SEQUENTIAL EXPERT ADVICE: SUPERIORITY OF CLOSED‐DOOR MEETINGS

• Author: Tridib Sharma,Parimal K. Bag
• Published date: 01 November 2019
• DOI: http://doi.org/10.1111/iere.12407
• Date: 01 November 2019

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 4, November 2019 DOI: 10.1111/iere.12407

SEQUENTIAL EXPERT ADVICE: SUPERIORITY OF CLOSED-DOOR MEETINGS∗

BYPARIMAL K. BAG AND TRIDIB SHARMA1

National University of Singapore, Singapore; Instituto Tecnol´

ogico Aut´

onomo de M´

exico,

Mexico

Two career-concerned experts sequentially give advice to a Bayesian decision maker (D). We find that secrecy

dominates transparency, yielding superior decisions for D.Secrecy empowers the expert moving late to be pivotal

more often. Further, (i) only secrecy enables the second expert to partially communicate her information and

its high precision to Dand swing the decision away from first expert’s recommendation; (ii) if experts have

high average precision, then the second expert is effective only under secrecy. These results are obtained when

experts only recommend decisions. If they also report the quality of advice, fully revealing equilibrium may exist.

1. INTRODUCTION

Many decisions are based on advice given sequentially by multiple experts. Parliamentarians

debate over issues of national importance—whether to go to war, what health reforms to

implement, whether to tighten immigration policy, agree to a trade treaty, or whether to put

to referendum the decision about breaking away from a club such as the European Union.

Similarly, in modern corporations, CEOs may consult their deputies for opinions on crucial

decisions such as business expansion, joint venture, r&d, etc.

In many cases, the advice provided may not be able to adequately transmit all the relevant

information. For instance, members of a committee may convey information through voting

(see footnote 4, below). Although votes reflect opinions, they do not convey the quality of

information on which the opinions are based. Relevant information may also not be transmitted

due to psychological or behavioral reasons. For example, self-certification of the quality of

recommendations may not always be realistic: An expert can hardly be expected to declare

even privately that her advice is not of great reliability. Our primary focus in this article will

be on a scenario where two experts sequentially provide cheap talk advice in two stages. The

advice is constrained by the messages available.2

We then go on and relax this constraint and focus on two alternative procedures of advice—

detailed recommendation and deliberation. Detailed recommendation captures the case where

experts are allowed to express their views in full—the advice as well as any qualification to

∗Manuscript received August 2017; revised February 2019.

1We thank Masaki Aoyagi and three anonymous referees for detailed comments and suggestions on earlier drafts.

Also, for criticisms, related observations, and help at various stages of this work, we thank Murali Agastya, Sourav Bhat-

tacharya, Martin Bodenstein, Lawrence Christiano, Sudipto Dasgupta, Alessandro Lizzeri, Andy McLennan, Nicolas

Melissas, Neng Qian, Arijit Sen, Teck Yong Tan, Levent Ulku, Ko Chiu Yu, and seminar/conference participants at

University of Queensland, University of Durham, Singapore Management University, Indian Institute of Management

(Calcutta and Bangalore), Delhi School of Economics, ISI-Delhi Growth and Development Conference, Canadian

Economic Theory Conference, and the Royal Economic Society Conference at Bristol. A supporting research grant

from the Singapore Ministry of Education is gratefully acknowledged. For errors or omissions, we remain responsible.

Please address correspondence to: Parimal Bag, Department of Economics, National University of Singapore, Faculty

of Arts and Social Sciences - AS2 level 6, 1 Arts Link, Singapore, 117570. E-mail: ecsbpk@nus.edu.sg.

2Caillaud and Tirole (2007) propose that processing information may be costly for the decision maker. High pro-

cessing cost naturally calls for constraining the messages.

1877

C

(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1878 BAG AND SHARMA

it.3Under deliberation, experts have the option of revising their recommendations in light of

the opinion of others. Deliberations are sequential in nature with commentators giving their

views, endorsing or countering prevailing opinions. Such a procedure may allow experts to

transfer all their information. In monetary policy committees, select members debate over the

inflation target or interest rate.4The heads of state, such as the Prime Minister, or the leader

of a major political party may rely on their trusted advisors, who give their conflicting views

about the suitability of important decisions in closed-door meetings in a more discussion and

deliberative style. A judge may conduct cases in camera (or in chambers), that is, hear evidence

and arguments in private as opposed to open court trial.5

We ask whether a decision maker, in order to select a decision corresponding with an un-

known state, should make the experts’ recommendations public by disclosing who made what

recommendations when (transparency) or maintain secrecy by informing the public of only the

summary decision. The true state will eventually become known. One principal assumption will

be that the experts have “career concerns,” an idea in organizational economics introduced by

Holmstrom (1999): They care mainly about the perception of outsider(s), that is, the public,

about their ability in predicting the true state. In the examples of parliamentary and political

debates as well as advice by corporate managers, there is no explicit payment involved per each

advice. Instead, giving opinions are seen as part of the job.6

When the decision maker has the final authority to make a yes/no decision, he may base

his decision not just on the number of each type of recommendation (or votes) but also on

the order of recommendations. This is so especially when the experts can see and, hence,

learn from each other’s recommendation. In choosing to take the same decision following the

same recommendations but in different orders, the decision maker may be wasting valuable

information. In this regard, sequentiality of advice introduces a new dynamic not prevalent in

simultaneous decision making with an exogenous rule, for example, in one-shot voting.

In the two-stage sequential advice game with constrained messages, one of our main results is

that a Bayesian decision maker would prefer secrecy over transparency (Proposition 4). Interac-

tions among three principal forces shape the experts’ information revelation incentives: a prior

3Secrecy of advice or any of its limitations are guaranteed, for instance, at top-level intelligence services for a

country’s national security. It is also plausible to consider communication of key information (say, the hiding place of

Osama Bin Laden or the planned attack by terrorists or whether there has been any give-and-take by the countries’

top officials/politicians in influencing election, etc.) to be a cheap talk, because the original source might not want to

leave any trail of having supplied the expert the confidential information.

4In the Bank of England’s monetary policy committee consisting of nine members, policy decisions on a number

of issues (e.g., the setting of rate of interest) are made by a simple majority rule instead of a sophisticated voting

rule that is sensitive to the degree of emphasis of the voters’ declared votes reflecting all relevant information. See

https://www.bankofengland.co.uk/faq#anchor_1516787784054; specifically, “The MPC’s final meeting—its second pol-

icy meeting—is normally held on the Wednesday. Following further discussion on the appropriate stance for monetary

policy, the Governor puts to the meeting the policy that he believes will command a majority and members of the

MPC vote. Any member in a minority is asked to say what level of interest rates they would have preferred. If there

is an even split between the MPC members present, the Governor has the casting vote. The interest rate decision is

published alongside the minutes of the MPC’s meetings at 12 noon on the Thursday.” The Governor can be put in the

position of our decision maker.

5See Jan. 4, 2010, report, “Democratic Leaders Plan Secret Health Reform Deliberations”; source: http://www.

usnews.com/opinion/blogs/peter-roff/2010/01/04/democratic-leaders-plan-secret-health-reform-deliberations. A rece-

ntly edited book titled Secrecy and Publicity in Votes and Debates (2015; edited by Jon Elster) discusses a range of

issues involving secret versus open debates in politics. In Chapter 12 (“Secret Votes and Secret Talk”), one of the

authors, John Ferejohn, discusses publicness of votes (leading to decisive public choices) by elected representatives but

also talks about background political deliberations that “are either completely or partly veiled from outside scrutiny.”

See also some of the other chapters, especially, “Secret-Public Voting in FDA Advisory Committees” by P. Urfalino

and P. Costa.

6Politicians (Congressmen in the United States of America) appeal to a higher level audience—heads of important

committees in the House or the Senate, electorate who may win him or her a Senate seat in future election, etc. “Skills”

and “achievements” (e.g., “sponsoring major pieces of legislation, delivering famous speeches, casting decisive votes

on important issues,” etc.) are reckoned to be important considerations in influencing a politician’s career prospects

(see Diermeier et al., 2005).

SEQUENTIAL EXPERT ADVICE 1879

bias, a lead opinion bias, and conformity bias. The first and second biases are exogenous and im-

pact on the experts’ beliefs about the likely state. We shall focus on the case where the common

prior strictly favors one of two possible states, that is, there is a prior bias.Thelead opinion bias

suggests how seriously the second expert should view the first expert’s recommendation when

her own signal indicates otherwise. As the experts’ average precision levels improve, so does

the lead opinion bias. The third bias, if and when it exists (and it can arise only endogenously),

is induced by the beliefs of the outsider. Typically, when an expert’s recommendation (actual or

perceived) does not match the realized state, the outsider updates his beliefs toward the expert

having low predictive skills. If such downward revision were to be greater when the alternative

to status quo is found to have been wrongly predicted, one would expect experts to sometimes

recommend in favor of the status quo even if they expect it to occur with probability less than

one-half. This we call the conformity bias. It inclines the experts toward recommending the

decision favored by the prior.

With transparency, at times the second expert is able to overturn a recommendation made

against the favored state. But under secrecy, the second expert may also be able to overturn a

recommendation made in support of the favored state. For small prior biases, the lead opinion

bias comes into play. Under transparency, when the lead opinion bias is large the second expert

herds and thus becomes redundant (Proposition 1). Under secrecy, however, an endogenous

conformity bias acts against the lead opinion bias, making the second expert’s recommenda-

tion relevant over a larger range of parameters (Proposition 3 and inequality (18)). When the

conformity bias is absent, under secrecy the second expert may be able to sometimes communi-

cate, through partial herding, all relevant information—her signal about the state as well as its

quality when the quality is high (Proposition 2). In fact, this mixed equilibrium (type revelation

combined with herding) also yields the highest payoff for the decision maker among all the

equilibria identified under secrecy (Proposition 5). Surprisingly, all these gains from secrecy

accrue despite the constraints of a limited message set.

The merit of secret advice is enhanced when the restriction on message sets is removed.

Under detailed advice where experts make their recommendations as well as qualify their

reliability (i.e., of high or low quality), sometimes the experts are able to reveal all their private

information leading to efficient decisions (Proposition 6).7This, however, is not always true.

At times, even with expanded messages full revelation of information may break down; see the

discussion on noncongruence of incentives under secrecy in Section 7.

1.1. Related literature. Our article follows the sequential cheap-talk advice literature started

by Scharfstein and Stein (1990) and studied extensively by Ottaviani and Sorensen (2001, 2006a,

2006b, 2006c). These papers focused on how financial experts, who care about their reputation

in predicting assets’ returns or an unknown state, tend to herd in their recommendations or

conform to some prior expectation of the unknown state. Although these papers address an

important class of problems, what has not been considered before is whether the transparency

of advice is indeed an ideal protocol for good decision making. Studying within the same

sequential advice framework, we argue that conducting the sequential advice in closed-door

meetings, which is very plausible in many political and organizational decision contexts, yields

clearly superior decisions.

Also related are the papers of Levy (2007a, 2007b), and Visser and Swank (2007), who have

studied information transmission by experts but in the context of voting. There are important

differences between these two papers and our model: First of all, sequencing of expert advice

in our analysis, as opposed to simultaneous voting, allows the second expert to learn from the

first expert’s action. Second, our decision maker does not commit to a decision rule and instead

updates his prior and optimally selects a decision.

7A similar result obtains when experts engage in back-and-forth deliberations, possibly changing their advice in light

of the other expert’s earlier advice.