How many voters are needed for paradoxes?

Summary. This paper presents a general procedure for finding profiles with the minimum number of voters required for many important paradoxes. Borda's and Condorcet's classic examples are revisited as well as generalizations. Using Saari's procedure line, we obtain an upper bound for the minimum number of voters needed for a profile for which the Condorcet winner is not strictly top ranked for all weighted positional procedures. Also we give a simple upper bound on the minimum number of voters needed for a set of prescribed voting outcomes. In contrast to situations wherein small numbers of voters are needed, we consider paradoxes requiring arbitrarily large numbers of voters as well as large numbers of alternatives. Finally we indicate connections with statistical rank based tests. Received: April 18, 2001; revised version: May 25, 2001     

An efficiency characterization of plurality social choice on simple preference domains

Summary. We consider a model of social choice dealing with the problem of choosing a subset from a set of objects (e.g. candidate selection, membership, and qualification problems). Agents have trichotomous preferences for which objects are partitioned into three indifference classes, goods, bads, and nulls, or dichotomous preferences for which each object is either a good or a bad. We characterize plurality-like social choice rules on the basis of the three main axioms, known as Pareto efficiency, anonymity, and independence.Received: 29 August 2003, Revised: 3 June 2004, JEL Classification Numbers: D70, D71, D72.Biung-Ghi Ju: I am grateful to William Thomson and Jianbo Zhang for their helpful comments and discussions. I also thank Brandon Dupont, the participants in seminars at Iowa State University, University of Kansas, and the Midwest Theory Meeting at University of Notre Dame. I thank an anonymous referee for detailed comments and suggestions that were very helpful in simplifying the proof of Theorem 1 and in revising the paper.     

The welfare consequences of strategic behaviour under approval and plurality voting

This paper studies the welfare consequences of strategic behaviour under approval and plurality voting by comparing the utilitarian efficiencies obtained in simulated voting under two behavioural assumptions: expected utility-maximising behaviour and sincere behaviour. Under approval voting utilitarian efficiency is relatively high irrespective of the behavioural assumption, and under the plurality rule strategic voting significantly increases utilitarian efficiency.     

Violations of Independence under Amendment and Plurality Rules with Anonymous Voters

Under the impartial anonymous culture assumption (IAC), we evaluate the proportion of anonymous profiles at which the amendment and plurality voting procedures violate the property of independence of irrelevant alternatives (IIA). We also examine the relation to single-peakedness of preferences and election of a Condorcet winner.      

Efficiency in the Degree of Compromise: A New Axiom for Social Choice

We introduce a social choice axiom called efficiency in the degree of compromise. Our axiom is based on the trade-off between the quantity and quality of support that an alternative receives. What we mean by the quantity of support is the number of voters behind an alternative, while the quality of support is about the definition of being behind depending on the rank of an alternative in voters' preference orderings. Naturally, one can increase the quantity of support of an alternative to the expense of giving up from its quality. We say that an alternative is an efficient compromise if there exists no other alternative with at least an equal quantity of support with a higher quality. Our efficient compromise axiom is based on not choosing inefficient compromises. We introduce it and show that many standard social choice rules of the literature, such as Condorcet-consistent rules, plurality with a runoff, the Borda count and the single transferable vote, may choose inefficient compromises.     

Strategy-proofness of the plurality rule over restricted domains

We give a complete characterization of preference domains over which the plurality rule is strategy-proof. In case strategy-proofness is required to hold under all tie-breaking rules, strategy-proof domains coincide with top-trivial ones where the range of the plurality rule admits at most two alternatives. This impossibility virtually prevails when strategy-proofness is weakened so as to hold under at least one tie-breaking rule: unless there are less than five voters, the top-triviality of a domain is equivalent to the (weak) non-manipulability of the plurality rule. We also characterize the cases with two, three or four voters. I am grateful to Attila Tasnadi for his thorough reading of the paper and pointing to an error in an earlier version. I thank Levent Kutlu, Clemens Puppe, Arunava Sen, an anonymous referee and an anonymous AE for their comments. This research is part of the project “Social Perception—A Social Choice Perspective” supported by Istanbul Bilgi University Research Fund. I also acknowledge the support of the Turkish Academy of Sciences Distinguished Young Scientist Award Program (TUBA-GEBIP).     

Frequency based analysis of collective aggregation rules

A new property for collective aggregation rules called positive discrimination is introduced. This property is satisfied by many anonymous and neutral collective aggregation rules. We discuss unimodal profiles (or distributions) for which this property on its own determines the outcome as the mode of a unimodal distribution. We investigate relaxations of this unimodal distribution condition and show that the Condorcet consistent rules as well as the Borda rule and the plurality rule have the mode as the outcome at such profiles. Further, we show, by an example, how the addition of unimodal profiles and the property of positive discrimination can help to determine an outcome in the case of a large number of voters.     

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.     

On the generic strategic stability of Nash equilibria if voting is costly

Summary. We prove that for generic plurality games with positive cost of voting, the number of Nash equilibria is finite. Furthermore all the equilibria are regular, hence stable sets as singletons.JEL Classification Numbers: C72, D72.We would like to thank Luisa Bassotto, Marco Celentani, Mamoru Kaneko, and participants at the 6 International Conference on Current Trends in Economics for helpful comments. We also thank an anonymous referee of this journal for precious advices that have substantially improved this paper. This paper was partially written while Francesco was visiting Tor Vergata University, which he thanks for hospitality and financial support. The usual disclaimer applies.