciation of political capital can be easily incorporated into our framework.

16

In practice there may be reputational components to political capital such that, when the leader does not spend political capital, $k_{2} = k_{1} + N (θ)$ ⁠, with $N (1) ⩽ 0 ⩽ N (0)$ ⁠. In Supplementary Appendix, we show that our qualitative results carry over if such reputational concerns are small compared to $B (θ) - c$ ⁠.

17

Our qualitative results hold if α_t is modeled as a continuous rather than a binary variable.

18

For example, if c < 1∕2, then Assumption 1 precludes the function $P (k_{t}) = c$ for k_t = c, $P (k_{t}) = 1$ for all $k_{t} > c$ ⁠, and $P (k_{t}) = 0$ otherwise.

19

That is, $\Pr (θ_{1} = 1 | s_{1} = 0) (P (k_{1} + B (1) - c) - P (k_{1})) + (1 - \Pr (θ_{1} = 1 | s_{1} = 0)) (P (k_{1} + B (0) - c) - P (k_{1})) ⩽ 0$ ⁠.

20

That is, $\bar{α} = \Pr (α^{H}) α^{H} + (1 - \Pr (α^{H})) α^{L}$ ⁠.

21

This precision-of-information cutoff is a function of all parameters of the model. However, in Proposition 1 and throughout the paper, we will simply denote this cutoff as a function of the leader’s period-1 stock of political capital k₁, that is, $σ^{*} (k_{1})$ ⁠, where the dependency on other parameters is implicit. We do this because the focus of the paper is on the effect of political capital on the leader’s behavior.

22

When the leader’s information is less precise, so that $σ < σ^{*} (k_{1})$ ⁠, the leader’s power remains constant whenever $α_{1} = α^{L}$ ⁠. Nevertheless, her power is expected to decline whenever she optimally chooses to spend her political capital, that is, $α_{1} = α^{H}$ and $s_{1} = 1$ ⁠.

23

This threshold is no larger than 1 because we assumed $B (1) > c$ ⁠, that is, it is possible for the leader’s political capital (and therefore power) to increase.

24

The only difference between the two leaders is that the leader with lower precision will spend her capital with slightly higher probability.

25

Of course, leaders with so little political capital that they have no power to influence decisions at all adopt a fourth style: irrelevant.

26

For example, they find that active-MBE leaders are more likely to have greater expertise than passive-MBE leaders.

27

Recall that c > 0 is the fixed cost of spending capital in favor of alternative a_t = 1.

28

The result that more capital may decrease a leader’s propensity to spend capital is driven by the shape of the function P. In particular, for P = P_L, leaders with capital just above c or just below 1 face asymmetric gains/losses in power. In the former case, the leader faces little downside risk from spending capital; in the latter case, the leader faces little upside benefit from spending capital.

29

Note that the length of $Σ^{P} (k_{1})$ is greater than the length of $Σ^{P} (k_{1}^{'})$ if and only if $Σ^{P} (k_{1}^{'}) \subseteq Σ^{P} (k_{1})$ ⁠.

30

Formally, Proposition 6 is stated under the assumption that P admits a right-hand derivative $P'$ everywhere. It is straightforward to extend the statement to cases where the right-hand derivative need not exist by considering the “discrete” derivative of P.

31

In the next section, we endogenize the choice this function, P. We take the quality of the leader σ as given in the organizational design problem. Intuitively, an organization that is unconstrained in both σ and k₁ would choose σ = 1 and k₁ maximal.

32

We assume that allocating capital, and therefore power, is costless. However, more concentration of political capital may be costly if a powerful leader alienates other members of the organization or reduces their inventive to acquire information. The key result of this section is actually reinforced when allocating political capital is costly.

33

This tension arises because of the concavity of the function, P, close to k_t = 1.

34

As can be inferred from Figure 4, when either (6) does not hold or (5) holds for some $k_{1} ⩽ \bar{k}$ ⁠, if the loss in power needed to induce a loud leader is sufficiently small but strictly positive for very low values of σ, the optimal allocation of power is (strictly) increasing in σ and never induces a patient leader. Nevertheless, a U-shaped allocation of power may still be optimal, even if both (6) does not hold and (5) holds for some $k_{1} ⩽ \bar{k}$ ⁠, if the loss in power needed to induce a loud leader is sufficiently large for very low values of σ, but becomes small (and positive) for larger values of σ.

35

See Kreps (1986) and Young (1993) for early economic models of organizational culture, and Hermalin (2013) for a particularly pertinent contribution on leadership and corporate culture.

36

Here we restrict our attention to the effect of culture on capital accumulation. However, one could also consider the effect of organizational culture on the shape of the function P.

37

In our simple two-period model, an increase in the culture of reward is equivalent to increasing $P (k_{1} + B (1) - c)$ and $P (k_{1} + B (0) - c)$ ⁠. However, if $P (k_{1} + B (1) - c) ⩾ 1$ ⁠, only an increase in the culture of reward can affect the leader’s behavior in the future because it increases the stock of capital that she may spend in future periods.

38

Compare the incomplete contracts literature, which also has a well-defined notion of economic power (Grossman and Hart 1986; Aghion and Tirole 1997; Aghion and Holden 2011).

39

See Gibbons (2006), Chassang (2010), and Ellison and Holden (2014) among many other contributions.

40

This lower bound on η is sufficient to ensure that Assumption 1 is satisfied.

Appendix

A. Omitted Proofs

Proof of Lemma 1. First note that, since $σ > π$ ⁠, the leader prefers alternative $a_{2} = 1$ to alternative $a_{2} = 0$ if and only if $s_{2} = 1$ ⁠.

Let k₂ be a nonirrelevant leader’s period-2 stock of political capital. Spending political capital in period 2 yields expected utility equal to

α_{2} (1 - \Pr (θ_{2} = 1 | s_{2})) + α_{2} (2 \Pr (θ_{2} = 1 | s_{2}) - 1) P (k_{2});

not spending political capital yields expected utility equal to

α_{2} (1 - \Pr (θ_{2} = 1 | s_{2}))

⁠. The net benefit of spending capital is then given by

α_{2} (2 \Pr (θ_{2} = 1 | s_{2}) - 1) P (k_{2}) .

(A1)

Since

σ > π

⁠,

\Pr (θ_{2} = 1 | s_{2}) {\begin{array}{l} > 1 / 2 & if s_{2} = 1; \\ < 1 / 2 & otherwise . \end{array}

(A2)

Furthermore, because the leader is not irrelevant, $P (k_{2}) > 0$ ⁠. Hence, the net benefit of spending political capital is positive (negative) if $s_{2} = 1$ (⁠ $s_{2} = 0$ ⁠). □

Proof of Proposition 1. Let k₁ be a stock capital that makes the leader not irrelevant. Recall that the value of holding a stock k₂ of political capital in period 2 is given by

V (k_{2}) = \bar{α} π + \bar{α} (2 \Pr (θ_{2} = 1 | s_{2} = 1) - 1) \Pr (s_{2} = 1) P (k_{2}),

(A3)

where

\bar{α}

is the expected value of α₂.

Spending political capital in period 1 yields expected utility equal to

\begin{array}{l} α_{1} (1 - \Pr (θ_{1} = 1 | s_{1})) + α_{1} P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1}) - 1) \\ + \Pr (θ_{1} = 1 | s_{1}) V (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1})) V (k_{1} + B (0) - c); \end{array}

(A4)

not spending political capital yields expected utility equal to

α_{1} (1 - \Pr (θ_{1} = 1 | s_{1})) + V (k_{1}) .

(A5)

Thus, the leader spends capital in period 1 if and only if the difference between (A4) and (A5) is positive, that is, if

\begin{array}{l} α_{1} P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1}) - 1) + \Pr (θ_{1} = 1 | s_{1}) V (k_{1} + B (1) - c) \\ + (1 - \Pr (θ_{1} = 1 | s_{1})) V (k_{1} + B (0) - c) - V (k_{1}) > 0. \end{array}

(A6)

We now consider three different cases for the value of the period-1 signal, $s_{1} \in {0, 1}$ ⁠, and the issue’s importance, $α_{1} \in {α^{L}, α^{H}}$ ⁠.

s_{1} = 1

and

α_{1} = α^{H}

⁠. We now show that the leader always spends capital in this case. By substituting (A3) into (A6) and simplifying, we obtain that the leader spends political capital if and only if

\begin{array}{l} α^{H} P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1} = 1) - 1) + \bar{α} (2 \Pr (θ_{2} = 1 | s_{2} = 1) - 1) \Pr (s_{2} = 1) \times (\Pr (θ_{1} = 1 | s_{1} = 1) P (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) P (k_{1} + B (0) - c) - P (k_{1})) > 0. \end{array}

(A7)

Dividing by

(2 \Pr (θ_{1} = 1 | s_{1} = 1) - 1) = (2 \Pr (θ_{2} = 1 | s_{2} = 1) - 1),

which is positive for all

σ > π

⁠, gives an equivalent condition for (A7):

\begin{array}{l} α^{H} P (k_{1}) + \bar{α} \Pr (s_{2} = 1) \times \\ (\Pr (θ_{1} = 1 | s_{1} = 1) P (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \\ P (k_{1} + B (0) - c) - P (k_{1})) > 0. \end{array}

Since

α^{H} > \bar{α}

and

B (1) > c

⁠, the left-hand side of the above inequality is strictly greater than

\begin{array}{l} \bar{α} P (k_{1}) + \bar{α} \Pr (s_{2} = 1) (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) (P (k_{1} + B (0) - c) - P (k_{1})) \\ ⩾ \bar{α} P (k_{1}) - \bar{α} \Pr (s_{2} = 1) (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) P (k_{1}) \\ > 0, \end{array}

since

P (\cdot)

is non-negative and

\Pr (s_{2} = 1) (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) < 1

⁠. We conclude that the inequality (A7) holds.

s_{1} = 1

and

α_{1} = α^{L}

⁠. We now show that there exists a threshold value

σ^{*} (k_{1})

such that the leader spends political capital if and only if

σ > σ^{*} (k_{1})

⁠. By substituting (A3) into (A6) and simplifying in a similar manner as the above case, we obtain that the leader spends political capital if and only if

\begin{array}{l} α^{L} P (k_{1}) + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{2} = 1) (P (k_{1} + B (1) - c) - P (k_{1})) \\ - (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{2} = 1) (P (k_{1}) - P (k_{1} + B (0) - c)) > 0. \end{array}

(A8)

Recall that

B (1) > c

and

0 > B (0)

⁠, and so

P (k_{1} + B (1) - c) - P (k_{1}) ⩾ 0 and P (k_{1}) - P (k_{1} + B (0) - c) ⩾ 0.

It then follows that the left-hand side of inequality (A8) is increasing in σ, since

\Pr (θ_{1} = 1 | s_{1} = 1) \Pr (s_{2} = 1) = \Pr (θ_{1} = 1 | s_{1} = 1) \Pr (s_{1} = 1) = σ (1 - π)

is increasing in σ, and

(1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \Pr (s_{2} = 1) = (1 - σ) π

is decreasing in σ. Furthermore, for σ sufficiently close to one, inequality (A8) holds. We conclude that there exists a threshold value

σ^{*} (k_{1}) < 1

that solves (A8) with equality such that the leader spends political capital if and only if

σ > σ^{*} (k_{1})

⁠.

s_{1} = 0 and α_{1} \in {α^{L}, α^{H}}

⁠. From (A6), the leader spends capital if and only if

\begin{array}{l} α_{1} P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1} = 0) - 1) + \Pr (θ_{1} = 1 | s_{1} = 0) [V (k_{1} + B (1) - c) \\ - V (k_{1})] + (1 - \Pr (θ_{1} = 1 | s_{1} = 0)) [V (k_{1} + B (0) - c) - V (k_{1})] > 0. \end{array}

(A9)

But by Assumption 1 we have

\begin{array}{l} \Pr (θ_{1} = 1 | s_{1} = 0) (P (k_{1} + B (1) - c) - P (k_{1})) \\ + (1 - \Pr (θ_{1} = 1 | s_{1} = 0)) (P (k_{1} + B (0) - c) - P (k_{1})) ⩽ 0, \end{array}

(A10)

and, substituting the value of

V (\cdot)

⁠, as per (A3), we infer that the left-hand side of (A9) has strict upper bound

α_{1} P (k_{1}) (2 \Pr (θ_{1} = 1 | s_{1} = 0) - 1)

⁠. This upper bound is negative, since

\Pr (θ_{1} = 1 | s_{1} = 0) < 1 / 2

⁠, and so the inequality (A9) never holds. We conclude that the leader does not spend political capital.

Since the three cases are exhaustive, we have proven the proposition. □

Proof of Proposition 2. Consider a nonirrelevant leader with initial stock of political capital

k_{1} \in ℝ

⁠, period-1 power

P (k_{1}) > 0

⁠, and precision of information σ. By Proposition 1, a non-irrelevant leader spends political capital in period 1 only if she receives a signal

s_{1} = 1

⁠. Therefore, when the leader optimally spends political capital in period 1, her expected period-2 power is equal to

\Pr (θ_{1} = 1 | s_{1} = 1) P (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) P (k_{1} + B (0) - c) .

Thus, when the leader spends political capital, her power is expected to grow if and only if

\Pr (θ_{1} = 1 | s_{1} = 1) P (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) P (k_{1} + B (0) - c) ⩾ P (k_{1}) .

(A11)

The left-hand side of above inequality increases with σ because $\Pr (θ_{1} = 1 | s_{1} = 1)$ increases with σ; the right-hand side is constant in σ. We conclude that there exists a threshold value $\bar{σ} (k_{1})$ that solves (A11) with equality such that if the leader chooses to spend her political capital, then

if $σ > \bar{σ} (k_{1})$ ⁠, the leader’s power is expected to grow over time;
if $σ < \bar{σ} (k_{1})$ ⁠, the leader’s power is expected to decline over time.

It remains to prove that $\bar{σ} (k_{1}) ⩽ 1$ and $\bar{σ} (k_{1}) > σ^{*} (k_{1})$ ⁠.

$\bar{σ} (k_{1}) ⩽ 1$ . If σ = 1, then $\Pr (θ_{1} = 1 | s_{1} = 1) = 1$ ⁠. It is then immediate that (A11) holds, since P is increasing and $B (1) > c$ ⁠. We conclude that $\bar{σ} (k_{1})$ is bounded by 1.

\bar{σ} (k_{1}) > σ^{*} (k_{1})

. By definition of

σ^{*} (k_{1})

⁠, a leader with

σ = σ^{*} (k_{1})

must be indifferent between spending and saving capital on an

α_{1} = α^{L}

issue when

s_{1} = 1

⁠. That is, the following equality must hold:

\begin{array}{l} α^{L} P (k_{1}) + \bar{α} \Pr (s_{1} = 1) \Pr (θ_{1} = 1 | s_{1} = 1) P (k_{1} + B (1) - c) \\ + \bar{α} \Pr (s_{1} = 1) (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) P (k_{1} + B (0) - c) = \bar{α} \Pr (s_{1} = 1) P (k_{1}) . \end{array}

(A12)

By contradiction, suppose $\bar{σ} (k_{1}) ⩽ σ^{*} (k_{1})$ ⁠. Then there exists $σ^{'}$ such that (A11) and (A12) both hold. Given (A11), the left-hand side of Equation (A12) is bounded below by $α^{L} P (k_{1}) + \bar{α} \Pr (s_{1} = 1) P (k_{1}),$ which strictly exceeds the right-hand side of Equation (A12) because $P (k_{1}) > 0$ and $α^{L} > 0$ —a contradiction. □

Proof of Proposition 3. Follows immediately from the definition of the four leadership styles (see Section 4.2) and Propositions 1 and 2. □

Proof of Proposition 4. Let k₁ be a non-irrelevant leader’s initial stock of political capital. By Proposition 1, if

σ ⩾ σ^{*} (k_{1})

⁠, the leader optimally chooses to spend political capital in period 1 whenever she prefers alternative

a_{1} = 1

⁠, which occurs with probability

\Pr (s_{1} = 1) = π - σ (2 π - 1);

if

σ < σ^{*} (k_{1})

⁠, she optimally chooses to spend political capital in period 1 if she prefers alternative

a_{1} = 1

and

α_{1} = α^{H}

⁠, which occurs with probability

\Pr (s_{1} = 1) \Pr (α^{H}) = \Pr (α^{H}) π - σ (2 π - 1) \Pr (α^{H}) .

Because $π > 1 / 2$ ⁠, both probabilities are decreasing in $σ .$ Furthermore, the probability of spending political capital is discontinuous at $σ^{*} (k_{1})$ ⁠. This discontinuous jump is positive and equal to $\Pr (s_{1} = 1) (1 - \Pr (α^{H}))$ ⁠. We conclude that the probability of spending capital in period 1 is strictly decreasing in σ for all $σ \neq σ^{*} (k_{1})$ and has local maxima at $σ = π$ and $σ = σ^{*} (k_{1})$ ⁠. □

Proof of Proposition 5. This result is a special case of Proposition 6, where the general function P is substituted from the piece-wise linear function $P_{L} : P_{L} (k_{t}) = 0 \forall k_{t} < c$ ⁠, and $P_{L} = \max {k_{t}, 1}$ otherwise, and $B (1) = - B (0) \equiv b > c$ ⁠. For simplicity, within this proof, we assume $2 b + c < 1$ ⁠; however, the result holds more generally and can be shown similarly.

Proposition 6 says that, for non-empty

Σ^{P} (k_{1})

⁠, if

P' (k_{1}) \neq 0

then

σ^{*} (k_{1})

is increasing in k₁ if and only if

\begin{array}{l} \Pr (θ_{1} = 1 | s_{1} = 1, σ = σ^{*} (k_{1})) \frac{P' (k_{1} - c + b) - P' (k_{1})}{P' (k)} < \\ \Pr (θ_{1} = 0 | s_{1} = 1, σ = σ^{*} (k_{1})) \frac{P' (k_{1}) - P' (k_{1} - c - b)}{P' (k_{1})} \\ - \frac{α^{L}}{\bar{α} \Pr (s_{1} = 1 | σ = σ^{*} (k_{1}))} . \end{array}

(A13)

Recall that when

σ = σ^{*} (k_{1})

the following indifference condition must hold

\begin{array}{l} α^{L} P (k_{1}) + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{1} = 1) (P (k_{1} + b - c) - P (k_{1})) \\ + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{1} = 1) (P (k_{1} - b - c) - P (k_{1})) = 0, \end{array}

(A14)

where (with some abuse of notation) we omit the

σ = σ^{*} (k_{1})

dependencies in the above indifference condition. This condition comes from (A8) in the proof of Proposition 1; note that

\Pr (s_{1} = 1) = \Pr (s_{2} = 1)

⁠.

We wish to show that when P = P_L, $Σ^{P} (k_{1})$ —equivalently: $σ^{*} (k_{1})$ is increasing in the political capital regions $R_{1} : = [c, 2 c + b)$ and $R_{2} : = [1 - (b - c), 1)$ ⁠, and otherwise is decreasing. We divide the argument into four cases.

k_{1} \in R_{1}

. For all

k_{1} \in R_{1}

⁠, we have

P' (k_{1}) = 1, P' (k_{1} - b - c) = 0

⁠, and

P' (k_{1} - c + b) = 1

⁠, since P = P_L. Thus, the condition for

Σ^{P} (k_{1})

to be increasing (A13) simplifies to

0 < \Pr (θ_{1} = 0 | s_{1} = 1, σ = σ^{*} (k_{1})) - \frac{α^{L}}{\bar{α} \Pr (s_{1} = 1 | σ = σ^{*} (k_{1}))},

(A15)

for

k_{1} \in R_{1}

⁠. Furthermore, in region R₁ the indifference condition (A14) simplifies to

\begin{array}{l} α^{L} k_{1} + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{1} = 1) (k_{1} + b - c - k_{1}) \\ - (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{1} = 1) k_{1} = 0, \end{array}

since for all

k_{1} \in R_{1}

we have

P_{L} (k_{2}) = k_{2}

for

k_{2} \in {k_{1}, k_{1} + b - c}

⁠, and

P_{L} (k_{1} - b - c) = 0

⁠, and after rearranging we attain

\frac{α^{L}}{\bar{α} \Pr (s_{1} = 1 | σ = σ^{*} (k_{1}))} = - \Pr (θ_{1} = 1 | s_{1} = 1) \frac{k_{1} + b - c}{k_{1}} + 1.

Returning to (A15), we see that the right-hand side can be expressed as

\Pr (θ_{1} = 0 | s_{1} = 1) + \Pr (θ_{1} = 1 | s_{1} = 1) \frac{k_{1} + b - c}{k_{1}} - 1,

which is strictly larger than

\Pr (θ_{1} = 0 | s_{1} = 1) + \Pr (θ_{1} = 1 | s_{1} = 1) - 1 = 0.

It is immediate that the right-hand side of (A15) is positive. Thus, the inequality (A15) holds and we infer that $Σ^{P} (k_{1})$ is increasing in the region R₁.

k_{1} \in R_{2}

⁠. For all

k_{1} \in R_{2}

⁠, we have

P' (k_{1}) = 1, P' (k_{1} + b - c) = 0

and

P' (k_{1} - c - b) = 1

⁠. Thus, the condition for

Σ^{P} (k_{1})

to be increasing (A13) simplifies to

- \Pr (θ_{1} = 1 | s_{1} = 1, σ = σ^{*} (k_{1})) < - \frac{α^{L}}{\bar{α} \Pr (s_{1} = 1 | σ = σ^{*} (k_{1}))} .

(A16)

Furthermore, in region R₂ the indifference condition (A14) simplifies to

\begin{array}{l} α^{L} k_{1} + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{1} = 1) (1 - k_{1}) \\ + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{1} = 1) (k_{1} - b - c - k_{1}) = 0, \end{array}

since for all

k_{1} \in R_{2}

we have

P_{L} (k_{2}) = k_{2}

for

k_{2} \in {k_{1}, k_{1} - b - c}

⁠, and

P_{L} (k_{1} + b - c) = 1

⁠, and after rearranging we attain

\frac{α^{L}}{\bar{α} \Pr (s_{1} = 1 | σ = σ^{*} (k_{1}))} = - \Pr (θ_{1} = 1 | s_{1} = 1) \frac{1}{k_{1}} - (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \frac{k_{1} - b - c}{k_{1}} + 1.

Returning to (A16), we see that the right-hand side can be expressed as

\begin{array}{l} \Pr (θ_{1} = 1 | s_{1} = 1) \frac{1}{k_{1}} + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \frac{k_{1} - b - c}{k_{1}} - 1 \\ > \Pr (θ_{1} = 1 | s_{1} = 1) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \frac{k_{1} - b - c}{k_{1}} - 1 \\ > - \Pr (θ_{1} = 0 | s_{1} = 1), \end{array}

but this exceeds the left-hand side of (A16). We conclude that (A16) holds and

Σ^{P} (k_{1})

is increasing in the region R₂.

k_{1} \in R_{3} : = [2 c + b, 1 - (b - c))

. For all

k_{1} \in R_{3}

we have

P' (k_{1}) = P' (k_{1} - c \pm b) = 1

⁠. Thus, the condition for

Σ^{P} (k_{1})

to be increasing (A13) simplifies to

0 < - \frac{α^{L}}{\bar{α} \Pr (s_{1} = 1 | σ = σ^{*} (k_{1}))} .

This inequality never holds since $α^{L} > 0$ ⁠. We conclude that $Σ^{P} (k_{1})$ is decreasing in the region R₃.

$k_{1} \in R_{4} : = [1, \infty)$ ⁠. For all $k_{1} \in R_{4}$ ⁠, we have $P' (k_{1}) = 0$ ⁠. By Proposition 6, $Σ^{P} (k_{1})$ is decreasing in the region R₄.

Since the four cases are exhaustive, we have proven the proposition. □

Proof of Proposition 6. For non-empty $Σ^{P} (k_{1})$ ⁠, the length of $Σ^{P} (k_{1})$ is simply $σ^{*} (k_{1}) - π$ ⁠. Note that the length of $Σ^{P} (k_{1})$ is weakly increasing in $σ^{*} (k_{1})$ ⁠.

To prove the proposition, we consider the effect of a marginal increase in k₁ on the length of $Σ^{P} (k_{1})$ ⁠, or equivalently the value of $σ^{*} (k_{1})$ ⁠.

From (A8) in the proof of Proposition 1, if

σ = σ^{*} (k_{1})

⁠, then the following indifference condition holds:

\begin{array}{l} Φ (k_{1}, σ) \equiv α^{L} P (k_{1}) + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{2} = 1) (P (k_{1} + B (1) - c) \\ - P (k_{1})) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{2} = 1) (P (k_{1} + B (0) - c) \\ - P (k_{1})) = 0. \end{array}

(A17)

Φ (k_{1}, σ)

is the net benefit of spending capital in period 1 when

α_{1} = α^{L}

and

s_{1} = 1

⁠. Note that

Φ (k_{1}, σ)

is increasing and continuous in σ.

Lemma 2

For a given capital level k₁, a marginal increase in capital has opposite effects on

Φ (k_{1}, σ) |^{σ = σ^{*} (k_{1})}

and

σ^{*} (k_{1})

⁠:

\frac{\partial Φ (k_{1}, σ)}{\partial k_{1}} |^{σ = σ^{*} (k_{1})} > 0 if and only if \frac{\partial σ^{*} (k_{1})}{\partial k_{1}} < 0.

Proof. Suppose that a marginal increase in capital from k₁ to

k_{1}^{'}

results in an increase in the

σ^{*} (k_{1})

-leader’s net benefit, that is,

Φ (k_{1}^{'}, σ^{*} (k_{1})) > Φ (k_{1}, σ^{*} (k_{1})) = 0.

Then, since

Φ (k_{1}^{'}, σ)

is increasing in σ, the value

σ'

such that

Φ (k_{1}^{'}, σ') = 0, or equivalently σ' = σ^{*} (k_{1}^{'}),

is strictly less than

σ^{*} (k_{1})

⁠. Similarly, if a marginal increase in k₁ results in a decrease in the

σ^{*} (k_{1})

-leader’s net benefit then

σ^{*} (k_{1}^{'}) > σ^{*} (k_{1})

⁠. □

From the above lemma, we have that

Σ^{P} (k_{1})

is increasing if and only if

\begin{array}{l} \frac{\partial Φ (k_{1}, σ)}{\partial k_{1}} |^{σ = σ^{*} (k_{1})} = α^{L} P' (k_{1}) + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{2} = 1) \\ (P' (k_{1} + B (1) - c) - P' (k_{1})) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \\ \bar{α} \Pr (s_{2} = 1) (P' (k_{1} + B (0) - c) - P' (k_{1})) \\ < 0. \end{array}

Rearranging and simplifying terms yields (4) in the proposition. □

Proof of Proposition 7. We begin by stating two facts that will be useful in proving the proposition.

Lemma 3

For any given initial stock of political capital, the organization strictly prefers an active (loud or strong) leader to a patient leader.

Proof. Suppose $α^{L} = α^{H} > 0$ so that the leader’s payoff function is a monotonic transformation of the organization’s payoff function. By Proposition 1 (in particular, see (A8) in the proof of Proposition 1) the leader strictly prefers to spend political capital in period 1 whenever she prefers alternative $a_{1} = 1$ ⁠. Therefore, the organization strictly prefers the leader to spend political capital in period 1 whenever she prefers alternative $a_{1} = 1$ ⁠. □

Lemma 4

Fix a leadership style in $patient, loud, strong$ ⁠, the organization strictly prefers a leader with a greater initial stock of political capital.

Proof. To see this, fix the leader’s style. A higher initial stock of political capital strictly increases the leader’s power in period 1 and, for any realization of events, weakly increases the leader’s power in period 2. Since whenever the leader spends political capital, the organization strictly prefers alternative $a_{1} = 1$ to be implemented, absent a change in the leader’s style, the organization prefers a leader with a greater initial stock of political capital. □

We now prove that if (5) holds when

k_{1} = \bar{k}

⁠, then

k^{*} (σ) = \bar{k}

for all

σ \in (π, 1)

⁠. Let (5) hold at

k_{1} = \bar{k}

⁠. Recall from the proof of Proposition 1 (in particular, see (A6)) that a leader with initial stock of political capital equal to

\bar{k}

adopts an active leadership style if and only if

\begin{array}{l} (2 \Pr (θ_{1} = 1 | s_{1} = 1) - 1) (α^{L} P (\bar{k}) + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{2} = 1) \\ (P (\bar{k} + B (1) - c) - P (\bar{k})) - (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{2} = 1) \\ (P (\bar{k}) - P (\bar{k} + B (0) - c))) > 0. \end{array}

Notice that $2 \Pr (θ_{1} = 1 | s_{1} = 1) - 1$ is strictly positive for all $σ > π > 1 / 2$ ⁠. Furthermore, the term in the second parenthesis is (i) increasing in σ (see (A8) in the proof of Proposition 1) and (ii) non-negative for $σ = π$ since (5) holds at $k_{1} = \bar{k}$ ⁠. Therefore, a leader with initial stock of political capital equal to $\bar{k}$ adopts an active leadership style for all $σ > π$ ⁠. By Lemmas 3 and 4, then the optimal allocation of political capital equals $\bar{k}$ for all $σ \in (π, 1)$ ⁠.

We now prove that if (5) does not hold for all

k_{1} ⩽ \bar{k}

and the length of

Σ^{P} (k_{1})

increases with k₁ at

k_{1} = \bar{k}

⁠, then there exists a unique

\hat{σ} \in (π, 1)

such that

k^{*} (σ) = \bar{k}

for

σ < \hat{σ}, k^{*} (\hat{σ}) < \bar{k}

⁠, and

k^{*} (σ)

increases with σ for

σ ⩾ \hat{σ}

⁠. That is, the optimal allocation of political capital is U-shaped. Recall from Proposition 6 that

Σ^{P} (k_{1})

increases with k₁ at

k_{1} = \bar{k}

if

\begin{array}{l} (1 - π) σ^{*} (\bar{k}) P' (\bar{k} + B (1) - c) + π (1 - σ^{*} (\bar{k})) P' (\bar{k} + B (0) - c) < \\ [(1 - π) σ^{*} (\bar{k}) + π (1 - σ^{*} (\bar{k})) - \frac{α^{L}}{\bar{α}}] P' (\bar{k}) . \end{array}

(A18)

We prove this in four steps:

Step 1. Because (5) does not hold for all $k_{1} ⩽ \bar{k}$ ⁠, from the proof of Proposition 1 (in particular, see (A6)), there exists a unique $\underset{̱}{σ}$ such that the leader optimally chooses to be patient for any $k_{1} ⩽ \bar{k}$ if and only if $σ < \underline{σ}$ ⁠. By Lemma 4, the optimal allocation of political capital equals $\bar{k}$ for all $σ < \underline{σ}$ ⁠.

Step 2. By Propositions 2 and 3, a leader with $σ > σ^{*} (\bar{k})$ optimally chooses to be active for $k_{1} = \bar{k}$ ⁠. By Lemmas 3 and 4, then the optimal allocation of political capital equals $\bar{k}$ for all $σ > σ^{*} (\bar{k})$ ⁠.

Step 3. Because (5) does not hold for all

k_{1} ⩽ \bar{k}

and (A18) holds, there exist an interval

\hat{Σ} = [\underline{σ}, σ^{*} (\bar{k}))

such that a leader with information of precision

σ \in \hat{Σ}

optimally chooses a patient style if

k_{1} = \bar{k}

but optimally chooses an active style for

k (σ) < \bar{k}

such that

k (σ) = \max {k : σ = σ^{*} (k)} .

(A19)

By Lemmas 3 and 4, for any $σ \in \hat{Σ}$ ⁠, the optimal allocation of political capital is either equal to $\bar{k}$ or to $k (σ)$ ⁠.

Step 4. By Proposition 6 and (A18), $d σ^{*} (k) / d k |_{k = \bar{k}} > 0$ ⁠. Therefore there exists $σ \in \hat{Σ}$ for which the optimal allocation of political capital is equal to $k (σ) < \bar{k}$ ⁠. Since $σ^{*} (k)$ is an increasing function there exists a unique $\hat{σ} \in \hat{Σ}$ such that $k^{*} (σ) = \bar{k}$ for $σ < \hat{σ}, k^{*} (\hat{σ}) < \bar{k}$ ⁠, and $k^{*} (σ)$ increases with σ for $σ ⩾ \hat{σ}$ ⁠. □

Proof of Proposition 8. Consider the case where $B (1) = - B (0) \equiv b > c$ ⁠. We begin by introducing some notation. Let $q = \Pr [α_{t} = α^{H}], ω = \Pr [s_{t} = 1]$ ⁠, and $p_{s} (θ) = \Pr [θ_{t} = θ | s_{t} = s]$ ⁠. For a given function P, a leader with initial stock of political capital k₁ and precision of information σ, let $V (σ, k_{1}; P)$ denote the expected utility of the organization over the two periods.

Consider the function

P_{M} : P_{M} (k_{1}) = {\begin{matrix} 1 & for k ⩾ \underset{̱}{k} \\ 0 & otherwise, \end{matrix}

and suppose there is a leader with initial stock of political capital

k_{1} \in [\underset{̱}{k}, \underset{̱}{k} + b - c)

and precision of information σ. When P = P_M, it follows from (A8) that she is loud if and only if

σ \geq σ_{M}^{*} : = \frac{\bar{α} π - α^{L}}{\bar{α} π} .

If

σ < σ_{M}^{*}

(i.e., the leader is patient), then the organization’s expected utility is

\begin{array}{l} V (σ, k_{1}; P_{M}) = (1 - ω) p_{0} (0) + ω (1 - q) p_{1} (0) + ω q p_{1} (1) \\ + [(1 - ω) + ω (1 - q)] E [v_{2} | k_{1}; P_{M}] \\ + ω q [p_{1} (1) E [v_{2} | k_{1} + b - c; P_{M}] + p_{1} (0) E [v_{2} | k_{1} - b - c; P_{M}]], \end{array}

(A20)

where

E [v_{2} | k_{2}; P] = ω p_{1} (1) P (k_{2}) + ω p_{1} (0) (1 - P (k_{2})) + (1 - ω) p_{0} (0)

(A21)

denotes the organization’s period-2 expected utility from a leader with period-2 capital k₂ and function P. Define the values

E_{+}

and

E_{-}

such that

E_{+} : = E [v_{2} | k_{1} + b - c; P_{M}] = ω p_{1} (1) + (1 - ω) p_{0} (0),

and

E_{-} : = E [v_{2} | k_{1} - b - c; P_{M}] = ω p_{1} (0) + (1 - ω) p_{0} (0) .

Thus, (A20) can be expressed as

\begin{array}{l} V (σ, k_{1}; P_{M}) = (1 - ω) p_{0} (0) + ω (1 - q) p_{1} (0) + ω q p_{1} (1) \\ + [(1 - ω) + ω (1 - q)] E_{+} + ω q [p_{1} (1) E_{+} + p_{1} (0) E_{-}], \end{array}

(A22)

Now consider the function

P_{η} : P_{η} (k_{1}) = {\begin{array}{l} 1 & for k ⩾ \underset{̱}{k} + b - c \\ η & for \underset{̱}{k} ⩽ k < \underset{̱}{k} + b - c \\ 0 & otherwise, \end{array}

where

1 / 2 ⩽ η < 1

⁠,⁴⁰ and suppose there is a leader with initial stock of political capital

k_{1} \in [\underset{̱}{k}, \underset{̱}{k} + b - c)

and precision of information σ. When

P = P_{η}

⁠, it follows from (A8) that she is loud (or strong) if and only if

σ ⩾ σ_{η}^{*} : = \frac{\bar{α} π η - α^{L} η}{\bar{α} [(1 - π) (1 - η) + π η]}

Notice that

σ_{η}^{*} < σ_{M}^{*}

for all

η < 1

and equality holds for η = 1. If

σ > σ_{η}^{*}

(i.e., she is a loud or strong leader), then the expected utility of the organization is

\begin{array}{l} V (σ, k_{1}; P_{η}) = (1 - ω) p_{0} (0) + ω [p_{1} (1) η + p_{1} (0) (1 - η)] \\ + [(1 - ω)] E [v_{2} | k_{1}; P_{η}] + ω [p_{1} (1) E [v_{2} | k_{1} + b - c; P_{η}] \\ + p_{1} (0) E [v_{2} | k_{1} - b - c; P_{η}]] . \end{array}

Noting that

E [v_{2} | k_{1} + b - c; P_{η}] = E_{+}

and

E [v_{2} | k_{1} - b - c; P_{η}] = E_{-}

⁠, it follows that

\begin{array}{l} V (σ, k_{1}; P_{η}) = (1 - ω) p_{0} (0) + ω [p_{1} (1) η + p_{1} (0) (1 - η)] \\ + [(1 - ω)] E [v_{2} | k_{1}; P_{η}] + ω [p_{1} (1) E_{+} + p_{1} (0) E_{-}] . \end{array}

(A23)

We now show that when

α^{L} / \bar{α} < (1 - π) π

there exist values of

η \in [1 / 2, 1)

and a distribution F with full support over

(π, 1] \times [\underset{̱}{k}, \infty)

such that an organization with function

P = P_{η}

attains strictly higher expected utility than an organization with P = P_M, that is,

\int_{(σ, k_{1})} V (σ, k_{1}; P_{η}) - V (σ, k_{1}; P_{M}) d F (σ, k_{1}) > 0.

(A24)

This will suffice to show that the optimal function (which need not be $P_{η}$ ⁠) is strictly increasing for some $k ⩾ \underset{̱}{k}$ ⁠. The assumption that $α^{L} / \bar{α} < (1 - π) π$ ensures that $σ_{M}^{*} > π$ and, hence, $[σ_{η}^{*}, σ_{M}^{*}) \cap (π, 1]$ is non-empty.

Let the distribution F be concentrated in the region

R : = [σ_{η}^{*}, σ_{M}^{*}) \times [\underset{̱}{k}, \underset{̱}{k} + b - c]

so that

\int_{(σ, k_{1}) \in R} d F (σ, k_{1}) > 1 - ε,

for some

ε > 0

sufficiently small. A lower bound on the LHS of (A24) is then

\int_{(σ, k_{1}) \in R} V (σ, k_{1}; P_{η}) - V (σ, k_{1}; P_{M}) d F (σ, k_{1}) - 2 ε,

(A25)

since

0 < V (σ, k_{1}; P) ⩽ 2

for any function P.

Now notice that for any leader with

(σ, k_{1}) \in R

she will be patient if the organization has P = P_M and she will be loud (or strong) if

P = P_{η}

⁠. The former provides the organization with expected utility (A22) and the latter provides expected utility (A23). Furthermore, for any

(σ, k_{1}) \in R

⁠, as

η \to 1^{-}

V (σ, k_{1}; P_{η}) \to \bar{V} (σ, k_{1}) : = (1 - ω) p_{0} (0) + ω p_{1} (1) + [(1 - ω)] E_{+} + ω [p_{1} (1) E_{+} + p_{1} (0) E_{-}] .

Simple algebra shows that

\bar{V} (σ, k_{1}) > V (σ, k_{1}; P_{M})

for any

(σ, k_{1}) \in R

and

\bar{V} (π, k_{1}) = V (π, k_{1}; P_{M})

⁠. However, since

σ_{M}^{*} > π

⁠, for η sufficiently close to one

σ_{η}^{*} > π

⁠, and

\bar{V} (σ, k_{1}) - V (σ, k_{1}; P_{M})

will be bounded away from 0 for all

(σ, k_{1}) \in R

⁠. That is,

L : = \inf_{(σ, k_{1}) \in R} (\bar{V} (σ, k_{1}) - V (σ, k_{1}; P_{M})) > 0.

Hence, there exists

\bar{η} \in [1 / 2, 1)

such that for all

η > \bar{η}

V (σ, k_{1}; P_{η}) - V (σ, k_{1}; P_{M}) > L / 2 for all (σ, k_{1}) \in R .

It follows that for

η > \bar{η}

\int_{(σ, k_{1}) \in R} V (σ, k_{1}; P_{η}) - V (σ, k_{1}; P_{M}) d F (σ, k_{1}) - 2 ε

> L / 2 (1 - ε) - 2 ε .

Thus, if $ε ⩽ L / (L + 4)$ (i.e., F is sufficiently concentrated in the region R) then an organization with $P = P_{η}$ such that $η > \bar{η}$ will attain strictly higher expected utility than an organization with P = P_M. This shows that for parameter values and distributions specified above, the optimal function must be strictly increasing for some $k ⩾ \underset{̱}{k}$ ⁠; this completes the proof. □

Proof of Proposition 9. Recall from the proof of Proposition 6 that the length of

Σ^{P} (k_{1})

is simply

σ^{*} (k_{1}) - π

if it is nonempty, and the value

σ^{*} (k_{1})

is defined to be the σ-value such that the following indifference condition holds

α^{L} P (k_{1}) + \Pr (θ_{1} = 1 | s_{1} = 1) \bar{α} \Pr (s_{1} = 1) (P (k_{1} + B (1) - c) - P (k_{1}))

+ (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) \bar{α} \Pr (s_{1} = 1) (P (k_{1} + B (0) - c) - P (k_{1})) = 0.

(A26)

We denote the left-hand side of Equation (A26) by the function $Φ (k_{1}, σ | B) .$

We wish to show that an increase in the culture of reward decreases

σ^{*} (k_{1})

⁠. First, note that

Φ (k_{1}, σ | B)

is increasing and continuous in σ. Second, because the function P is weakly increasing,

Φ (k_{1}, σ | B)

is increasing in the culture of reward: for

B, \hat{B}

such that

B (1) ⩾ \hat{B} (1)

and

B (0) ⩾ \hat{B} (0)

we have

Φ (k_{1}, σ | B) ⩾ Φ (k_{1}, σ | \hat{B}) for all k_{1}, σ .

(A27)

Now, by definition, we have

Φ (k_{1}, σ^{*} (k_{1}) | B) = 0

⁠, where

σ^{*} (k_{1})

is defined with respect to the culture function B. Let

\hat{B}

be a lower culture of reward function, that is,

\hat{B} (1) ⩽ B (1)

and

\hat{B} (0) ⩽ B (0)

⁠. It is immediate from (A27) that

Φ (k_{1}, σ^{*} (k_{1}) | \hat{B}) ⩽ 0.

If equality holds, then

σ = σ^{*} (k_{1})

satisfies the indifference condition under the lower culture of reward parameters given by

\hat{B}

and so

Σ^{P} (k_{1})

has unchanged length. If strict inequality holds, then, since

Φ

is increasing and continuous in σ, there exists a value

\hat{σ} > σ^{*} (k_{1})

such that

Φ (k_{1}, \hat{σ} | \hat{B}) = 0.

Thus, the length of $Σ^{P} (k_{1})$ increases as the culture of reward decreases. This completes the proof.

In a similar manner, we can show that an increase in the culture of reward increases

Σ^{S} (k_{1})

⁠. This follows since the value

\bar{σ} (k_{1})

is defined such that

\Pr (θ_{1} = 1 | s_{1} = 1) P (k_{1} + B (1) - c) + (1 - \Pr (θ_{1} = 1 | s_{1} = 1)) P (k_{1} + B (0) - c) = P (k_{1}) .

It is straightforward to see that an increase in B(1) or B(0), leads to a decrease in $\bar{σ} (k_{1})$ and hence an increase in $Σ^{S} (k_{1})$ ⁠, as required. □

Supplementary Material

Supplementary material is available at Journal of Law, Economics, & Organization online.

Conflict of interest statement. None declared.

References

Aghion

Philippe

,

Tirole

Jean

.

1997

.

“Formal and Real Authority in Organizations

,”

105

Journal of Political Economy

1

–

29

.

Google Scholar

Crossref

WorldCat

Aghion

Philippe

,

Holden

Richard

.

2011

.

“Incomplete Contracts and the Theory of the Firm: What Have We Learned over the past 25 Years

,”

25

Journal of Economic Perspectives

181

–

97

.

Google Scholar

Crossref

WorldCat

Al-Ubaydli

Omar

,

Andersen

Steffen

,

Gneezy

Uri

,

List

John A.

2015

.

“Carrots That Look like Sticks: Toward an Understanding of Multitasking Incentive Schemes

,”

81

Southern Economic Journal

538

–

61

.

Google Scholar

Crossref

WorldCat

Alvarez

Rodolfo.

1968

.

“Informal Reactions to Deviance in Simulated Work Organizations: A Laboratory Experiment

,”

33

American Sociological Review

895

–

912

.

Google Scholar

Crossref

WorldCat

Arrow

Kenneth J.

1999

. “Observations on Social Capital,” in

Partha

Dasgupta

and

Ismail

Serageldin

, eds.,

Social Capital: A Multifaceted Perspective

.

Washington, DC

:

World Bank Publications

,

3

–

5

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Atwater

Leanne E.

,

Yammarino

Francis J.

,

1996

.

“Bases of Power in Relation to Leader Behavior: A Field Investigation

,” 11

Journal of Business and Psychology

3

–

22

.

Google Scholar

OpenURL Placeholder Text

WorldCat

Bass

Bernard M.

1985

.

Leadership and Performance beyond Expectations

.

New York, NY

:

Free Press

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Bass

Bernard M.

1988

.

“The Inspirational Process of Leadership

,”

7

Journal of Management Development

21

–

31

.

Google Scholar

Crossref

WorldCat

Bass

Bernard M.

1990

.

Bass and Stogdill’s Handbook of Leadership

.

New York, NY

:

Free Press

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Belot

Michèle

,

Schröder

Marina

.

2016

.

“The Spillover Effects of Monitoring: A Field Experiement,”

62

Management Science

37

–

45

.

Google Scholar

Crossref

WorldCat

Bénabou

Roland

,

Tirole

Jean

.

2003

.

“Intrinsic and Extrinsic Motivation

,”

70

Review of Economic Studies

489

–

520

.

Google Scholar

Crossref

WorldCat

Bertrand

Marianne

,

Schoar

Antoinette

.

2003

“Managing with Style: The Effect of Managers on Firm Policies

,”

118

Quarterly Journal of Economics

1169

–

208

.

Google Scholar

Crossref

WorldCat

Bouton

Laurent

,

Llorente-Saguer

Aniol

,

Malherbe

Frédéric

.

2018

.

“Get Rid of Unanimity Rule: The Superiority of Majority Rules with Veto Power

,”

126

Journal of Political Economy

107

–

49

.

Google Scholar

Crossref

WorldCat

Burns

James M.

1978

.

Leadership

.

New York, NY

:

Harper & Row

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Caillaud

Bernard

,

Tirole

Jean

.

2007

.

“Consensus Building: How to Persuade a Group

,”

97

American Economic Review

1877

–

900

.

Google Scholar

Crossref

WorldCat

Campbell

Arthur.

2017

. “Spending Political Capital.” Working Paper.

Chassang

Sylvain.

2010

.

“Building Routines: Learning, Cooperation, and the Dynamics of Incomplete Relational Contracts

,”

100

American Economic Review

448

–

65

.

Google Scholar

Crossref

WorldCat

Crawford

Vincent P.

,

Sobel

Joel

.

1982

.

“Strategic Information Transmission

,”

50

Econometrica

,

1431

–

51

.

Google Scholar

Crossref

WorldCat

Cyert

Richard M.

,

March

James

.

1963

.

A Behavioral Theory of the Firm

.

Englewood Cliffs, NJ

:

Prentice-Hall

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Dessein

Wouter.

2002

.

“Authority and Communication in Organizations

,”

69

Review of Economic Studies

811

–

38

.

Google Scholar

Crossref

WorldCat

Dessein

Wouter

,

Prat

Andrea

.

2017

. “Organizational Capital, Corporate Leadership, and Firm Dynamics.” Columbia Business School Research Paper No.

17

–

89

.

Ellison

Glenn

,

Holden

Richard

.

2014

.

“A Theory of Rule Development

,”

30

Journal of Law Economics and Organization

649

–

82

.

Google Scholar

Crossref

WorldCat

Farson

Richard

,

Keyes

Ralph

.

2002

. “The Failure-Tolerant Leader,” August, Harvard Business Review.

Fudenberg

Drew

,

Levine

David K.

1983

.

“Subgame-Perfect Equilibria of Finite and Infinite Horizon Games

,”

31

Journal of Economic Theory

251

–

68

.

Google Scholar

Crossref

WorldCat

Fudenberg

Drew

,

Levine

David K.

1986

.

“Limit Games and Limit Equilibria

,”

38

Journal of Economic Theory

261

–

79

.

Google Scholar

Crossref

WorldCat

Gibbons

Robert.

2006

.

“What the Folk Theorem Doesn’t Tell Us

,”

15

Industrial and Corporate Change

381

–

86

.

Google Scholar

Crossref

WorldCat

Gibbons

Robert.

2019

. “March-ing Towards Organization Economics.” MIT Working Paper.

Grossman

Sanford J.

,

Hart

Oliver

.

1986

.

“A Theory of Vertical and Lateral Integration

,”

94

Journal of Political Economy

691

–

719

.

Google Scholar

Crossref

WorldCat

Groysberg

Boris

,

Lee

Jeremiah

,

Price

Jesse

,

Yo-Jud Cheng

J.

2018

. “The Leader’s Guide to Corporate Culture,” January-February, Harvard Business Review.

Hermalin

Benajmin E.

2013

.

The Handbook of Organizational Economics

.

Princeton, NJ

:

Princeton University Press

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Hermalin

Benjamin E.

1998

.

“Toward an Economic Theory of Leadership: Leading by Example

,”

88

American Economic Review

1188

–

206

.

Google Scholar

OpenURL Placeholder Text

WorldCat

Hollander

Edwin P.

1958

.

“Conformity, Status, and Idiosyncrasy Credit

,”

65

Psychological Review

117

–

27

.

Hollander

Edwin P.

1960

.

“Competence and Conformity in the Acceptance of Influence

,”

61

Journal of Abnormal and Social Psychology

365

–

69

.

Hollander

Edwin P.

1978

. “Leadership Dynamics: A Transactional Perspective,” February, Technical Report No. 6.

Hollander

Edwin P.

2009

.

Inclusive Leadership: The Essential Leader-Follower Relationship

.

Abingdon

:

Routledge/Taylor & Francis Group

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Holmström

Bengt

,

Milgrom

Paul

.

1991

.

“Multitask Principal-Agent Analyses: Incentives Contracts, Asset Ownership and Job Design

,”

7

Journal of Law, Economics and Organization

24

–

52

.

Google Scholar

Crossref

WorldCat

Homans

George C.

1961

.

Social Behavior: Its Elementary Forms

.

New York, NY

:

Harcourt Brace

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Kamenica

Emir

,

Gentzkow

Matthew

.

2011

.

“Bayesian Persuasion

,”

101

American Economic Review

2590

–

615

.

Google Scholar

Crossref

WorldCat

Kreps

David M.

1986

.

Technology, Innovation, and Business Strategy

.

Tokyo, Japan

:

Nippon Keizai Shumbunsha Press

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Kreps

David M

,

Wilson

Robert

.

1982

.

“Reputation and Imperfect Information

,”

27

Journal of Economic Theory

253

–

79

.

Google Scholar

Crossref

WorldCat

Kreps

,

Milgrom

David M Paul

,

Roberts

John

,

Wilson

Robert

.

1982

.

“Rational Cooperation in the Finitely Repeated Prisoner’s Dilemma

,”

27

Journal of Economic Theory

245

–

52

.

Google Scholar

Crossref

WorldCat

Kuang

,

Huang Ni

Lini

,

Hong

Yili

,

Yan

Zhijun

.

2019

.

“Spillover Effects of Financial Incentives on Non-Incentivized User Engagement: Evidence from an Online Knowledge Exchange Platform

,”

36

Journal of Management Information Systems

289

–

320

.

Google Scholar

Crossref

WorldCat

Lazear

Edward P.

2000

.

“Performance Pay and Productivity

,”

90

American Economic Review

1346

–

61

.

Google Scholar

Crossref

WorldCat

Li

Jin

,

Matouschek

Niko

,

Powell

Michael

.

2017

.

“Power Dynamics in Organizations

,”

9

American Economic Journal: Microeconomics

217

–

41

.

Google Scholar

OpenURL Placeholder Text

WorldCat

Linck

James S.

,

Netter

Jeffry M.

,

Yang

Tina

.

2009

.

“The Effects and Unintended Consequences of the Sarbanes-Oxley Act on the Supply and Demand for Directors

,”

22

The Review of Financial Studies

3287

–

328

.

Google Scholar

Crossref

WorldCat

Majumdar

Sumon

,

Mukand

Sharun W.

2004

.

“Policy Gambles

,”

94

American Economic Review

1207

–

22

.

Google Scholar

Crossref

WorldCat

March

James.

1981

. “Decisions in Organizations and Theories of Choice,” in

Van de Ven

A.

and

Joyce

W.

, eds.,

Perspectives on Organization Design and Behavior

.

New York, NY

:

Wiley Interscience

,

205

–

244

.

Google Scholar

Google Preview

OpenURL Placeholder Text

WorldCat

Milgrom

Paul

,

Roberts

John

.

1982

.

“Predation, Reputation, and Entry Deterrence

,”

27

Journal of Economic Theory

280

–

312

.

Google Scholar

Crossref

WorldCat

Milgrom

Paul

,

Roberts

John

.

1988

.

“An Economic Approach to Influence Activities in Organizations

,” 94

American Journal of Sociology

154

–

79

.

Google Scholar

OpenURL Placeholder Text

WorldCat

Prendergast

Canice

,

Stole

Lars

.

1996

.

“Impetuous Youngsters and Jaded Old-Timers: Acquiring a Reputation for Learning

,”

104

Journal of Political Economy

1105

–

134

.

Google Scholar

Crossref

WorldCat

Rotemberg

Julio J.

,

Saloner

Garth

.

1993

.

“Leadership Style and Incentives

,”

39

Management Science

1299

–

318

.

Google Scholar

Crossref

WorldCat

Rotemberg

Julio J.

,

Saloner

Garth

.

2000

.

“Visionaries, Managers, and Strategic Direction

,”

31

RAND Journal of Economics

693

–

716

.

Google Scholar

Crossref

WorldCat

Singh

Amarjit.

2009

.

“Organizational Power in Perspective

,”

9

Leadership and Management in Engineering

165

–

76

.

Google Scholar

Crossref

WorldCat

Yang

Inju.

2015

.

“Positive Effects of Laissez-Faire Leadership: Conceptual Exploration

,”

34

Journal of Management Development

1246

–

61

.

Google Scholar

Crossref

WorldCat

Yang

Inju

,

Li

Ming

.

2017

.

“Can Absent Leadership Be Positive in Team Conflicts? An Examination of Leaders’ Avoidance Behavior in China

,”

28

International Journal of Conflict Management

146

–

65

.

Google Scholar

Crossref

WorldCat

Young

H. Peyton.

1993

.

“The Evolution of Conventions

,”

61

Econometrica

57

–

84

.

Google Scholar

Crossref

WorldCat

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Article Contents

Political Capital

Abstract

1. Introduction

2. The Model

2.1 Discussion of the Model

3. The Leader’s Optimal Strategy

4. Leadership and Power

4.1 The Evolution of Power

4.2 Leadership Styles

4.3 Political Capital and Leadership Styles

5. Organization Design

5.1 Optimal Allocation of Political Capital

5.2 Institutional Design

5.3 Organizational Culture

6. Concluding Remarks

Footnotes

Appendix

A. Omitted Proofs

Supplementary Material

References

Supplementary data

Citations

Views

Altmetric

Email alerts

Citing articles via

Latest

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Article Contents

Political Capital

Abstract

1. Introduction

2. The Model

2.1 Discussion of the Model

3. The Leader’s Optimal Strategy

4. Leadership and Power

4.1 The Evolution of Power

4.2 Leadership Styles

4.3 Political Capital and Leadership Styles

5. Organization Design

5.1 Optimal Allocation of Political Capital

5.2 Institutional Design

5.3 Organizational Culture

6. Concluding Remarks

Footnotes

Appendix

A. Omitted Proofs

Supplementary Material

References

Supplementary data

Citations

Views

Altmetric

Email alerts

Citing articles via

Latest

Most Read

Most Cited

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