Size approval voting

We propose a new class of voting procedures, called Size Approval Voting, according to which, the effective weight of a vote from a given individual depends on how many other candidates that individual votes for. In particular, weights are assumed to be non-negative and weakly decreasing in the number of approved candidates. Then, for a given profile of individual votes, all candidates with the maximal sum of weighted votes are elected. We show in our axiomatic analysis that the family of all Size Approval Voting procedures is characterized by a set of natural properties.     

Deliberative voting

We analyze a model of jury decision making in which jurors deliberate before casting their votes. We consider a wide range of voting institutions and show that deliberations render these equivalent with respect to the sequential equilibrium outcomes they generate. In particular, in the context of a jury setup, all voting rules excluding the two types of unanimity rules (one requiring a unanimous consensus to acquit, one requiring a unanimous consensus to convict) induce the same set of equilibria outcomes. We show the robustness of our results with respect to several restrictions on communication protocols and jurors’ strategies. Furthermore, we demonstrate that our observations extend to practically all of the voting structures commonly studied in the voting literature. The paper suggests the importance of accounting for communication in models of collective choice.     

Strategic candidacy for multivalued voting procedures

Dutta et al. (Econometrica 69 (2001) 1013) (Dutta, Jackson, and Le Breton—DJLeB) initiate the study of manipulation of voting procedures by a candidate who withdraws from the election. A voting procedure is candidate stable if this is never possible. We extend the DJLeB framework by allowing: (a) the outcome of the procedure to be a set of candidates; (b) some or all of the voters to have weak preference orderings of the candidates. When there are at least three candidates, any strongly candidate stable voting selection satisfying a weak unanimity condition is characterized by a serial dictatorship. This result generalizes Theorem 4 of DJLeB.     

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare.We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium.We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.     

The premiss-based approach to judgment aggregation

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. oligarchy), either just on the premisses or on the whole agenda. Our analysis is inspired by the doctrinal paradox of legal theory and is arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory.     

On the universally beneficial manipulation conjecture

The universally beneficial manipulation conjecture of Campbell and Kelly states that for a social choice rule, if everyone gains as a result of any optimal manipulation, then the rule satisfies universally beneficial manipulation, i.e., everyone gains as a result of any manipulation, optimal or not. We prove the conjecture for three alternatives and any number of individuals. We also construct a counterexample in a general form with more than three alternatives and at least two individuals.     

Justifiable group choice

We study the judgment aggregation problem from the perspective of justifying a particular collective decision by a corresponding aggregation on the criteria. In particular, we characterize the logical relations between the decision and the criteria that enable justification of a majority decision through a proposition-wise aggregation rule with no veto power on the criteria. While the well-studied “doctrinal paradox” provides a negative example in which no such justification exists, we show that genuine possibility results emerge if there is a gap between the necessary and the sufficient conditions for the decision. This happens, for instance, if there is only a partial consensus about the appropriate criteria for the decision, if only a subset of these criteria can be elicited, or if the judgment on criteria is based on probabilistic acceptance thresholds.     

Factoring out the impossibility of logical aggregation

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow's and arguably enhances its paradoxical value.     

Introduction to judgment aggregation

This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals' judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium.     

The possibility of judgment aggregation on agendas with subjunctive implications

The new field of judgment aggregation aims to find collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic.     

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.     

Multi-stage voting, sequential elimination and Condorcet consistency

A class of voting procedures based on repeated ballots and elimination of one candidate in each round is shown to always induce an outcome in the top cycle and is thus Condorcet consistent, when voters behave strategically. This is an important class as it covers multi-stage, sequential elimination extensions of all standard one-shot voting rules (with the exception of negative voting), the same one-shot rules that would fail Condorcet consistency. The necessity of repeated ballots and sequential elimination are demonstrated by further showing that Condorcet consistency would fail in all standard voting rules that violate one or both of these conditions.     

Between liberalism and democracy

We study and characterize axiomatically a class of voting rules, called consent rules, that incorporate aspects of majoritarianism and liberalism. An outcome of the vote specifies who among the voters are eligible to a certain right or qualification. Each outcome serves also as a permissible ballot. Consent rules are parameterized by the weights given to individuals in determining their own qualification. In one of these rules, the liberal rule, each individual's qualification is determined by her. In other rules, an individual's qualification requires social consent in various degrees. We also show the relation between self-determination and the liberal rule.     

Community standards

I introduce a model of community standards relevant to the judicial determination of obscenity. Standards are defined as subjective judgments restricted only by a simple reasonableness condition. Individual standards are aggregated to form the community standard. Several axioms reflect legal concerns. These require that the community standard (a) preserve unanimous agreements, (b) become more permissive when all individuals become more permissive, and not discriminate, ex ante, (c) between individuals and (d) between works. I show that any rule which satisfies these properties must be “similar” to unanimity rule. I also explore the relationship between the model and the doctrinal paradox of Kornhauser and Sager [12].     

Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation

Recently, Hermandez-Lamoneda et al. (2008) and independently Chameni and Andjiga (2008) gave an analytic formulation for all valued solutions to the n-person TU-games that satisfy linearity, efficiency and symmetry axioms. Our main purpose in this paper is to recast the proposed formulation to a more potentially interpretational one. We are focused on an interpretation based on the idea of marginal contribution, a concept already familiar in the Shapley value and the Solidarity value. A general null player axiom is introduced, and it turns out that any valued solution satisfying the three properties is characterized by a null player model.     

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.     

Role of linking mechanisms in multitask agency with hidden information

We investigate the adverse selection problem where a principal delegates multiple tasks to an agent. We characterize the virtually implementable social choice functions by using the linking mechanism proposed by Jackson and Sonnenschein (2007) [20] that restricts the message spaces. The principal does not require any incentive wage schemes and can therefore avoid any information rent and welfare loss. We show the resemblance between the functioning of this message space restriction and that of incentive wage schemes. We also extend the results of the single-agent model to the multi-agent model.     

Efficiency and consistency for locating multiple public facilities

In the problem of locating multiple public facilities studied by Barberà and Beviá [Self-selection consistent functions, J. Econ. Theory 105 (2002) 263-277; Locating public facilities by majority: stability, consistency and group formation, Games Econ. Behav. 56 (2006) 185-200], we offer simple necessary and sufficient conditions for efficiency, decentralizability of efficient decisions in a game of community division and local public goods provision, and a constructive algorithm for efficient and consistent decisions.     

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.