Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions

Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I prove three theorems. First, every strategy-proof voting procedure is dictatorial. Second, this paper's strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, non-negative response, and citizens' sovereignty conditions for social welfare functions. Third, Arrow's general possibility theorem is proven in a new manner.     

Voting by veto

This paper describes a voting procedure for revealing preferences for public goods. The procedure consists of two steps: a proposal by each committee member to be added along with the status quo to form the issue set, and then, subsequent to a random determination of voting order, the elimination of one proposal from the issue set by each committee member. For any set of proposals and a given order of voting the procedure determines a unique, winning proposal. Under the procedure's incentives, the winning proposal tends to contain an equal sharing of the potential gains from collective action among the committee members.     

Cooperative bargaining foundations of the Shapley–Shubik index

In a recent paper, we provide an interpretation of the Shapley–Shubik index as a measure of the ‘bargaining power’ that a voting rule gives to each member of a committee negotiating in search of consensus. It is assumed that negotiation takes place under the condition that every winning coalition can impose any agreement. In this paper we further investigate the axiomatic foundations of this interpretation of the Shapley–Shubik index. To this end a wider framework admitting random voting rules is considered.     

An Incentive‐Compatible Condorcet Jury Theorem*

We consider a group of individuals who face a binary collective decision. Each group member holds some private information, and all agree about what decision should be taken in each state of nature. However, the state is unknown, and members can differ in their valuations of the two types of mistakes that might occur, and in their prior beliefs about the true state. For a slightly randomized majority rule, we show that informative voting by all voters is the unique Nash equilibrium, that this equilibrium is strict, and that the Condorcet asymptotic efficiency result holds in this setting.     

Search by committee

We consider the problem of sequential search when the decision to stop is made by a committee and show that a unique symmetric stationary equilibrium exists given a log concave distribution of rewards. We compare search by committee to the corresponding single-agent problem and show that committee members are less picky and more conservative than the single agent. We show how (i) increasing committee size holding the plurality fraction constant and (ii) increasing the plurality rule affect the equilibrium acceptance threshold and expected search duration. Finally, we show that unanimity is optimal if committee members are sufficiently patient.     

Optimal agenda-setter timing

Abstract .  We analyze the optimal timing problem of an agenda setter who can propose a project that is then voted on by a committee. The payoff consists of a common stochastic component and an idiosyncratic component that differs among committee members. The agenda setter may be biased for or against the project, relative to the median committee member, and chooses when to call the vote. We analyze how the timing decision depends on the political environment and the bias of the agenda setter. We show that both positively and negatively biased agenda setters can implement decisions that differ from those preferred by the median committee member.     

An experimental test of a committee search model

The objective of this paper is to design a laboratory experiment for an infinite-horizon sequential committee search model in order to test some of the implications obtained by the model in Albrecht et al. (2010) (AAV). We find that, compared with single-agent search, the search duration is longer for committee search under the unanimity rule, but is shorter for committee search in which at least one vote is required to stop searching. In addition, according to estimates from round-based search decisions, subjects are more likely to vote to stop searching in committee search than in single-agent search. This confirms that agents are less picky in committee search. Overall, the experimental outcomes are consistent with the implications suggested by the AAV model. However, despite the prediction from the AAV model, we could not obtain a significant outcome in relation to the size order of the probabilities of voting to stop searching in committee search for the various plurality voting rules.     

Inferring hawks and doves from voting records

We analyze revealed policy preferences of the Monetary Policy Committee of the Bank of England. From the voting records we estimate the policy preferences with spatial models of voting. We find that internal committee members tend to hold centrist policy preferences, while more extreme policy preferences, both hawkish and dovish, are generally held by external members. An industry background is associated with more hawkish preferences.     

Eliciting information from a committee

The paper addresses the mechanism design problem of eliciting truthful information from a committee of informed experts who collude in their information disclosure strategies. It is shown that under fairly general conditions full information disclosure is possible if and only if the induced outcome is Pareto undominated for the committee members.     

The stability of decision making in committees: The one-core

We study the stability of decision making in committees. A policy proposal introduced by a committee member is either adopted or abandoned in favor of a new proposal after deliberations. If a proposal is abandoned, it is in spite of the committee member who introduced it, who does not cooperate in any effort to defeat it. Shenoy (1980) proposes the one-core as a solution concept for this game, and shows that this solution may be empty. We provide a necessary and sufficient condition for the existence of a stable policy under the majority rule. This result highlights a trade-off between the size of a committee, the number of competing policy options, and the existence of a stable outcome. Our findings imply a tension between political stability and the existence of a large number of competing interests in democracies.     

Voting in small committees

We analyze the voting behavior of a small committee that has to approve or reject a project proposal whose return is uncertain. Members have diverse preferences: some of them want to maximize the expected value, while others have a bias towards project approval and ignore their information on the project value. We focus on the most efficient use of scarce information when members cannot communicate prior to voting, and we provide insights on the optimal composition of the committee. 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 diverse members perform as well as homogeneous committees, and even better in some cases. In particular, when value-maximizing members outnumber biased members by one vote, the optimal equilibrium becomes unique.     

Group play in games and the role of consent in network formation

We study games played between groups of players, where a given group decides which strategy it will play through a vote by its members. When groups consist of two voting players, our games can also be interpreted as network-formation games. In experiments on Stag Hunt games, we find a stark contrast between how groups and individuals play, with payoffs playing a primary role in equilibrium selection when individuals play, but the structure of the voting rule playing the primary role when groups play. We develop a new solution concept, robust-belief equilibrium, which explains the data that we observe. We provide results showing that this solution concept has application beyond the particular games in our experiments.     

Would NAFTA have been Approved by the House of Representatives under President Bush? Presidents,Parties, and Trade Policy

This paper examines five trade policy votes in the United States House of Representatives, one during each of the last five presidential terms. The paper investigates the determinants of representative voting and shows that Congress members are more likely to support trade liberalization if the President is a member of their own party. The estimation allows a prediction to be made of the likely House trade votes under alternative presidential election outcomes. The model predicts that the probability of NAFTA being approved would have been greatly reduced by a victory for President Bush (41) in the 1992 election. Neither the trade promotion authority granted to President Bush (43) in 2001 nor the CAFTA signed in 2005 would likely have been approved under Democratic Presidents.     

Information transfer and aggregation in an uninformed committee: A model for the selection and use of biased expert advice

A committee of five uses majority rule for decisions on two public goods. Individual committee member preferences depend on a state of nature that is unknown to the committee members but the state of nature is known to two experts who have preferences about committee decisions. Experts have no vote on the committee but provide a recommendation to the committee at the opening of a meeting. Two experts who have known, opposing biases are selected – a dyadic mechanism. The results reveal that experts do not tell the truth but committee decisions are as if committee members know what the experts know. The information transfer occurs because committee members anticipate the biases and properly infer the information held by the experts.     

Voter turnout and government's legitimate mandate

The paper studies a group-mobilization model of costly voting in which citizens care about the legitimate mandate of the government formed by the winning group. This, as a function of the electorate's voting behavior, depends on both the margin of victory and the total turnout rate. Citizens prefer a high mandate when their own group forms the government but a low one if the government is formed by an opposing group. As such, the eventual losing group faces a trade-off: a higher participation from its members decreases the margin of victory but increases the total turnout. In equilibrium, a second fundamental trade-off arises, which overturns the supposed positive relationship between turnout and mandate: as the total turnout becomes more important for the government's mandate, the first decreases but the second strengthens. The key mechanism at play is a shift in the relative participation of the two groups, which favors the majority and raises its margin of victory, thus yielding a bandwagon effect. The implications for the evolution of turnout and the occurrence of election boycotts are discussed.     

Noncooperative foundations of bargaining power in committees and the Shapley–Shubik index

In this paper we explore the noncooperative foundations of the bargaining power that a voting rule gives to each member of a committee that bargains in search of consensus over a set of feasible agreements under a voting rule. Assuming complete information, we model a variety of bargaining protocols and investigate their stationary subgame perfect equilibria. We show how the Shapley–Shubik index and other power indices can be interpreted as measures of ‘bargaining power’ that appear in this light as limit cases.     

Information transmission in coalitional voting games

A core allocation of a complete information economy can be characterized as one that would not be unanimously rejected in favor of another feasible alternative by any coalition. We use this test of coalitional voting in an incomplete information environment to formalize a notion of resilience. Since information transmission is implicit in the Bayesian equilibria of such voting games, this approach makes it possible to derive core concepts in which the transmission of information among members of a coalition is endogenous. Our results lend support to the credible core of Dutta and Vohra [Incomplete information, credibility and the core, Math. Soc. Sci. 50 (2005) 148-165] and the core proposed by Myerson [Virtual utility and the core for games with incomplete information, Mimeo, University of Chicago, 2005] as two that can be justified in terms of coalitional voting.     

Committees with supermajority voting yield commitment with flexibility

A fundamental problem for government is how to combine commitment to certain policies with the flexibility required to adjust them when needed. Rogoff (1985) [Rogoff, K., 1985. The optimal degree of commitment to an intermediate monetary target, Q. J. Econ. 100(4) 1169–1189] showed that a way to strike the right balance is to appoint an optimally “conservative” policy-maker. In real life, however, policy-makers also have power over decisions where optimal plans are time-consistent, so delegating to a conservative person could be undesirable. A flexible delegation device can be found in a large committee of randomly appointed members voting over policy after observing a shock. When facing dynamic inconsistency, under a single-crossing property, there exists a supermajority rule that implements the population median's optimally conservative policy-maker with certainty. Another single-crossing property guarantees that if simple majority voting is used to select the voting rule that will govern policy choice, the supermajority preferred by the median is chosen. For problems where dynamic inconsistency vanishes, the committee will choose to make decisions by simple majority, implementing median outcomes. An application to monetary policy is developed. We show that the optimal supermajority is higher when dynamic inconsistency is more severe, when preferences are more homogeneous, and when the economy is less volatile.     

Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation

Recent research on the Condorcet Jury Theorem has proven that informative voting (that is, voting according to one’s signal) is not necessarily rational. With two alternatives, rational voting typically leads to the election of the correct alternative, in spite of the fact that not all voters vote informatively. We prove that with three alternatives, there are cases in which informative voting is rational and yet leads to the election of a wrong alternative.