GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 281

Asking One Too Many? Why Leaders Need to Be Decisive

Junichiro Ishida and Takashi Shimizu

October 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Asking One Too Many? Why Leaders Need to Be
Decisive∗
Junichiro Ishida† and Takashi Shimizu‡
October 23, 2012

Abstract
It is often touted that decisiveness is one of the most important qualities to be possessed by leaders, broadly defined. To see how and why decisiveness can be a valuableasset in organizations, we construct a model of strategic information transmission where:(i) a decision maker solicits opinions sequentially from experts; (ii) how many experts
to solicit opinions from is the decision maker’s endogenous choice. We show that communication is less efficient when the decision maker is indecisive and cannot resist thetemptation to ask for a second opinion. This result suggests that the optimal diversity of
information sources depends critically on the strategic nature of communication: whencommunication is strategic, it is optimal to delegate information acquisition to a single
party and rely exclusively on it; when it is not, it is optimal to diversify information
sources and aggregate them via communication.
Keywords: Decisiveness, Cheap talk, Multiple senders, Commitment.
JEL Classification Number: D23; D82.

∗

The second author was financially supported by Kansai University’s Overseas Research Program for theyear of 2009. Of course, any remaining errors are our own.
†
Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki-shi, Osaka 567-0047
JAPAN (E-mail: jishida@iser.osaka-u.ac.jp)‡
Faculty of Economics, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680 JAPAN (E-mail:tshimizu@ipcku.kansai-u.ac.jp)

“If I had to sum up in a word what makes a good manager, I’d say decisiveness.”– Lee Iacocca“In any moment of decision, the best thing you can do is the right thing, the next
best thing is the wrong thing, and the worst thing you can do is nothing.”– Theodore Roosevelt

1

Introduction

It is often touted that decisiveness is one of the most important qualities to be possessedby leaders. However, while this type of assertion is intuitively appealing and appears to
be well received within the business community, it is not exactly clear how the leader’s
decisiveness works to improve the organization efficiency in any way. In this paper, weconstruct a simple model of strategic information transmission with multiple senders, whichfalls into a class of cheap-talk models, to explore into this issue. Using the model, we illustrate
how the presence of a decisive leader keeps the followers’ incentives straight and mitigates
opportunistic strategic behaviors by them.
The model we consider is as follows. There are a decision maker (female) and two experts(male), each of whom has his own private information. As always in this type of model, thepreferences of the decision maker and those of each expert are not perfectly aligned, making
truthful communication an issue to be reckoned with. The key departure, which distinguishes
our setup from the existing models of cheap talk with multiple senders, is that it is the decision
maker’s discretion how many experts to solicit opinions from. In this setting, we ask whether
there are such things as “asking too many opinions,” i.e., a situation in which the decision
maker cannot resist the temptation to ask for a second opinion even though she would bebetter off making up her mind after soliciting one opinion and immediately initiating anaction. We say that the decision maker is indecisive when she cannot resist the temptation
to ask for a second opinion.
The current framework shows that there is indeed a case where the decision maker’s
indecisiveness proves to be costly for the organization as a whole, as it obstructs efficient
information transmission by making each expert’s problem highly strategic in nature. The
basic logic behind this result stems from an insight recently developed in the analyses ofcheap-talk models with an imperfectly informed receiver or multiple imperfectly informed
senders (Chen [4], Lai [14], Moreno de Barreda [6], Ishida and Shimizu [13] for models with aninformed receiver; Austen-Smith [2], Morgan and Stocken [15], Galeotti et al. [11] for models
2with multiple senders).1 In this growing body of literature, it is found that under a wide rangeof circumstances, the more informed the receiver becomes, the less information she can extractfrom the sender. This implies that the incentive for each of the experts to communicate
truthfully diminishes when he knows that the decision maker will solicit opinions from analternative source and becomes “more informed” (from the expert’s viewpoint). Building on
this logic, we show that there exists no truth-telling equilibrium when the decision maker isknown to be indecisive and cannot resist the temptation to ask for a second opinion, meaningthat information cannot be aggregated efficiently under the lead of an indecisive leader. This
also means that the decision maker may be made better off by committing herself to the“one-and-done” strategy, i.e., soliciting only one opinion and initiating an action right away,
if such an option is ever feasible.
As one of the main contentions, our analysis provides an insight into the optimal diversityof information sources within an organization. To see this, consider an environment where thedecision maker has some discretion over the distribution of information, so that the numberof information sources is her endogenous choice. Intuitively, there is a gain from diversifying
information sources and obtaining information from many different angles, as it allows thedecision maker to aggregate different sources of information to make a better estimate of
the current state. The argument indeed holds true when the underlying environment is
nonstrategic, and information can be solicited via communication at no cost: in this case, it
is optimal to diversify information sources to complement each other and aggregate them via
communication. This argument does not necessarily apply, though, when there is a potential
conflict of interests between the decision maker and the experts, and communication is morestrategic in nature. Our analysis suggests that having multiple information sources can be
an impediment to efficient information transmission and actually lower the decision maker’s
welfare. In strategic environments, therefore, it is optimal to delegate information acquisition
to a single party and rely on it exclusively.
While the importance of leadership has been widely recognized in various fields,
economists have paid relatively less attention to this issue until recently. There is now a
growing body of literature which explores the nature of leadership in formal economic analyses; most of the existing studies largely focus on the informational aspect of leadership,
as giving a sense of direction or a focal point to coordinate beliefs and behaviors. One of
the early attempts is made by Hermalin [12] who formalizes the notion of leadership in thecontext of “leading by example” where a leader transmits private information by moving
1
There is evidently a close connection between models with an informed receiver and those with multiple
receivers. The case with an informed receiver can be regarded as a subgame of models with multiple sender
after one of the senders reports truthfully.

3

first. Rotemberg and Saloner [17] model vision as a bias which makes the manager favor one
project over the other. Hiring a manager with a vision can be beneficial because it reduces
uncertainty as to what kind of employee initiatives will be favored later.2 Van den Steen [7]also formalizes the notion of vision and shows that a leader with strong beliefs would attract
employees with similar beliefs. This sorting effect gives direction to the firm and improves
coordination, suggesting a channel through which strong vision can affect the firm’s performance. Dewan and Myatt [8] [9] [10] and Bolton et al. [3] explore the role of leadershipin the beauty-contest type setting where adaptation and coordination are the main concern.
The current work differs from the existing literature in that our explicit focus is on the roleof the leader’s “decisiveness” and its impact on the quality of communication in strategic
environments.
We illustrate our main contention by building on and extending a model of strategic
information transmission developed in Ishida and Shimizu [13].3 The paper proceeds asfollows. In section 2, we outline the basic framework. In section 3, we analyze two extreme
cases to show how the decision maker’s decisiveness facilitates information transmission in
strategic environments. In section 4, we provide some implications of the model. Finally, in
section 5, we offer some concluding remarks.

2

A model of public consultation

Setup: Consider a two-period model with a decision maker (female) and two experts (male).4
The decision maker’s task in each period t = 1, 2 is to collect information about the state ofnature, either by garnering evidence on her own or by communicating with an expert, andtake an appropriate action based on the acquired information. For clarity, we refer to an
expert who is called upon to make advice in period t as expert t. The (time-invariant) stateof nature is denoted by θ ∈ {0, 1}, where each state is equally likely ex ante:Pr(θ = 0) = Pr(θ = 1) = 0.5.
The state of nature is not directly observable to anyone.
2

Similarly, Rotemberg and Saloner [16] argue that a firm could be better off by committing to a specificbusiness strategy.
3
It is important to note that, although our analytical framework builds on a particular model of strategic
information transmission, our logic can be applied to many other cases as long as the base model has a featurethat communication becomes less effective when the receiver amasses more information. The class of models
with this feature includes many variants of the canonical model of cheap talk such as Morgan and Stocken[15].
4
Since the decision maker can solicit one opinion in one period, she can ask for at most two opinions. We
assume that there are only two periods strictly to keep the analysis as simple as possible while keeping thesubstance of the model. As we will later argue, this assumption is quite inessential for our main results.

4[Remark] Here, we consider the case of public consultation in which each expert knows
whether he is the first or second one to make advice. This assumption of public consultation
is made mostly for analytical clarity and does not affect our main contention in a qualitative
sense: we later extends the analysis to the case of private consultation in which communication is done in private and each expert does not know whether he is the first or second one
to make advice.
Information: At the beginning of each period, nature randomly draws a signal θ̂t ∈ {0, 1}
which is imperfectly correlated with θ. The conditional distribution of the signal is given byPr(θ̂t = i | θ = i) = r, t = 1, 2, i = 0, 1,
where r ∈ (0.5, 1) measures the accuracy of the signal. We assume that expert t, with enoughexpertise, can always observe θ̂t . Lacking expertise (or resources to expend) on the problem
at hand, however, the decision maker can observe a signal only with some probability: let pt
denote the probability that she directly observes θ̂t .5 If the decision maker fails to observea signal in period t, she must then consult expert t to solicit this information via (strategic)
communication as we describe below.
Throughout the analysis, we focus on the case where things unfold over time and it becomes more likely for the decision maker to come across useful information by chance: for
instance, one can conceive of a situation where uncertainty regarding the state of nature partially resolves due to some exogenous events or the arrival of “news” from some nonstrategic
outside sources. Formally, we capture this situation by supposing p1 = 0 and p2 = p > 0.6
The parameter p is one of the key parameters of the model which measures how difficult it
is for the decision maker to obtain unbiased information about θ and hence how much sheneeds to rely on the experts to make up her mind.
Communication: When the decision maker fails to observe a signal on her own, she needs
to solicit this information via communication. We consider a simple (cheap-talk) message
game: in each period t, upon observing θ̂t , expert t sends a costless message mt ∈ {0, 1}
to the decision maker. We assume that expert 2 can observe m1 , although this assumption
turns out to be totally irrelevant.7
Action: Given all the available information, the decision maker must take some actionat ∈ {0, 1, W } in each period, where at = W denotes the “wait” option. For expositional5

If the decision maker happens to observe a signal, the information-acquisition stage ends immediately as
no more information is available for the period.
6
Alternatively, one can regard that we focus on the case where the decision maker fails to observe a signal
in period 1.
7
As we will see shortly, expert 2 is called upon to make advice only when m1 = 1 and hence effectively
knows what message is sent by expert 1 anyway.

5

purposes, we say that the decision maker takes an action immediately when a1 6= W and that
she waits and asks for a second opinion when a1 = W . The game ends at the end of period
1 if the decision maker chooses to take an action immediately. If she chooses to wait, i.e.,
a1 = W , on the other hand, the game proceeds to the next period with an additional cost d.8
Preferences: Each player has his or her own preferred action and derives a private benefit
from implementing the preferred action. We assume that the decision maker prefers a = 0
while each expert prefers a = 1, so that their preferences are not perfectly aligned. The
payoff for the decision maker when she takes an action in period t, i.e., at 6= W , is given byud (θ, a, t) = I(θ = a) + bI(a = 0) − d(t − 1),
while that for each expert isue (θ, a) = I(θ = a) + bI(a = 1),
where b > 0 is the parameter which measures the salience of the private benefit. If thedecision maker takes no action at all (a1 = a2 = W ), the payoff is zero for all players.

3

Analysis

3.1

The decision maker’s problem

We first consider the decision maker’s problem in period 2. Let σt = Pr(θ = 1 | Ωt ) denotethe decision maker’s belief in period t, where Ωt denotes her information set available inperiod t. Given all the available information, the decision maker chooses a2 = W (taking noaction at all) if
max{1 − σ2 + b, σ2 } < 0.
It follows from this that it is never optimal for the decision maker to choose a2 = W .9
8

To focus on more meaningful cases, we assume throughout the analysis that it is always optimal for thedecision maker to solicit at least one opinion. Formally, we circumvent this issue by assuming that the costof soliciting the first opinion is zero. In general, the model can be applied to any circumstances where it isprohibitively costly for the decision maker to choose an action based solely on her own prior information. For
instance, the state of nature may be two-dimensional, consisting of θ and the other unmodeled state, andthe sender sends a message about both of these dimensions. There are sufficiently many states along thisunmodeled dimension and at least one of them yields a prohibitively low payoff to both players when thecorresponding action is mistakenly chosen, as assumed in Aghion and Tirole (1997). The first opinion is thenalways desirable to avoid this mistake when its cost is sufficiently large for both players.
9
We assume throughout the analysis that the decision maker chooses either at = 0 or at = 1 over at = W
if she is indifferent between the two. Similarly, she always chooses at = 0 (her preferred action) over at = 1
when she is indifferent.

6Given this, the decision maker in period 2 chooses a2 = 0 over a2 = 1 if
1 − σ2 + b ≥ σ2 ⇔ B :=1+b
≥ σ2 .
2

The expected payoff conditional on the posterior belief, denoted by x(σ2 ), is then given by(σ2
if σ2 > B,x(σ2 ) =1 − σ2 + b if B ≥ σ2 .
The decision maker’s problem in period 1 is more complicated because the problem is
now dynamic in nature. First, it is clear from the argument above that one can at least ruleout a1 = 1 if B ≥ σ1 and a1 = 0 if σ1 > B. For B ≥ σ1 , the receiver chooses a1 = 0 over
a1 = W if
1 − σ1 + b ≥ E(x(σ2 ) | σ1 ) − d.

(1)

For σ1 > B, the receiver chooses a1 = 1 over a1 = W if
σ1 ≥ E(x(σ2 ) | σ1 ) − d.

(2)

We seek for a PBE in which communication matters.10 Since the model admits a plethoraof equilibria, many of which are not particularly illuminating for the purpose of the current
analysis, we focus the following parameter space to restrict our attention to more relevantcases.
Assumption 1 r >

1
+ b.
2

The assumption assures that each expert’s information is accurate enough to be valuable tothe decision maker by itself. What this assumption means is as follows. Suppose that expert
1 observes θ̂1 = 1 and recommends m1 = 1. If the decision maker follows the advice, theexpected payoff is r. If she does not rely on the expert’s information and chooses a1 = 0, on
the other hand, the expected payoff is 1/2 + b. The assumption thus states that the decision
maker can be made better off with the expert’s advice, even in the worst case for her, than
without it. Note also that the assumption implies r > B.
Within this environment, we say that there exists a fully separating truth-telling equilibrium if all of the experts, who are called upon to make advice on the equilibrium path, adopt
the truth-telling strategy, i.e., mt = θ̂t . The following two forms are feasible candidates forour notion of truth-telling equilibrium:
10
As in prototype cheap-talk models, there always exists a babbling equilibrium in each stage where theexpert lies and the decision maker simply ignores the message. For any parameter values, therefore, there
exists an uninformative equilibrium where both experts always lie and the decision maker always chooses
a1 = 0 regardless of m1 . Here, we disregard this possibility and seek for equilibria where at least one of theexperts communicates truthfully with positive probability on the equilibrium path.

7• The decision maker always takes an action immediately, and expert 1 adopts the truthtelling strategy (regardless of expert 2’s strategy off the equilibrium path);• The decision maker asks for a second opinion with some positive probability, and bothof the experts adopt the truth-telling strategy.

3.2

Communication when the receiver is decisive

We first consider the case where the cost of waiting, captured by d, is relatively high andthe decision maker takes an action immediately after one period. This greatly simplifies theanalysis because expert 1 knows that he is the only one to make advise on the equilibrium
path. The problem is thus effectively reduced to a simple static one.
Under Assumption 1, the decision maker simply takes an action recommended by theexpert, provided that he adopts the truth-telling strategy. The expert truthfully reveals his
private information if
r ≥ 1 − r + b ⇔ r ≥ B,
which also holds by Assumption 1.
This means that under the maintained assumption that each expert’s information is sufficiently accurate, there is always a truth-telling equilibrium as long as the decision makertakes an action immediately after one period. The question then eventually comes down towhether the decision maker is able to do so in a credible manner. To this end, there are twocases we need to consider, depending on the first message m1 . Suppose first that the decision
maker deviates and asks for a second opinion when m1 = 0. In this case, even if expert 2
also communicates truthfully, the decision maker always chooses a2 = 0 regardless of m2 .
This means that the decision maker has no incentive to deviate because she cannot gain any
useful information in period 2.
The decision maker thus has an incentive to deviate only when m1 = 1: in this case,she may change her choice of action, depending on the information she obtains in period 2.
Now suppose that she deviates and asks for a second opinion. One can then show that the
incentive compatibility constraint for expert 2 cannot be satisfied; this fact is the driving
force of the model, and we will explore this point in greater detail in the next subsection(and also in the proof of Proposition 1). The decision maker can thus gain useful information
only if she can gain useful information on her own, which occurs with probability p. If thisinformation is not valuable enough, the decision maker takes an action immediately, thereby
making full separation feasible.

8Proposition 1 There exists a fully separating truth-telling equilibrium if d ≥ 2pr(1 − r)b.
In equilibrium, the decision maker adopts the one-and-done strategy, i.e., always takes anaction immediately after soliciting an opinion from expert 1.
Proof: See Appendix.

3.3

Communication when the receiver is indecisive

The decision maker is tempted to ask for a second opinion only when m1 = 1, i.e., the firstnews is not favorable to her. When d goes below the threshold provided in Proposition 1, she
may start asking for a second opinion upon receiving a bad news. The nature of the gamethen alters substantially, now that there are two experts to communicate with the decision
maker.
The first question to be asked is whether there could exist a fully separating equilibrium
when the decision maker asks for a second opinion. To see this, suppose that expert 2 adopts
the truth-telling strategy and investigate expert 1’s incentives. If expert 1 also communicatestruthfully when θ̂1 = 0, the decision maker takes an action immediately and the expected
payoff is r. If the expert deviates and claims m1 = 1, on the other hand, the decision maker
will ask for a second opinion. If m2 = 0 (which occurs with probability r 2 + (1 − r)2 , giventhat expert 2 communicates truthfully), the decision maker chooses a2 = 0 which is correctwith probability r 2 /[r 2 + (1 − r)2 ]; if m2 = 1 (which occurs with probability 2r(1 − r)), shechooses a2 = 1 which is correct with probability 1/2. Given this argument, the condition fortruth telling (for expert 1) is obtained asr ≥ r 2 + r(1 − r) + 2r(1 − r)b = r + 2r(1 − r)b,
which is clearly never satisfied as long as b > 0, no matter how small it is. This means that
there exists no truth-telling equilibrium when the decision maker cannot resist the temptation to ask for a second opinion, thereby illuminating a virtue of being decisive in strategic
environments.
Intuitively, the driving force of this result is the diversification of responsibility: when
there are multiple exerts to make advise, each expert’s opinion carries less weight in thedecision-making process.11 To see this, suppose that expert 1 observes θ̂1 = 0 but claims
m1 = 1. In this case, the decision maker chooses a2 = 1 if and only if m2 = 1. Given
that expert 2 adopts the truth-telling strategy, however, this means θ̂2 = 1, in which case11

The logic behind this result is discussed in greater detail in Ishida and Shimizu [13].

9the unbiased probability of θ = 1 is exactly one half.12 At this point, therefore, exert 1
has nothing to lose by recommending m1 = 1. In contrast, when θ̂2 = 0, expert 2 claims
m2 = 0 and the decision maker follows this advice by choosing a2 = 0. From the viewpointof expert 1, his advice is ignored when it is more likely to be wrong (when θ̂1 = θ̂2 = 0),
which substantially lowers the cost of lying. Although it is ex post optimal to overrule expert
1’s advise, this capability makes full separation less feasible.
It is certainly true that amassing more information generally leads to a better choice
when there are no incentive issues and truthful information can be solicited at no cost. Thisnatural conclusion does not necessarily hold true, however, when information is disclosed
strategically, i.e., there are indeed such things as “asking too many opinions” in strategic
environments. We summarize this observation as follows (the proof omitted).
Proposition 2 There exists no fully separating truth-telling equilibrium if 2pr(1 − r)b > d.
The proposition states that when the cost of waiting is relatively low, there is no way to
induce truthful information from both of the agents. The important point here is that thedecision maker can no longer obtain any useful information once she becomes (or is expected
to become) as informed about the current state of nature as each expert: in the current
setting, the decision maker can obtain useful information only from one expert because thatwill make her as informed. This logic thus applies to a more general T -period setting in which
the decision maker can solicit opinions from at most T > 2 experts. To see this, consider a
T -period version of the model where pt = 0 for t = 1, 2, ..., T − 1 and pT = p. In this extended
setup, the condition for truth telling cannot be satisfied for any expert t0 , t0 = 1, 2, ..., T − 1
if expert T adopts the truth-telling strategy while all the other experts lie.
It is worth noting here that in the static setting, Assumption 1 is sufficient to assure
the existence of fully separating equilibria. One interesting fact about this result is thatin the current dynamic setting, the existence of fully separating equilibria hinges on suchparameters as d (which measures how costly it is to wait) and p (which measures how strategic
the underlying environment is), which would normally have no impact on the feasibility oftruthful communication. The proposition shows that full separation cannot be attained inequilibrium if the cost of soliciting a second opinion is too small (d is too small), or if thelikelihood of obtaining useful information on her own is too large (p is too large). This resultoffers several interesting implications which we discuss later in section 4.
12
This is the case because we assume the symmetric information structure where the two states are equally
likely ex ante and the two signals are equally informative. This assumption is obviously made to simplify theargument and make our point more emphatically, as our logic holds even when we allow for some degree ofasymmetries in the information structure.

10Given this impossibility result, we now seek for equilibria where the decision maker gains
some useful information when she is not decisive enough. To this end, it is useful to note that
there is no equilibrium where no expert (with dissonant preferences) communicates truthfully
under Assumption 1 either, because if one expert lies, there is always an incentive for theother to communicate truthfully.13 This eventually leaves us with two possibilities, which welabel as PIE-1 and PIE-2 for clarity (PIE for “partially informative equilibrium”), when thedecision maker asks for a second opinion.
PIE-1: Expert 1 always communicates truthfully while expert 2 always claims m2 = 1 when
he is called upon to make advice.14 The decision maker asks for a second opinion when
m1 = 1.
PIE-2: Expert 2 always communicates truthfully when he is called to make advice while
expert 1 always claims m1 = 1. The decision maker always asks for a second opinion.
Proposition 3 (i) PIE-1 exists if (1 − p)(r − B) ≥ pr(1 − r)b and 2pr(1 − r)b > d. (ii) PIE-2
exists if r − B > d.
Proof: See Appendix.
Some remarks are in order. First, among the two possibilities, PIE-2 is far more likely
than PIE-1. To see this, note that r − B > d implies 2pr(1 − r)b > d, so that whenever the
fully separating equilibrium fails to exist, there always exists PIE-2. This also indicates that
there exists a range D := [2pr(1− r), r − B) such that multiple equilibria exist for d ∈ D. The
intuition for the emergence of multiple equilibria is as follows. On one hand, as we have seen,
the incentive to communicate truthfully diminishes when the decision maker is more likely
to obtain a second opinion. On the other hand, the incentive to ask for a second opinion
is stronger when expert 1’s information is less reliable than what she can expect to gain inperiod 2. This relationship thus suggests a possibility that the decision maker’s (possibly
irrelevant) personal characteristics or reputations may make a difference: when d ∈ D, thedecision maker may not be able to achieve full separation when the expert believes that she
is not decisive enough to take an action immediately, which in turn makes her indeed lessdecisive in a self-fulfilling way. We will explore more on this point later in section 4.
To summarize, Figure 1 illustrates the region under which each type of equilibrium exists.
Note that we restrict attention to the case where the bias b is small relative to the accuracy
13

See the proof of Proposition 3 for more details.
Of course, in this equilibrium, there is no point in communicating with expert 2 once the decision makerhas failed to observe any signal on her own, so she may not ask for advice anyway.
14

11

of information r, so that communication is supposed to be easy. Even under this restriction,
one can see that partially informative equilibria exist for a fairly wide range of the parameter
space.
[figure 1]

3.4

The virtue of decisivenessWe have thus far seen three different types of equilibrium: fully separating, PIE-1, and PIE2. In partially informative equilibria such as PIE-1 and PIE-2, there is always some typeof expert who would not communicate truthfully, and the decision maker hence needs moretime to solicit useful information. This possibility can be eliminated altogether, however, if
the decision maker can somehow commit to the one-and-done strategy under which expert
1, the only expert to make advise, always has an incentive to communicate truthfully. Here,
we suppose that such a commitment is indeed feasible, e.g., by intentionally raising the costof waiting d, and explore when it is desirable for the decision maker to give up the discretion
to ask for a second opinion by committing to the one-and-done strategy.
Proposition 4 The commitment to the one-and-done strategy weakly increases the decision
maker’s expected payoff if one of the following conditions is satisfied: (i) d ≥ 2pr(1 − r)b or(ii) 2pr(1 − r)b ≥ d and pr(1 − r)b > (1 − p)(r − B) .
Proof: See Appendix.
The proposition shows that the commitment to the one-and-done strategy is indeed beneficial for the decision maker under a wide range of circumstances.15 What is particularly
intriguing is the fact that the commitment is always desirable when d ∈ D and both the fully
separating equilibrium and PIE-2 exist. When there exist multiple equilibria, the actual outcome may depend on intrinsically irrelevant factors such as the decision maker’s reputation
as a decisive leader or her trustfulness. For instance, when the decision maker is perceived
as indecisive for some reason, the expert is less willing to communicate truthfully, which inturn justifies the decision maker’s decision to ask for a second opinion. On the other hand,when the decision maker does not trust her expert’s ulterior motive, she is effectively forced
to ask for a second opinion, which in turn makes the expert less willing to communicate
15Note that the value of the commitment is evaluated only from the viewpoint of the decision maker, where
the cost of waiting is given by d. A delay to take an action can be costly for the organization in many
regards, however, which include the costs that are not necessarily internalized by the decision maker. One canthus argue that when a delay yields an additional external cost to the organization, the commitment to the
one-and-done strategy is even more valuable from the viewpoint of the organization as a whole.

12truthfully. In either case, as the proposition implies, the organization is trapped in the lessefficient equilibrium, i.e., PIE-2, where the experts withhold useful information until the end.
The commitment to the one-and-done strategy, if it is feasible at all, is quite effective inputting an end to this vicious circle, by keeping expert 1’s incentives straight and making theunderlying environment less strategic.

4

Discussion

4.1

Interpretations

The analysis presented above suggests that full separation is feasible only when the decision
maker adopts the one-and-done strategy. We say, mostly for expositional clarity, that thedecision maker is decisive when she can do so in a credible manner. It is up to interpretation,
though, what actually makes a decision maker “decisive” in the current context, as being decisive in this model merely refers to a superficial behavioral characteristic which endogenously
arises in the model. Here, we offer several interpretations of our main result by relating thisbehavioral characteristic to the primitives of the model.
Biased preferences hurt: As can be seen from Proposition 1, an increase in b makes
truthful communication less likely. This means that the presence of the preference bias limits
the decision maker’s ability to extract information from experts. Of course, the presence ofthe preference bias is almost always an obstacle to efficient information transmission: in a
canonical model of cheap talk a la Crawford and Sobel [5], only the babbling equilibrium
survives when the preference bias exceeds some threshold.16 In this context, however, thepresence of the preference bias impedes efficient communication in a little different way. Here,a biased decision maker cannot extract truthful information from experts because they knowthat the decision maker is not open to the unfavorable opinion: whenever the decision makerreceives a bad news, she goes on to ask for a second opinion, rather than to take an action
recommended by the expert. The lack of commitment to abide by the first opinion, however,diminishes the first expert’s to incentive to report truthfully because his opinion weighs less inthe decision-making process when the decision maker solicits multiple opinions. This result
hence suggests that an effective leader is the one who is fair and open-minded enough toaccept any opinions even when they are in direct conflict with her own personal interests.
Friendly environments may hurt: The driving force of the model is the fact that themore informed the decision maker is, the less information she can extract from each expert
16

Similarly, in the current model, communication becomes totally meaningless when the bias is sufficiently
large, because the decision maker simply chooses her preferred action regardless of the messages.

13via communication. The decision maker is less tempted to ask for a second opinion when
it is less likely to obtain any useful information by waiting. This could actually benefit her
because that works as a commitment device. In contrast, when the decision maker is more
likely to come across useful information by chance, through the exogenous (partial) resolutionof uncertainty, the temptation might be just too large and simply irresistable. One can thus
argue that the decision maker’s decisiveness is not only determined by her own personal
characteristics, but also by the underlying environment in which the decision is to be made.
Too many experts around?: Another environmental factor which could make a differenceis the cost of waiting, which is captured by d in this setup. It is obvious that the decision
maker is tempted to ask for a second opinion when d is close to zero and the cost of waiting
is relatively low. An obvious and straightforward interpretation of this fact is that thedecision maker tends to be indecisive when she is relatively patient, which lowers the relativevalue of taking an action today. Alternatively, the cost of waiting also depends on how
frequently the decision maker can an expert to solicit opinions from. According to this latterinterpretation, it is not necessarily better to have access to multiple information sources, as
it may only impede efficient communication. As we will discuss next, this fact yields somecritical implication when the distribution of information is to some extent under the decision
maker’s control.
Career concerns help: Suppose that the decision maker has a career concern and has anincentive to establish her reputations. Suppose also that outside parties can observe at whattiming the decision maker has made the decision. In this case, there arises an additional
benefit of taking an action in period 1, as it signals that she is more likely to be decisive. Let
this benefit be v. The total payoff for the decision maker is thenud (θ, a, t) = I(θ = a) + bI(a = 1) + v(2 − t) − d(t − 1).
Using this modified specification, the condition for full separation is given by
d + v ≥ 2pr(1 − r)b.
It is then clear from this that an increase in v makes full separation more likely. To see the full
impact of career concerns, we obviously need to see how v is determined in equilibrium. Asidefrom this, however, the presence of career concerns gives the decision maker an additional
reason to take an action immediately, which works as a credible commitment to induce
truthful information.

14

4.2

Implications

The main reason why communication cannot be made fully informative in the current setup
is the lack of commitment, on the part of the decision maker, not to ask for a second opinion.
In other words, the efficiency of communication can be restored if the decision maker can
put herself in an environment where it is simply not feasible or optimal to ask for a second
opinion. Here, we briefly discuss ways in which to raise the cost of obtaining a second opinion
in organizations so that the decision maker can credibly be decisive.
One way to do so is to set a deadline for the project, which might make it harder to findanother expert to solicit an opinion from in time. To put this possibility into the current
context, the difficulty for the decision maker arises precisely because she faces a dynamic
problem which gives her an opportunity to solicit two opinions. Now suppose that thedecision maker sets a deadline for the project and makes it a one-period static problem ina credible way. If this is feasible at all, as we have seen, there exists a fully separating
equilibrium under Assumption 1, irrespective of such parameters as d and p: full information
can be extracted no matter how indecisive the decision maker may be.
The analysis also suggests that communication becomes increasingly difficult in strategic
environments when information is dispersed sparsely among different sources. This meansthat if the decision maker can reasonably control the distribution of information, it might be
optimal to limit the number of information sources, e.g., by delegating or specializing information acquisition to a single party. The tradeoff is clear: on one hand, when each expert isendowed only with imperfect information, there is a benefit of aggregating information fromdifferent sources to make a better forecast; on the other hand, as we have shown, the existenceof multiple information sources can be an impediment to efficient communication in strategic
environments. When the cost outweighs the benefit, it is optimal to delegate informationacquisition to a single source and rely on it exclusively; when the benefit outweighs the cost,
it is optimal to diversify information sources and aggregate them via communication. The
deciding factor is the strategic nature of communication, namely how severe the conflict of interests is between the decision maker and each expert, which provides an implication for how
responsibility regarding information acquisition should be allocated in organizations. Whenthe conflict of interests is fairly severe and communication is highly strategic in nature, moreemphasis should be placed on facilitating communication, meaning that information acquisition should be more specialized.17 When there is no conflict of interests and communication
is nonstrategic, information sources should be more diversified to complement each other.
17

This logic illuminates yet another virtue of initiative, in a way different from Aghion and Tirole [1] andZabojinik [18].

155Extension: a model of private consultation

We have thus far assumed that each expert knows whether he is the first or second one to
make advice. In some cases, however, it is also plausible to assume that each expert does notknow how many opinions the decision maker has solicited in the past. This is more likely
to be the case when communication between the decision maker and each expert is done inprivate, which might be labeled as the case of private consultation. In this section, we briefly
consider this case to show that our insight generally applies, perhaps in a manner even moreemphatic.
To this end, we make two modifications to the basic setup. First and foremost, we assume
that each expert does not know whether he is the first or second one to make advice.18 Second,
while we assume that the decision maker may obtain information on her own in the model of
public consultation, this possibility is not necessary in the model of private consultation.19
We hence assume p = 0, i.e., the decision maker must always rely on the experts to makethe model symmetric between the two periods. We then seek for conditions under which
there exist fully separating truth-telling equilibria in which every expert who is called upon
to make advice chooses mt = θ̂t .
Again, since the condition for truth telling is naturally more stringent when θ̂t = 0, we
focus on that case. First, as above, if the decision maker adopts the one-and-done strategy,
the problem is exactly identical to that in the model of public consultation: the fact that t
is not observable to each expert has no bite since this is virtually a static problem with only
one expert, and the expert who is called upon to make advice knows that he must be the firstone. If the decision maker asks for a second opinion when m1 = 1, on the other hand, truth
telling cannot be induced on the equilibrium path. To see this, consider an expert who iscalled upon to make advice. Let q denote the expert’s belief that he is the first one to makeadvice. There are two cases we need to examine.
t = 1: If m1 = 0, then a1 = 0 which yields the expected payoff of r. If m1 = 1, the decision
maker asks for a second opinion. The expected payoff is r + 2r(1 − r)b.
t = 2: The fact that the decision maker asks for a second opinion means that m1 = θ̂1 = 1.
If m2 = 0, then a2 = 0 and the expected payoff is 1/2; if m2 = 1, then the expected payoff is
1/2 + b.
18

This also necessarily means that each expert cannot observe the message sent by the other expert.
This possibility is critical in the model of public consultation, because the decision maker can always gain
useful information with positive probability.
19

16

It follows from this that each expert has an incentive to communicate truthfully only if
qr +

1−q
(1 − q)(1 + 2b)≥ q[r + 2r(1 − r)b] +,22which is clearly never satisfied for any belief q < 1 as long as b > 0, no matter how small it
is.
This means that full separation is not feasible if the decision maker cannot resist thetemptation to ask for a second opinion, given that each expert adopts the truth-telling strategy. Under Assumption 1, it is optimal to choose a1 = 1, if not a1 = W , when m1 = 1.
The expected payoff in this case is then r. If the decision maker chooses to ask for a second
opinion, on the other hand, the expected payoff is r + 2r(1 − r)b − d. It is optimal for thedecision maker to adopt the one-and-done strategy ifd ≥ 2r(1 − r)b.

(3)

In other words, there exists no fully separating equilibrium when (3) fails to hold. We
summarize this finding below (the proof omitted).
Proposition 5 In the case of private consultation, there exists no fully separating truthtelling equilibrium if 2r(1 − r)b > d.

6

Conclusion

This paper provides a simple model of strategic communication where the decision makersolicits opinions sequentially from imperfectly informed experts. The entire argument hinges
on the observation that communication cannot be made fully informative when there are
too many information sources, which holds in a wide variety of circumstances which involve
strategic information transmission. Building on this logic, we show that the decision maker
can induce truthful information from the expert only when she can resist the temptation to
ask for a second opinion and get right to the task. This result illuminates a virtue of being
decisive in strategic environments, especially why it is often better to do the wrong thingrather than to do nothing.

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18

Appendix
Proof of Proposition 1: Let σ1 (m1 , m2 ) := Pr(θ = 1 | m1 , m2 ) denote the decision maker’s
posterior belief when she solicits advice from both of the experts. We first show that there
is no fully separating equilibrium in period 2, given that expert 1 adopts the truth-telling
strategy. Suppose, on the contrary, that expert 2 also adopts the truth-telling strategy. The
posterior beliefs are then given by1
r2
σ2 (1, 0) = , σ2 (1, 1) = 2.
2
r + (1 − r)2Expert 2’s message is pivotal because σ2 (1, 1) > B > σ2 (1, 0). If the expert communicatestruthfully when θ̂ = 0, the expected payoff is 1/2; if he lies, it is 1/2 + b. This means that the
incentive compatibility constraint cannot be satisfied for any b, no matter how small it is.
Given that expert 2 does not communicate truthfully, the decision maker can obtain useful
information only with probability p: in this case, she observes θ̂2 = 1 and chooses a2 = 1 withprobability r while she observes θ̂2 = 0 and chooses a2 = 0 with the remaining probability.
The decision maker then takes an action immediately when m1 = 1 ifr ≥ p[r 2 + r(1 − r)(1 + 2b)] + (1 − p)r − d,which is reduced to d ≥ 2pr(1 − r)b.
Proof of Proposition 3: We know that a1 = 0 when m1 = 0 and a2 = 0 if m1 = 1 andm2 = 0. Define `t as the probability that expert t sends mt = 1 when θ̂t = 0 and he is called
upon to make advice (for the case of expert 2).20 Given the experts’ strategies, one can showthat
σ2 (0, 0) =r(1 − r) + (1 − r)2 `2(1 − r)2
,
σ
(0,
1)
=
,
2
r 2 + (1 − r)2
2r(1 − r) + [r 2 + (1 − r)2 ]`2

σ2 (1, 0) =s(`1 )(1 − r),s(`1 )(1 − r) + [1 − s(`1 )]rs(`1 )[r + (1 − r)`2 ]s(`1 )[r + (1 − r)`2 ] + [1 − s(`1 )][1 − r(1 − `2 )][r + (1 − r)`1 ][r + (1 − r)`2 ].
=[r + (1 − r)`1 ][r + (1 − r)`2 ] + [1 − r(1 − `1 )][1 − r(1 − `2 )]σ2 (1, 1) = S(`1 , `2 ) :=20

As noted earlier, there exists an uninformative (babbling) equilibrium where both experts lie and thedecision maker chooses a1 = 0. Here, we do not consider this possibility and focus on the case where thedecision maker asks for a second opinion when m1 = 1.

19

wheres(`1 ) :=r + (1 − r)`1,
1 + `1

We have already seen that if one expert communicates truthfully, the incentive compatibility condition can never be satisfied for the other expert. This means that there are threepossible pure-strategy equilibria within the class of equilibria where the decision maker asks
for a second opinion when m1 = 1: (a) only expert 1 communicates truthfully; (b) only
expert 2 communicates truthfully; and (c) neither communicates truthfully. Given m1 = 1,
the decision maker asks for a second opinion if
max{s(`1 ), 1 − s(`1 ) + b} < p r + {s(`1 )(1 − r) + r[1 − s(`1 )]}b
+ (1 − p) s(`1 )[r + (1 − r)`2 ] + [1 − s(`1 )](1 − `2 )r+ (1 − `2 ){s(`1 )(1 − r) + r[1 − s(`1 )]}b − d.

(4)Only expert 1 communicates truthfully: The incentive compatibility condition for expert 2 can never be satisfied in this case. Given this and the decision maker asks for a second
opinion when m1 = 1, `1 = 0 ifr ≥ p[r + 2r(1 − r)b] + (1 − p)(1 − r + b),
which can be written as(1 − p)(2r − 1 − b) ≥ 2pr(1 − r)b ⇔ (1 − p)(r − B) ≥ pr(1 − r)b.
It also follows from (4) that the decision maker asks for a second opinion when m1 = 1 iff
2pr(1 − r)b > d.
Only expert 2 communicates truthfully: The incentive compatibility condition for expert 1 can never be satisfied in this case. Given this, `2 = 0 if
1−s(1)(1 − r)s(1)(1 − r)≥+ b,s(1)(1 − r) + r[1 − s(1)]s(1)(1 − r) + r[1 − s(1)]which can be written asr[1 − s(1)]= r ≥ B.
s(1)(1 − r) + r[1 − s(1)]It also follows from (4) that the decision maker asks for a second opinion when m1 = 1 if
r − B > d.

20

(5)

Neither communicates truthfully: It is easy to see that this type of equilibrium is not
feasible under Assumption 1. To see this, note that if `1 = 1, expert 2 also lies if (5) fails to
hold. This possibility is, however, ruled out by Assumption 1.
Proof of Proposition 4: Let πk denote the expected payoff for the decision maker in PIEk; also, let πF S denote the expected payoff when she commits to the one-and-done strategy.
One can then easily computeπ1 =b 2pr(1 − r)b − dr + b r + 2pr(1 − r)b − d
+
=r+ +
,
2
2
2
2
π2 = r +

b
− d,
2

b
πF S = r + .
2
It is immediate to see that πF S > π2 for any d > 0, meaning that PIE-2 always yields a lower
payoff to the decision maker than the fully separating equilibrium. Note also that πF S ≥ π1
ifd ≥ 2pr(1 − r)b.
This suggests that PIE-1 yields the highest payoff in the range where it exists. For theremaining part, the fully separating equilibrium is the most desirable for the decision makerand hence the commitment strictly raises the decision maker’s expected payoff. The two
conditions, (i) and (ii), show the range where PIE-1 fails to exist.

21

p
PIE-2

PIE-1 &PIE-2
FS & PIE-2

FSd
Figure 1: Equilibria when b is small

Note: FS indicates the region in which the fully separating equilibrium exists

22