COORDINATING PARTY ACTIVISTS

Our study of leadership builds upon a simple game in which players want to coordinate their actions in an uncertain environment. This basic game is strategically equivalent to the “beauty contest” scenario described by Morris and Shin (Reference Morris and Shin2002), although, as we explain in later sections, our information structure is richer. The terminology stems from Keynes (Reference Keynes1936), who described popular newspaper competitions in which entrants chose the prettiest faces from a set of photographs. The winners were those whose choices were also the most popular. It was foolish for an entrant to follow solely his own opinion of beauty: a winning strategy would anticipate the choices of others because the rules promoted conformity. Keynes (Reference Keynes1936, Chapter 12) explained:

Keynes (Reference Keynes1936) believed that this logic reflected elements of professional investment in the stock market. In recent years economic theorists have built formal models of the beauty contest parable (Angeletos and Pavan Reference Angeletos and Pavan2007; Morris and Shin Reference Morris and Shin2002) and used them to analyze public announcements in monetary economies (Amato, Morris, and Shin Reference Amato, Morris and Shin2002, Hellwig Reference Hellwig2005), complementary investments (Angeletos and Pavan Reference Angeletos and Pavan2004), and the role of higher order beliefs in asset pricing (Allen, Morris, and Shin Reference Allen, Morris and Shin2006).

As we will show, the beauty contest parable can be used to develop important insights into the focal role of leadership. We find it useful to describe our own version of the parable as a vehicle to convey our ideas. Rather than think of contestants choosing the prettiest faces, we can think of members of a political party advocating and campaigning for the best policies. The pressure for unity and conformity within political parties then provides an incentive to back a policy that is likely to be popular, which subsequently leads to the anticipation of the average opinion.

To tell this story more formally, we build a simultaneous-move game played by a unit mass of activist party members indexed by t ∈ [0,1].Footnote ³ An activist advocates a policy . This might be interpreted as the position he supports at a party conference, or the policy he promotes during an election campaign. Drawing together the actions of all party members, the “party line” is the average policy advocated: .

A party activist pursues two objectives. Firstly, he would like to advocate the policy θ that best meets the party's needs. Secondly, he wishes to coordinate with others in his party. That is, a concern for party unity drives him to conform to the party line. We represent these twin concerns via a pair of quadratic loss functions:

π indexes an activist's relative concern for choosing the ideal policy compared to maintaining party unity.Footnote ⁴ To ensure that both concerns are present, we assume that 0 < π < 1.

When activists share common knowledge of θ, then it is optimal for them to advocate the same ideal policy a _t = θ. In fact, this is the unique Nash equilibrium of the game.Footnote ⁵ When this is so, there is no tension between the activists' twin objectives. It is tempting to conclude that there is no disagreement between party members.

This, however, is not the case. When θ is unknown, an activist is unsure of the best policy and must use any information at his disposal to form beliefs about θ. Activists do not share the same information because their prior experiences will be varied. Holding different views, they are divided over the best course of action. Of course, their disagreement is not fundamental: if only they were able to discover the true value of θ, then they would all reach agreement. Instead, disagreement stems from differences of opinion rather than of ideology. This source of division is particularly relevant to a political party: the members share common values, but nevertheless there is scope for debate about policy.

This discussion suggests that our theory is only applicable to a world in which all fundamental disagreement is absent. Once again, however, this is not the case: our results hold when party activists fundamentally differ in their policy preferences. In fact, the appropriate interpretation of θ is not that it is the single ideal policy for all members of the party, but rather it is the average ideal policy across the spectrum of party members.

OPTIMAL ADVOCACY

Remaining within our parable of a party's coordination problem, we turn our attention to the optimal advocacy decisions of the party's members. When θ is unknown, an activist is unsure of the best policy. He may also be unsure of the likely actions of others. Given this uncertainty, he maximizes his expected payoff E[u _t], where the expectation is taken with respect to his beliefs about the true underlying ideal policy θ and the party line . This maximization is equivalent to the minimization of . The appropriate first-order condition yields the uniquely optimal advocacy choice

which is a weighted average of the expected ideal policy, from the perspective of the activist, and his understanding of the average policy advocated by the party at large.

An activist's expectations are based on any information available to him: activist t observes n informative signals, which form a collection capturing all information relevant to his play. A signal might represent the activist's own research, the understanding gained from communication with other party members, or the influence of a leader. We postpone our description of the statistical properties of the signals until the next section. However, we do assume that the distribution of signals is symmetric across activists. What this means is that if activists t and t′ observe the same signal realization, so that , then they share the same beliefs about the identity of the best policy and about the likely signals of other activists; put succinctly, activists are ex ante symmetric.

Whatever the informative signals represent, an activist's advocacy strategy is a mapping from signal realizations to policy choices; formally, . A strategy profile might involve the use of different strategies by different players. However, once we seek (Bayesian Nash) equilbria, it is without loss of generality to restrict attention to symmetric strategy profiles, so that every player uses the same advocacy strategy A(·). This is because each individual is neglibly small and so, conditional on observing the same signal realization, two different activists see their world in the same way. Because any best reply is unique (and hence strict), this implies that they behave similarly.

An advocacy strategy yields a Bayesian Nash equilibrium when it specifies an optimal choice for an activist, given his beliefs, and when those beliefs are consistent with the partywide use of the strategy. Given activists use a strategy A(·), an activist's expectation of the party line is for t′ ≠ t. Similarly, his expectation of the ideal policy is . Hence, the strategy A(·) forms an equilibrium if and only if

(⋆)

Thus, an activist's strategy is a weighted average of his expectation of the ideal policy and his understanding of the average policy advocated by party members.Footnote ⁶ To obtain a solution to Equation (⋆), we need to specify fully how signals help an activist form beliefs about the ideal policy θ and beliefs about the signals seen by other activists. To do this, we turn our attention to the details of the mechanism via which activists learn.

LEARNING FROM LEADERS

Leaders help a follower develop his beliefs about the world and about the likely moves of others. Once again, rather than explain how followers learn from leaders in an abstract setting, we describe our model within the context of the party activist story. Activists begin with no substantive knowledge of the ideal policy: they share a diffuse prior over θ.Footnote ⁷ They learn by listening to n party leaders indexed by i ∈ {1, . . ., n}. The term “leader” can be viewed as a label for an informative signal; indeed, the sources of information available might extend beyond leaders and include the activists' own research and intraparty communication. Nevertheless, this personification is useful for exposition and is relevant when we subsequently introduce a role for strategic leaders.

Each leader forms an independent, unbiased, and private opinion of the ideal policy for the party. Formally, leader i observes an informative signal s _i satisfying

where, conditional on θ, leaders' signals are statistically independent. These n underlying informative signals can be collected together to form the n × 1 vector s of information available to the entire set of leaders. The variance term κ_i² > 0 captures an important skill: a leader's ability to discern the correct state of the world. When κ_i² is small, she is better able to assess policy (she is a skilled technocrat), and so the precision 1/κ_i² indexes her sense of direction. A sharper sense of direction stems from the quality of the leader's judgement and also the quality of the information and advice that is available.

Our leaders address the mass of activists. It is perhaps easiest to think of each leader as speaking directly to her party's membership; for expositional ease, we will adopt this interpretation throughout most of our analysis. However, a “speech” is, more generally, a broad label for the channels of communication open to a leader.

A leader's speech conveys information about her opinion. We assume that her preferences over policy choices match those of party members, and so she describes the world as she sees it; strategic information transmission is ruled out. Alas, she is unable to communicate perfectly: each activist t observes the leader's signal plus noise. Formally,

Conditional on s, the final signals received by activists (that is, how they interpret a speech) are statistically independent across activists and leaders. The variance σ_i² > 0 reflects a second important leadership skill: a leader's ability to communicate clearly. The precision 1/σ_i² indexes her ability to express coherently her privately held opinions in a public forum. Because her clarity is imperfect, activists do not necessarily hear what the leader is trying to say and obtain different impressions of the leader's views.

The noise in speeches may seem comical. It is tempting to think of a leader suffering from some kind of speech impediment: she speaks to individual activists in turn, each time attempting to say the same thing, but stumbling over the words. This, however, is not our interpretation. Perhaps somewhat subtly, noisy speeches are consistent with words that are spoken perfectly but are interpreted in different ways: errors stem not from concerns about what is said but rather about what is meant. Thus, σ_i² will be large when a leader uses words to which the activists who follow her attach varying definitions.

Despite this interpretation, it might seem extreme to impose limits on the clarity of the communication process; presumably, a leader can choose unambiguous words and say precisely what she means, so that σ_i² = 0. We offer some justifications for setting σ_i² > 0.

Firstly, a leader's clarity is restricted whenever she is unable to speak directly and simultaneously to activists. Indeed, the ability to speak directly to an entire mass is a relatively recent phenomenon. Prior to radio and television, a leader would need to travel far and wide to reach an audience, her ability to communicate hindered by the physical demands of such a grueling schedule. As a substitute for direct communication, a leader might rely on interlocutors to provide accounts of her words. For example, in the United Kingdom, the Lobby serves as the gateway to the House of Commons. Ministerial briefings are delivered to lobby journalists. Although lobby members observe the same events, their account of proceedings will differ; imprecise reporting compromises clarity.

Secondly, even when a leader can communicate directly, comprehension may be limited. Given time, an articulate speaker may get her point across by removing, clause by clause, any vagueness. But such a legalistic approach can prove the antithesis of clarity—the language becomes long and tortuous, and the task of absorbing the message in its entirety moves beyond most listeners. The limits to the attention span of a listener may then impose a bound on the overall clarity of the message received. Such limits might be endogenously chosen by the listener: even if there is enough time for him to absorb a leader's words, doing so has an opportunity cost because it prevents him from paying careful attention to other leaders.

Thirdly, there may be endogenous limits to a leader's clarity. Even if a leader is able to speak succinctly using unambiguous words, she may choose not to do so. Indeed, in later sections, we argue that attention-seeking leaders will intentionally obfuscate. Rhetorical strategies that eschew clarity have been studied elsewhere, notably by Zeckhauser (Reference Zeckhauser1969) and by Shepsle (Reference Shepsle1972), who both considered the strategic advantage realized by a candidate who is vague over the policy she would implement if elected. Shepsle (Reference Shepsle1972), in particular, highlighted the “politician's advantage in speaking half-truths and in varying his appeals with variations in audience and political climate.”Footnote ⁸

Finally, whether a leader's views are less than perfectly clear is an empirical question. The evidence suggests that different people hold different opinions about the views of their leaders. For example, Alvarez and Franklin (Reference Alvarez and Franklin1994) described survey respondents who were far less certain of their senator's political views than of their own. Moreover, in his earlier study of campaign effects in senatorial elections, Franklin (Reference Franklin1991) noted that “candidate behavior has a substantial impact on the clarity of citizen perceptions.”

Taken together, the variance parameters κ_i² and σ_i² are inversely related to the two qualities of leadership—sense of direction and clarity of communication—which are central to our article. Consider a politician who arguably embodied both qualities. As a backbencher from 1936 to 1940, Winston Churchill advocated preparation for war while Prime Ministers Baldwin and Chamberlain vacillated in the light of uncertain German military ambitions. History suggests that Churchill had a sharp sense of direction: he identified the threat and a military strategy to deal with it. A further Churchillian skill was communication; his speeches created a common understanding of the perils faced by the allies.

Rarely, however, does an individual embody both characteristics, and in such abundance, that she trumps all rivals. More usually, different leaders (or potential leaders) vary across these dimensions. A contemporary example involves the former British Prime Minister Tony Blair and his successor Gordon Brown. Although Brown is perceived as being among the most intellectually astute of his cohort (low κ_i²), he is sometimes regarded as a poor communicator (high σ_i²). By contrast, although Blair's judgement was called into question (not least over his handling of the second Iraq war), he was widely perceived as one of the best communicators in the business. Blair's strength lay in the articulation of a coherent central message; it might be argued that he combined a lower σ_i² with a higher κ_i².

Before proceeding to analyze the response of activists to leaders, we pause to describe the relationship between our specification and that of Morris and Shin (Reference Morris and Shin2002). In the Morris--Shin world, agents learn via two information sources: an imperfect public signal that is commonly observed and interpreted, and private signals that are independently and identically distributed across agents. Interpreted in our framework, their public signal is a leader with perfect clarity of communication (σ_i² = 0) but an imperfect sense of direction (κ_i² > 0). Conversely, their private signal is a leader with a perfect sense of direction (κ_i² = 0) but imperfect clarity of communication (σ_i² > 0).Footnote ⁹ We analyze leaders (or, equivalently, information sources) with an arbitrary mix of these different attributes, and so our information structure is significantly richer than the Morris--Shin environment, because it allows for positive but imperfect correlation between the signals observed by activists.

FOLLOWING THE LEADERS

We now ask how activists react to the speeches they hear. When there is only one leader, an activist can do no better than to follow the advice given in her speech; this advice yields an unbiased estimate of the ideal policy and the party line, as long as others behave in the same way. However, when there is no clear leader apparent, different leaders must be assessed according to their competencies. This assessment is captured by an equilibrium policy advocacy strategy A(·) satisfying Equation (⋆).

In principle, an equilibrium strategy could take a complicated functional form. Fortunately, however, we are able to focus our attention on a simple, robust, and easily interpreted class of strategies. Activists employ a linear strategy if

where w _i is a coefficient attached to the speech of the ith leader; this provides a convenient measure of this leader's influence on the actions of the mass.

Our focus on linear advocacy strategies stems from the use of the normal distribution in the specification of our model. Normality ensures that the conditional expectations of the ideal policy , of other activists' signals , and of the leaders' underlying signals are all linear in . If another activist uses a linear strategy, then the conditional expectation of his action is also linear in . This implies that if all other activists use a linear strategy, then a best reply is to use a linear strategy. (That is, the class of symmetric and linear advocacy strategies is closed under best reply.) Pushing further, we obtain the following lemma (formal proofs are contained in the technical appendix.)

Lemma 1. There is a unique Bayesian Nash equilibrium involving the use of linear strategies, so that . This equilibrium satisfies w _i > 0 for all i and .

When the unique linear equilibrium is played, an activist advocates a weighted average of the policy recommendations that he hears. The weight w _i placed on a speech acts as an index of the orator's effectiveness; it can measure the success of a leader.

Of course, the possibility of nonlinear equilibria remains. Nevertheless, in the technical appendix, we explain how a mild further restriction on advocacy strategies rules out nonlinear equilibria. Furthermore, even if nonlinear equilibria exist (we conjecture that they do not), then further criteria suggest the selection of the unique linear equilibrium.Footnote ¹⁰

Focusing on the partywide deployment of a linear advocacy strategy, we must find the weights placed on the leaders' speeches. One “brute force” approach (described in the appendix) would be to compute the conditional expectations and , and then proceed to solve Equation (⋆). Here, however, we take a more subtle approach. We observe that the weights used by activists in equilibrium are precisely those that are desirable from the perspective of the entire party: they efficiently maximize party welfare.

Lemma 2. In the unique linear equilibrium, the weights placed on the speeches of the various leaders maximize the aggregate welfare of the party: the equilibrium is efficient.

To verify this claim, consider a change in a _t. This change imposes externalities on others: an increase in a _t pushes up the party line , and so activist t′ ≠ t enjoys a positive spillover if (his action is now closer to the party line) but suffers if . However, looking across the entire party membership, these externalities sum to zero. This is because the party line is the average policy advocated by the party, and so, in expectation, the policies advocated by individuals lie equally above and below . Because the various externalities from an activist's action cancel out, the total partywide effect of a marginal change in the policy he advocates is reflected in his own payoff. This means that he faces socially correct incentives (from the perspective of his party) at the margin.

We now calculate the weights that maximize welfare and so find the unique linear equilibrium. The party's welfare (the ex ante expected payoff of a party member) satisfies . Taking the first quadratic loss term, a _t is a weighted average of unbiased signals of θ, and so E[(a _t − θ)²] = var[a _t|θ]. Turning to the second quadratic loss term, a _t is equal to on average, and so , where s is the vector of signals seen by the leaders. Assembling these elements,

Notice that any noise in the information sources available to activists detracts from party welfare. Interestingly, the effective noise πκ_i² + σ_i² corresponding to a leader's speech does not equally incorporate the variances κ_i² and σ_i². A lack of clarity in a leader's communication frustrates activists' coordination and lessens the information content of her speech. By contrast, a failing in her sense of direction, while affecting an activist's ability to infer the ideal policy, has no impact on coordination; it thus attracts a reduced coefficient of π < 1. These observations regarding the different effects of our leadership skills are reflected in the equilibrium weights that maximize party welfare.

Proposition 1. The unique linear Bayesian Nash equilibrium advocacy strategy satisfies

Party welfare is . A leader's influence, indexed by , increases with both her sense of direction and her clarity of communication. The relative influence of relatively better communicators increases as activists' concern for party unity grows: if (σ_i²/σ_j²) < (κ_i²/κ_j²), so that i enjoys a comparative strength in communication, then is decreasing in π.

The index measures influence and therefore successful leadership; however, because welfare increases with , it also measures good leadership. An influential leader (with a high value of ) clearly communicates her sharp sense of direction. Unsurprisingly, a leader who excels on both dimensions enjoys more influence. Nevertheless, and because w _i > 0 for all i, even unskilled leaders enjoy some influence.

So which skill is more important? The presence of π in the index suggests that a leader's ability to express her views clearly is more important than her ability to understand the political environment. Of course, this claim relies on an implicit assumption that it is appropriate to compare directly the variances κ_i² and σ_i². Even if this comparison is inappropriate, Proposition 1 reveals that the relative influence of relatively clear communicators grows as cohesion looms larger in the minds of activists. Furthermore, an inspection of confirms that influence is entirely determined by absolute clarity (rather than relative clarity) as π vanishes to zero: if σ_i² < σ_j² then w _i > w _j when π is sufficiently small.

To obtain further insight, recall once again that a leader helps activists learn about policy and coordinate. Her message about policy is muddled by two sources of noise: any errors of judgement on her part (the variance κ_i²) plus any misunderstanding of what she says (the variance σ_i²). Combining these sources of noise,

If activists cared only about discovering the best policy (so that π = 1), then the two components of a leader's skill set would be equally important. Each activist would choose an action without reference to others. Indeed, Bayesian updating yields

so that the weight placed on each leader's speech is proportional to the quality of information ψ_i that the speech contains. However, when π < 1 activists care about coordination as well as policy, and so a leader's speech can act as a convenient focal point for them. For this to be true, it is useful if different activists tend to hear the same thing.

A measure of the commonality of messages received is the correlation between what is heard by different activists. To calculate this, note that the conditional covariance of two signals related to the same speech is . The correlation coefficient

depends on the relative strength of a leader's clarity of communication and sense of direction. When a leader becomes a perfect communicator (σ_i² → 0), the correlation satisfies ρ_i → 1 and everyone hears the same message; the speech becomes a public signal. However, when a leader becomes a perfect technocrat (κ_i² → 0), the correlation satisfies ρ_i → 0; the messages received become independent private signals of θ.

Correlation is important for expectations about what others hear. If ρ_i = 1 (a leader with perfect clarity), then : an activist knows that others hear what he hears. However, when ρ_i < 1, interpretations differ. In forming his beliefs, an activist recognizes that any information about the underlying ideal policy is useful in thinking about what the leader was trying to convey. Bayesian updating yields

A high correlation coefficient reinforces the party's response to a leader. If activists listen to that leader, then when ρ_i is large others will listen to that leader in order to anticipate the party line. In contrast, when ρ_i is small, they divert attention to others. Drawing these observations together, we can reformulate Proposition 1 in terms of ψ_i and ρ_i.

Proposition 2. The unique linear Bayesian Nash equilibrium advocacy strategy satisfies

and hence a leader's influence increases with the quality of information she offers to activists and the correlation of the messages that they hear. Comparing two leaders i and j satisfying ρ_i > ρ_j(so that leader i is a more coherent communicator) the influence of i relative to j grows as π falls. If leaders' labels are in strict order of decreasing correlation, so that ρ₁ > ρ₂ > . . . > ρ_n, then there is some k such that w_i is locally decreasing in π for i < k and locally increasing in π for i > k.

Because π is the weight placed on any deviation from the ideal policy, the remainder 1 − π is the desire for party unity. Proposition 2 reveals the determinants of good leadership:

Fixing the quality of information provided, coherent communication determines the effectiveness of leadership, and more so when there is a greater desire for party unity. In fact, it is useful to compare a perfect communicator (ρ_i ≈ 1, so that ) with a perfect technocrat (ρ_j ≈ 0, so that ). As π vanishes so that only party unity matters, the perfect communicator becomes far more influential than the perfect technocrat.

LISTENING TO LEADERS

To interpret our model, we might think of party members attending a large party conference where each listens to speeches made from the conference platform. An implicit assumption is that activists form a captive audience. Under this assumption, we concluded that the clearest communicators enjoy relatively more influence.

Of course, speeches convey information only if they are heard. Activists may abstain from listening to a particular speech or may not devote their full attention to it. The clarity of a leader's message depends on the willingness of her audience to listen; however, the decision to listen is endogenous. This is important when being informed is costly as, for example, when activists have limited attention spans and cannot listen to a leader indefinitely. Furthermore, there will be strategic interaction among activists when they decide to whom to listen. In common with Hellwig and Veldkamp (Reference Hellwig and Veldkamp2008), we recognize that there may be coordination motives in information acquisition so that, using their language, if an activist wants to do what others do (coordination of policy advocacy), then he wants to know what others know (coordination of attention).

To analyze these effects, we extend our model. Activists are given a single unit of time (perhaps the duration of a party conference) to allocate to different leaders: activist t spends a proportion x _it of his time listening to what leader i has to say. We think of him as observing a sample of (noisy) observations of the leader's views. In this sense, the time spent listening represents the sample size. In the usual way, the sample variance declines with the sample size; equivalently, the precision of the aggregate signal is linearly increasing in x _it. This leads us to the specification

so that the overall clarity of the message is the product of the leader's clarity of communication and the time spent deciphering what it is that she is trying to convey. A constraint captures the limited attention span of an activist: paying close attention to one leader carries an opportunity cost, because less attention is paid to others.

With this extension in hand, we analyze a game in which activists choose both to whom to listen and how to react to the speeches they hear. Specifically, activist t chooses , satisfying the budget constraint on her time and then, given what she hears, chooses a policy to advocate. Payoffs are as before, and activists use a linear advocacy strategy.

As previously, while an activist imposes externalities on others via his effect on the party line , the positive and negative externalities cancel out (Lemma 2). Thus, to find the equilibrium, we can again maximize aggregate party welfare. Any strict equilibrium involves the symmetric choice of attention; hence, we can drop the subscript t so that each activist devotes a fraction of time x _i to leader i. Whereas leader i's clarity of communication is still indexed by 1/σ_i², the clarity of the message received from her is now x _i/σ_i². Restricting attention to a linear advocacy strategy and exploiting Proposition 1,

and so the equilibrium x maximizes subject to . Because welfare is increasing in the attention paid to each leader, activists exhaust the time they have available. However, it may be that x _i = 0 for some i: activists may ignore some leaders. Evaluating which leaders receive attention can provide insights into the formation of a natural oligarchy of influential leaders; a necessary condition for a leader to have influence is that activists pay attention to her message. Before performing this evaluation, we label (without loss of generality) the leaders in order of decreasing clarity, so that σ₁² ≤ . . . ≤ σ_n².Footnote ¹¹

Proposition 3. When leaders' audiences are endogenous, there is a unique Bayesian Nash equilibrium involving the subsequent play of a linear advocacy strategy. Activists listen only to the clearest communicators: ordering leaders by decreasing clarity so that σ₁² ≤ . . . ≤ σ_n², there is a unique m ∈ {1, . . ., n} such that x _i > 0 for i ≤ m and x _i = 0 for all i > m. For i ≤ m,

The attention paid to a leader increases with her sense of direction, although not always with her clarity: for i ≤ m, the attention x_i paid to a leader is locally increasing in her clarity when σ_i > K _m/2, but locally decreasing when σ_i < K _m/2. The elite size m minimizes K_m. It increases with activists' relative concern π for policy, but decreases with each leader's sense of direction.

When all leaders share the same communication skills (σ_i = σ_j for all i ≠ j), then all leaders enjoy an audience, and the attention paid to each is proportional to her sense of direction. However, when leaders differ in their coherence, richer results emerge: activists gravitate toward the clearest communicators. Correspondingly, once a leader's clarity falls below a threshold (i.e., when σ_i > K _m) activists will ignore her; such a leader can have no influence. Although intuitively one might think that a good sense of direction would demand attention, our result highlights the importance of getting the message across.Footnote ¹²

Despite this finding, communicating too clearly can deflect attention toward others: when σ_i < K _m/2 for i ≤ m (the noise in a leader's speech is relatively low), an increase in her clarity reduces the attention paid to her. We return to this issue in due course, when we evalute a leader's incentive either to clarify or to obfuscate when speaking to her party.

Nevertheless, sufficient clarity is a prerequisite for successful leadership. One possibility emerging from Proposition 3 is that m = 1, so that activists listen only to the best communicator. Such a leader, should she exist, enjoys undivided attention and thus undiluted influence; she becomes a de facto dictator. But when will such a leader emerge?

Proposition 4. Recall that we have (without loss of generality) ordered the leaders by decreasing clarity, so that σ₁² ≤ . . . ≤ σ_n². The clearest communicator is a de facto dictator if and only if

This fails when σ₁²is sufficiently small. Hence, for the clearest communicator to enjoy exclusive attention, she needs to communicate imperfectly. The clarity σ₁² = πκ₁²that best supports her dictatorship (by minimizing the right-hand side of the inequality) increases with her sense of direction and the desire for unity. If σ₁² < σ₂², then she enjoys exclusive attention if π is small enough.

A de facto dictator must be the clearest communicator (Proposition 1). Her power and influence are maximized only when the attention of her followers is not diverted to others. For the dictator to enjoy this exclusive attention, however, the clarity of her clearest competitor must be sufficiently low; equivalently, σ₂² (and σ_i² for other leaders i > 2) must be large. Being the clearest communicator is not enough; σ₁² < σ₂² is sufficient for dictatorship in only two cases. The first case is when π → 0, so that activists care only about party unity, and the clearest communicator is best able to describe a focal policy around which the party can rally. The second case is when κ₁² → 0, so that the best communicator also enjoys an excellent sense of direction; she is a Churchillian leader who trumps all others.

A leader succeeds in monopolizing the agenda when the inequality in Proposition 4 is satisfied. This is easiest when σ₁² minimizes the right-hand side of the inequality; that is, when σ₁² = πκ₁² > 0. Figure 1 illustrates: with the parameter values shown, when Leader 1 chooses σ₁² = 0.25 (or σ₁ = 0.5 in the figure) and σ₂² ≥ 1, then Leader 2 receives no attention and enjoys no influence. However, if Leader 1 speaks more clearly, then eventually Leader 2 attracts an audience. The lesson is clear: should an ambitious leader want to monopolize the agenda, and so maintain complete influence, then she would need to avoid perfect clarity; better communication can sometimes divert attention toward others.Footnote ¹³ Moreover, the clarity 1/(πκ₁²) that maximizes the range of de facto dictatorship increases with a leader's sense of direction; if she is to maintain exclusive attention, then a leader can get away with speaking more clearly only when she has more to say.

FIGURE 1.

Paying Attention to a Single Leader

Propositions 3 and 4 suggest that a leader can sometimes attract attention by speaking less clearly; in fact, imperfect clarity is necessary if a leader is to maintain complete influence as a de facto dictator. To understand why this is so, recall that an activist gathers information to develop an understanding of his environment. Listening to leaders helps him to do this, but given time contraints he will not listen to a leader longer than he needs to. When a leader is a good communicator, an activist can discern her position in a short period of time; with time to spare, he moves on to gather more information.

It is also worthwhile noting that the focus of activists' attention depends upon their relative preference for policy versus party unity. From Proposition 3, m declines with the policy concern parameter π. Hence, as the desire for unity grows (so that π falls), the size of the elite shrinks; Proposition 4 reveals that a de facto dictator emerges when π is small enough. The intuition is natural: when activists care only about unity, then the information regarding policy provided by leaders is irrelevant, and all that matters is finding a clear focal point around which the membership can coalesce.

OBFUSCATION

So far, the characteristics of leaders have been exogenous. This seems reasonable for a leader's sense of direction, which, at the time of speaking to her followers, is likely to be beyond her control. However, a leader's clarity of communication may be more manipulable: the overall clarity of a message depends endogenously on both speaker and audience. For instance, a leader might be able to reduce her clarity; she may obfuscate.

Here, we extend our model by allowing for endogenous obfuscation. Of course, if a leader chooses her clarity, then we must consider her objectives. For instance, a benevolent party leader may want to maximize the welfare of her party's membership. Because activists make efficient decisions when choosing to whom to listen and whom to follow, the leader has no reason to distort her behavior. Indeed, she can best enhance her welfare by maximizing the information available, and she does so by speaking as clearly as possible.

Of course, the objectives of an ambitious leader may extend beyond benevolence, and therefore, there may be a variety of reasons for her to distort activists' decisions; obfuscation is one way to do this. For instance, a power-hungry leader may want to maximize her influence. We have already noted that such influence is maximized when a leader enjoys a position as a de facto dictator, and we have seen (Proposition 4) that this requires less than perfect clarity. The source of this requirement is the fact that a reduction in clarity can increase the attention devoted to a leader. Indeed, a leader must attract attention because it is a necessary component of exercising influence. To explore fully the desire for attention, we focus on this dimension of a leader's ambition and ask: what rhetorical strategy maximizes the attention paid to her? (Later in this article, we will return to consider other possible objectives and show that they too result in obfuscatory rhetoric.)

To answer this question, we study a simultaneous-move game in which each leader i chooses the variance σ_i² of the noise in her speech; her clarity of communication is the precision 1/σ_i². We impose exogenous restrictions on the clarity of our n leaders: their choices must satisfy . Under this specification, is an upper bound to a leader's clarity, which may represent her skill as an orator. Without loss of generality, we order leaders according to their communication skills so that .

A leader's payoff is the attention x _i emerging endogenously from the choices of activists (Proposition 3). Of course, if her communication skills are poor (so that is large), then she may be ignored. Such a leader is indifferent between her feasible clarities, and so her behavior is not uniquely defined. To simplify our exposition, we assume (without loss of generality) that such a leader speaks as clearly as she can. Similarly, there may be some range of σ_i² a leader dictates (Proposition 4). This dictator must be the clearest communicator, and so we label her as i = 1. For such a leader, we assume (again without loss of generality) that she chooses her clarity in order to maximize the range of other leaders' clarities for which x ₁ = 1, thereby defending her dictatorial position. Following Proposition 4, this means that she chooses σ₁² = πκ₁², as long as this is feasible, and otherwise will choose . Combining these cases, if x ₁ = 1, then we assume that .

An attention-seeking leader must convey some information and cannot simply babble; if the noise in her speech is too large (from Proposition 3, when σ_i > K _m), she will be ignored. But this does not imply that she wants to speak with perfect clarity. When σ_i < K _m/2, the attention paid to the leader increases with noise added to her speech, and so she obfuscates.Footnote ¹⁴ In fact, we can obtain an upper bound to her optimally chosen clarity.

Lemma 3. If a leader's communication skills are strong, so that is sufficiently small, then she obfuscates by choosing . Her optimally chosen clarity always satisfies , where

and so a sufficient condition for a leader to obfuscate is .

Further insight emerges from an economic analogy. In our model, each activist is a consumer of costly information. He allocates time (rather than money) to n competing information products (leadership speeches). His purchase from leader i is the clarity x _i/σ_i² of her message. When a leader chooses her clarity to maximize the attention paid to her, she acts as would a revenue-maximizing oligopolist. Adding noise to her communication is equivalent to a price hike: it directly increases her revenue (in the form of the attention paid to him or her) for a given quantity (clarity of message); however, obfuscation prompts an activist to lower her demand for her product (speech) by substituting to others. Balancing the two effects of a change in clarity generates an intermediate solution.

Lemma 3 reveals that leaders will sometimes obfuscate. To move further, however, we find the unique equilibrium of our attention-seeking game.

Proposition 5. There is a unique pure strategy Nash equilibrium of the attention-seeking game. Ordering leaders so that , their clarities satisfy σ₁² ≤ . . . ≤ σ_n². There is a unique such that leaders speak with maximum clarity (), whereas leaders obfuscate (). Those who obfuscate choose the same clarity: if , then σ_i² = σ_j².

If for all i (so that all leaders have good communication skills), then (they all obfuscate), and the unique Nash equilibrium is symmetric, satisfying for all i. Hence,

An increase in any leader's sense of direction and activists' desire for unity: (1) (weakly) increases every leader's clarity of communication, (2) (weakly) reduces the number of leaders who obfuscate, and (3) (weakly) reduces the size m of the elite who attract an audience.

Linking Propositions 3 and 5, there are (potentially) three groups of leaders. Firstly, those leaders have excellent communication skills and yet do not exploit them; with oratorical flair in abundance, they nevertheless attract maximum attention by obfuscating. (In fact, their choices all satisfy σ_i = K _m/2.) Because these leaders choose the same clarity, the relative influence of each individual is determined by her sense of direction. By contrast, leaders in the second group have less developed oratorical skills and must strain to be clear to the best of their abilities in order to attract an audience. The exogenous limits to their oratorical skills mean that they do not obfuscate, but they are heard so long as . A leader i > m talks only to herself. To enjoy an audience, she must improve her oratorical skills: only when the noise in her speech is no greater than twice that of the obfuscating (and hence clearest) communicators will her views be heard.

Of course, the three different classes of leader may collapse to a single group. For instance, when , every leader will obfuscate. This will be so when there are few exogenous limits to clarity, perhaps a world in which a leader is able to deliver a commonly heard speech directly to the entire activist mass. Perhaps surprisingly, the unique equilibrium identified by Proposition 5 (illustrated in Figure 2) reveals that all leaders speak with the same clarity, even though they do not share a common sense of direction.

FIGURE 2.

Endogenous Leadership Clarity

To understand why, consider the solution for x _i from Proposition 3. The attention (relative to others) paid to each leader increases proportionally with her sense of direction. However, the way in which it reacts to clarity is (approximately) the same for everyone via the term σ_i(K _m − σ_i).Footnote ¹⁵ Returning to our analogy, local to the equilibrium the demand curves (for clarity of message) faced by different leaders are the same shape; however, those with a better sense of direction benefit from proportionally higher demand for any given price. Because 1/κ_i² simply scales the demand curve along a quantity axis, the revenue-maximizing price is independent of it. This leads naturally to a symmetric equilibrium (Figure 2).

As suggested previously, communication skill may be due to a combination of natural ability and the information technology available to all leaders. When such technology is poor, we would expect to be large for everyone. If , then leaders speak with different clarities, and so attention (and influence) is biased away from those with poor communication skills. When information technology improves, may fall for everyone. If , then we shift to an equilibrium in which everyone speaks with equal clarity, and so the sole determinant of attention and influence is a leader's sense of direction.

For example, when leaders are constrained to use primitive media (e.g., a series of private audiences), only the most oratorically skilled leaders, who can speak clearly and concisely, attract attention. As technology improves so that the same leadership speech can simultaneously be broadcast to all activists, then exceptional oratorical flair is no longer a prerequisite for success. Thus, while a leader in the mold of Theodore Roosevelt—combining physical stamina, oratorical flair, and the ability to deliver an effective stump speech to many different audiences—enjoys influence despite technology constraints, others, not so well endowed, can flourish only as technology advances. For example, it is well documented that Calvin Coolidge lacked the capacity to succeed on the stump. He owed much to broadcasting; in his own words [Cornwell (Reference Cornwell1957)],:

Of course, if technology allows all leaders to communicate clearly, then all will obfuscate. This rhetorical behavior has (perhaps superficial) similarities with the “garbling” of messages in sender–receiver games analyzed by Crawford and Sobel (Reference Crawford and Sobel1982) and extended to political settings by Gilligan and Krehbiel (Reference Gilligan and Krehbiel1987) and Li, Rosen, and Suen (Reference Li, Rosen and Suen2001), among others. In these “cheap talk” scenarios, an informed politician is restricted to sending garbled messages due to her commonly understood policy bias. Our leaders have no inherent policy bias, but the strategic incentive to obfuscate arises nevertheless.

Although a leader may obfuscate, her payoff does not depend on the policies advocated by activists; she has no direct incentive to misrepresent the truth as she sees it. Her only strategic move is to change the precision of the information she transmits. Thus, our leaders' speeches are signals in the statistical, rather than the game theoretic, sense; an activist need not anticipate any bias.Footnote ¹⁶ Our model thus lacks the strategic tensions that arise when leaders have policy preferences that differ from those of their followers.

Nevertheless, such biases could arise endogenously from attention-seeking behavior. For example, suppose that when θ falls within a specific range of values, information is more easily conveyed than when θ falls outside that range. This might be so when there is a partywide consensus about the correct policy. For example, a policy that forms the status quo might easily be described to an audience, whereas elucidating an alternative path requires a longer exposition. Alternatively, a particular policy (say left or right) may require more (or less) clarification. In such scenarios, there is an incentive for a leader to dissemble, pretending that she observed something she did not, though this need not exclude obfuscation as a rhetorical strategy. Whenever such biases are present, activists face a harder task in extracting information from a leader's speech.

Before concluding this analysis of endogenous clarity, we note that the incentive to obfuscate arises due to the nature of the “beauty contest” played by activists and the competitive tensions between attention-seeking leaders. Beyond our policy advocacy parable, these ingredients combine in other social situations where obfuscation is pervasive, and so our analysis provides more general insights. Consider the following variation: our activists are members of a religious mass who seek guidance from spiritual leaders. They wish that their everyday acts are in accordance with a divine plan unknown to them, but as members of a community must also act in concert with their fellows. Through their readings of sacred texts, meditation and other methods, religious leaders receive signals of these unknown truths and convey messages through speech. Our results suggest that when religious leaders compete for the attention span of the mass, they obfuscate, and so provide an interpretation for why lucid prose rarely emanates from the pulpit.

PARTY PERFORMANCE

When the exogenous limits to communication are not binding, Proposition 5 predicts that the (common) clarity of leaders' communication increases with every leader's sense of direction. An increase in a leader's sense of direction enhances demand for her information as activists divert attention away from others. This has a knock-on effect because it forces other leaders to compete harder, by increasing the clarity of their communication. This feeds back, in turn, to the original leader. One aspect of this effect seems natural: an exogenous increase in a leader's judgement increases the clarity of everyone, and so a leader speaks more clearly when he or she has more to say. More subtly, however, a leader speaks more clearly when others have more to say.Footnote ¹⁷ This suggests that an exogenous increase in leadership quality (an enhanced sense of direction) can promote a further endogenous increase (clearer communication) and hence better party performance.

Proposition 5 also predicts that leaders' rhetoric reacts to the relative preferences of the party membership. As activists emphasize party unity relative to choosing the right policy, so that π falls, leaders speak with increasing clarity. Coordination requires precise communication, and leaders respond by speaking more clearly.

We observe the full importance of this point when we consider the welfare and policy performance implications of attention-seeking leaders. Recall (Proposition 1) that party welfare increases with , and so the index measures both good leadership and successful leadership; it reacts positively to a leader's clarity as well as her sense of direction. Allowing the attention paid to leaders (and hence the overall clarity of their messages) to be determined endogenously, the situation becomes more complex. Clarity of communication remains critical in ensuring that a leader receives some attention. However, whereas increased clarity benefits activists and is thus a component of good leadership, an attempt to seek attention or to monopolize the agenda may induce a leader to reduce her clarity; a successful leader (as opposed to a good leader) may obfuscate. The vanity of attention seekers separates good and successful leadership.

Allowing our leaders to play a game in which they simultaneously choose their rhetorical strategies might be expected to complicate things further. In practice, it simplifies matters. Because (when ) all leaders choose the same clarity, the attention paid to each leader is proportional to her sense of direction. The leadership index reduces to

and so party welfare increases with the combined judgement of the leadership, but falls with activists' relative concern for policy. The effect of π is unsurprising, because the policy component of an activist's loss function reacts to two sources of noise rather than one; even fixing the behavior of all actors, our welfare measure will fall with an increase in π.

A more surprising insight is obtained by considering an objective performance index. A party exhibits good policy performance if the policies advocated by its members are close to the ideal policy. An appropriate measure here is the loss function ∫₀¹(a _t − θ)²dt = E[(a _t − θ)²]. The inverse of this provides our measure of policy performance.

Proposition 6. If for all i, so that all leaders choose the same clarity, then the equilibrium influence of a leader is proportional to her sense of direction. Furthermore,

which increases with the leaders' combined sense of direction but decreases with the policy concern parameter π; a greater desire for party unity improves the policy performance of the party.

Paradoxically, activists become better at advocating the best policy as they care less about doing so. Recognizing the endogenous quality of leadership provides the correct intuition. When activists desire unity, they seek out a common party line, and so leaders respond by speaking clearly. Clearer communication allows activists to develop a better understanding of their environment. Moving away from a desire to back good policies generates a need for coherent unifying leadership; this reduces the obfuscation of attention seekers and so improves policy performance.

Our analysis of policy performance also suggests a further possible objective for leaders and so an additional source of obfuscation. Consider a leader who cares only about policy performance and not about party unity. From her perspective, followers place too much emphasis on the speeches of relatively clear communicators and hence too little on those with a good sense of direction. If such a leader is clear but has poor judgement, then she may prefer to lose influence to others: obfuscation is one technique for doing so.Footnote ¹⁸ In fact, it is straightforward to construct reasonable parameter configurations in which this phenomenon arises. More generally, whenever a leader's concern for policy relative to coordination differs from that of her followers, incentives to obfuscate emerge.

CONCLUDING REMARKS

A leader can be influential when political actors want (1) to make informed policy choices and (2) to coordinate with each other. A leader's relative influence depends on her own qualities and those of other leaders: two such skills are her ability to communicate clearly (clarity of communication) and to judge the best policy (sense of direction).

We studied party activists who want to advocate the best policy and also to act in concert with their fellow party members. Adopting the weight activists place on a leader's speech as a measure of her influence, we found that, when leadership skills are exogenous, clarity of communication is the most important leadership attribute. When the attention paid to leaders is endogenous, a natural leadership elite of the clearest communicators emerges. Activists apportion their time among these elite communicators, but may pay more heed to those with (relatively) inferior communicative ability. Correspondingly, when attention-seeking leaders choose their clarity, some may obfuscate to retain their audience: these leaders choose the same levels of clarity; their clarity is increasing in the combined sense of direction of the leadership elite; and so in contrast to our earlier results, a leader's sense of direction becomes relatively more important.

We also asked whether leaders can be both good and successful. A good leader enhances party performance, aiding activists in pursuit of their twin goals to the best of her abilities. A successful leader commands attention. Only when skills are exogenous do good and successful leadership necessarily coincide. Otherwise, a leader may increase her success by obfuscating her message; activists receive less information and consequentially are less informed about their environment. Perhaps surprisingly, there is less obfuscation when activists place more emphasis on following the party line than pursuing the best policy. When a party emphasizes unity, it provides leaders with the necessary incentives so that good and successful leadership coincide and policy performance improves.

Few would deny that leaders play an important role in influencing people's actions, and indeed there is experimental evidence that they do (Güth et al. Reference Güth, Levati, Sutter and van der Heijden2004; Humphreys, Masters, and Sandbu Reference Humphreys, Masters and Sandbu2006). Yet, there has been no recent formal work that evaluates the influence of different leaders. This article has attempted to fill this gap. Building on suggestions made by Levi (Reference Levi2006, 10) that “leadership—both of government and within civil society—provides the agency that coordinates the efforts of others” we have explored a world with multiple potential leaders differentiated by their skill sets and extended our analysis to a world where leadership skills emerge endogenously. Our work provides, we hope, a small step in response to Levi's (Reference Levi2006, 11) claim that “still lacking is a model of the origins and means of ensuring good leadership.”