Majority voting on restricted domains

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule.     

Majority cycles in a multi-dimensional setting

Summary. We consider a set of alternatives (electoral platforms, bills, etc. ...) defined as a Cartesian product of k finite discrete sets. We assume that the preferences of the individuals (voters) are marginally single-peaked and separable. The main result of this paper states that the pairwise majority relation satisfies these two properties but that it might exhibit several cycles. This result is important when related to classical problems of multi-dimensional decisions such as logrolling and vote trading. We relate our result with a continuous version of it (McKelvey, 1976). Received: March 21, 2000; revised version: April 12, 2001     

Viewpoint: Decision-making in committees

Abstract .  This article reviews recent developments in the theory of committee decision-making. A committee consists of self-interested members who make a public decision by aggregating imperfect information dispersed among them according to a pre-specified decision rule. We focus on costly information acquisition, strategic information aggregation, and rules and processes that enhance the quality of the committee decision. Seeming inefficiencies of the committee decision-making process such as over-cautiousness, voting, and delay emerge as partial remedies to these incentive problems.     

Voting by committees under constraints

We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters’ preferences are separable or additively representable.     

To Majority through the Search for Unanimity

The relative majority rule is characterized, when there are only two alternatives, in terms of axioms of unanimity, reducibility, ontoness (which expresses citizen sovereignty), and no veto power (a weakening of almost unanimity). The strongest axiom is reducibility, which embodies the preference aggregation procedure that successively synthesizes two divergent preferences until divergence disappears and, therefore, unanimity can be applied.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.     

Central bankers in government appointed committees

I study the policy choices of members of a central bank committee, who are appointed by the government. Central bankers balance their desire to protect the Central Bank's reputation against their interest to be reappointed. Committees can be more successful than single central bankers at reducing inflation and insulating policy from government pressures. These gains are only achieved if the turnover rate of committee members is low and the committee is small. The former is associated with a low risk of being replaced for not supporting the government's preferred policy. The latter, meanwhile, implies high probability that a single vote affects policy, making any individual member more weary of potentially affecting the Central Bank's reputation through his vote.     

Monetary policy committees and interest rate setting

This paper shows that it is preferable for monetary policy to be conducted by a committee instead of a single policy maker if there is uncertainty about potential output. We examine three decision procedures - an optimal procedure, averaging and voting - and find that the latter is the appropriate way to reach decisions if policy makers are not equally skilled. Finally, we demonstrate that efficient decision procedures reduce the persistence of shocks.     

信息不对称、大股东掠夺与投资者保护

大部分中国的企业股权是相当集中的,现实中大股东有时无助于监督管理者,而且还会掠夺小股东,使公司治理趋于恶化。大股东通过各种手段对上市公司进行利益输送,对上市公司造成危害,也损害了中小股东的利益。文章论述了我国大股东“隧道行为”的几种主要具体形式并分析其产生的原因,并基于中小投资者保护立场进一步提出了治理的方法。     

Majority voting on tax parameters: Some further results

Earlier analysis of properties of tax functions chosen by majority rule is extended to include more general characterization of individual preferences. Outcomes when preferences are not single-peaked are discussed in some detail.     

A Solution Concept for Majority Rule in Dynamic Settings

We define and explore the notion of a Dynamic Condorcet Winner (DCW), which extends the notion of a Condorcet winner to dynamic settings. We show that, for every DCW, every member of a large class of dynamic majoritarian games has an equivalent equilibrium, and that other equilibria are not similarly portable across this class of games. Existence of DCWs is guaranteed when members of the community are sufficiently patient. We characterize sustainable and unsustainable outcomes, study the effects of changes in the discount factor, investigate efficiency properties, and explore the potential for achieving renegotiation-proof outcomes. We apply this solution concept to a standard one-dimensional choice problem wherein agents have single-peaked preferences, as well as to one involving the division of a fixed aggregate pay-off.     

Veto power in committees: an experimental study

Veto power consists of the right of one or more players to unilaterally block decisions but without the ability to unilaterally secure their preferred outcome. Our experiment shows that (i) committees with a veto player take longer to reach decisions (are less efficient) and generate less consensus than without a veto player, (ii) veto power substantially enhances proposer’s power, and (iii) non-veto players are substantially more willing to compromise than veto players. We relate our results to the theoretical literature on the impact of veto power as well as to concerns about the impact of veto power in real-life committees.     

A note on plurality distortion in large committees

Simple plurality voting allows the somewhat surprising possibility that a majority of a committee or an electorate may prefer one of the defeated alternatives to the plurality winner. This paradox is distinct from Condorcet's paradox and has received less attention in the literature. Recently, however, the frequency of the Borda effect anticipated under different cultures has been computed and some empirical results have also been reported. Here results are obtained for both impartial and partial cultures using a class of Polya urn models. Emphasis is on asymptotic investigations and results valid for large committees.     

Effectiveness of Weighted Majority Rules with Random Decision Power Distribution

There is a large body of research studying the conditions under which majority decisions are best. In particular, in many circumstances, the probability of a group to decide correctly is higher than that of a random subgroup. Moreover, the latter probability increases as the subgroup size grows. Here we generalize those results by showing that, in the same setup, the simple majority rule is the most effective of all weighted majority rules when weights are distributed randomly between group members. For special families of weighted majority rules, rule effectiveness increases as we get “closer” to the simple majority rule.     

Composition of Government Budget, Non-Single Peakedness, and Majority Voting

In this paper we study whether majority voting equilibria exist when preferences over public policies are not single peaked. The government levies a proportional income tax. Tax revenue is used to finance a uniform lump-sum transfer and public education. Individuals vote on the composition of the government budget. We show that the single-crossing property cannot be invoked to establish existence of a majority voting equilibrium. In a simple parametric example we find that cycles are pervasive.     

Bargaining in committees as an extension of Nash's bargaining theory

This paper addresses the following issue: if a set of agents bargain on a set of feasible alternatives ‘in the shadow’ of a voting rule, that is, any agreement can be enforced if a ‘winning coalition’ supports it, what general agreements are likely to arise? In other words: what influence can the voting rule used to settle (possibly nonunanimous) agreements have on the outcome of consensus? We model the situation as an extension of the Nash bargaining problem in which an arbitrary voting rule replaces unanimity. In this setting a natural extension of Nash's solution is characterized.     

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.     

Majority Voting over Publicly Provided Goods, Redistribution, and Income Taxation

Federal, state, and many local governments make decisions that involve taxation, redistribution, and provision of public goods. Positive models to study these issues encounter the well‐known problem that majority‐voting equilibrium (MVE) may fail to exist in such multidimensional models. In this paper, with reasonable restrictions on preferences, I provide sufficient conditions for the existence of an MVE in a model with linear income tax and government expenditure policies that affect individual labor/leisure choices. My majority‐voting result takes account of the possibility that low‐skill individuals will drop out of the labor force under some tax and expenditure configurations.