Eliciting Information From Multiple Experts

A decision maker has to elicit information from informed experts regarding the desirability of a certain action from experts who share similar preferences which differ significantly from those of the decision maker. The question is how much information the decision maker can elicit, despite the difference in interests. The focus here is on ways in which the decision maker can take advantage of the multiplicity of experts. if the decision maker cannot commit to a mechanism and there is no communication among the experts, then no useful information is elicited from the experts in the equilibrium. If the experts can be partitioned into groups such that the members of each group can communicate with each other before they report their information to the decision maker, then more information can be elicited. Obviously, if all experts are allowed to communicate, they can be induced to reveal the relevant information, at least, when their aggregate information makes it desirable for them to undertake the project. The more interesting observation is that, if communication among the experts can be restricted to certain subsets, then even more information can be elicited. Finally, if the decision maker can commit to a mechanism, the information elicited in some cases is sufficient to implement the decision maker's best outcome in all but one state. All these observation make straightforward use of the idea that experts choose their report with the understanding that it matters only when they are pivotal.

Eliciting Socially Optimal Rankings from Unfair Jurors

A jury must provide a ranking of contestants (students applying for scholarships or Ph. D. programs, gymnasts in a competition, etc.). There exists a true ranking which is common knowledge among the jurors, but it is not verifiable. The socially optimal rule is that the contestants be ranked according to the true ranking. The jurors are not impartial and, for example, may have friends (contestants that they would like to benefit) and enemies (contestants that they would like to prejudice). We study necessary and sufficient conditions on the jury under which the socially optimal rule is Nash implementable. We also propose a simple mechanism that Nash implements the socially optimal rule under these conditions.Ranking of contestants; Implementation Theory; Nash Equilibrium

Consulting an Expert with Potentially Conflicting Preferences.

In this paper, two modes of non-binding communication between an expert and a decision- maker are compared. They are distinguished mainly by the nature of the information transmitted by the expert. In the first one, the expert reports only his opinion (soft information) concerning the desirability of a certain action, whereas in the second one, he is consulted to provide evidence (hard information) to convince the decision-maker. The expert's ability to provide evidence increases with the precision of his information. The paper shows that requiring evidence is always beneficial to the decision-maker whereas it is bene�cial to the expert if and only if the preferences of both agents are different enough.

Voting in Small Committees

We analyze the voting behavior of a small committee that has to approve or reject a proposal whose return is uncertain. Members have heterogenous preferences: some members want to maximize the expected value while other members have a bias toward project approval and ignore their private information. We analyze different voting games when information is costless and communication is not possible, and we provide insights on the optimal composition of these committees. Our main result is that the presence of biased members can improve the voting outcome by simplifying the strategies of unbiased members. Thus, committees with heterogeneous members can function at least as well as homogeneous committees and in some cases they perform better. In particular, when value-maximizing members hold 51% of votes, the socially optimal equilibrium becomes unique.Voting, Small committees.

Contracts for Experts with Opposing Interests

We study the problem of optimal contract design in an environment with an uninformed decision maker and two perfectly informed experts. We characterize optimal contracts and observe that consulting two experts rather than one is always beneficial; this is so even if the bias of a second expert is arbitrary large and this expert would have no value in a cheap talk environment. We also provide conditions under which these contracts implement the first best outcome; our sufficient condition is weaker than the conditions in the literature on the environments without commitment. In order to derive optimal contracts, we prove a Òconstant-threatÓ result that states that one can restrict attention to contracts in which the action implemented in case of a disagreement among the experts is independent of their reports. A particular implication of this result is that an optimal contract is constant for a large set of expertsÕ preferences and hence is robust to mistakes in their specification.information; optimal contracts; experts; constant-threat principle

Voting in Small Committees

A small committee has to approve/reject a project with uncertain return. Members have different preferences: some are value-maximizers, others are biased towards approval. We focus on the efficient use of scarce information when communication is not guaranteed, and we provide insights on the optimal committee composition. We show that the presence of biased members can improve the voting outcome by simplifying the strategies of unbiased members. Thus, heterogeneous committees perform at least as well as homogeneous committees. In particular, when value-maximizers outnumber biased members by one vote, the optimal equilibrium becomes unique. Finally, allowing members to communicate brings no improvement.voting, small committees, committees composition, communication in committees

Learning from Experts

The survey is concerned with the issue of information transmission from experts to non-experts. Two main approaches to the use of experts can be traced. According to the game-theoretic approach expertise is a case of asymmetric information between the expert, who is the better informed agent, and the non-expert, who is either a decision-maker or an evaluator of the expert’s performance. According to the Bayesian decision-theoretic approach the expert is the agent who announces his probabilistic opinion, and the non-expert has to incorporate that opinion into his beliefs in a consistent way, despite his poor understanding of the expert’s substantive knowledge. The two approaches ground the relationships between experts and non-experts on such different premises that their results are very poorly connected.Expert, Information Transmission, Learning

Decision Rules for Experts with Opposing Interests

This paper studies optimal decision rules for a decision maker who can consult two experts in an environment without monetary payments. This extends the previous work by Holmstr�m (1984) and Alonso and Matouschek (2008) who consider environments with one expert. In order to derive optimal decision rules, we prove a "constant-threat" result that states that any out-of-equilibrium pair of recommendations by the experts are punished with an action that is independent of their reports. A particular property of an optimal decision rule is that it is simple and constant for a large set of experts' preferences and distribution of their private information. Hence, it is robust in the sense that it is not affected by errors in specifying these features of the environment. By contrast, the constructions of optimal outcomes absent commitment or with only one expert are sensitive to model details.Communication, Information, Noise, Experts, Constant threat