1 Choosing and Ranking. Let’s Be Logical About It

Journal of Economic Interaction and …, 2011

Social choice models usually assume that choice is among exogenously given and non decomposable alternatives. Often, on the contrary, choice is among objects that are constructed by individuals or institutions as complex bundles made of many interdependent components. In this paper we present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained, depending upon initial conditions and agenda, intransitive cycles and median voter dominance may be made appear or disappear, and that, finally, decidability may be ensured by increasing manipulability or viceversa.

2008

Abstract We propose two ways of how to measure the consensus of opinions within a given group of individuals. According to the first rule, the consensus is determined by calculating first, for every pair of alternatives, the differences in the support of one alternative over the other and, in a second step, by averaging the differences in the support over all possible pairs of alternatives.

arXiv (Cornell University), 2008

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. The proposed method is proved to satisfy certain desirable conditions, among which there is a majority principle, a property of clone consistency, and the continuity of the rates with respect to the data. One can view this method as a quantitative complement for a qualitative method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.

2014

We consider the problem of making a collective choice by means of approval-preferential voting. The existing proposals are briefly overviewed so as to point out several issues that leave to be desired. In particular, and following Condorcet's last views on elections, we pay a special attention to making sure that a good option is chosen rather than aiming for the best option but not being so sure about it. We show that this goal is fulfilled in a well-defined sense by a method that we introduced in a previous paper and whose study is deepened here. This procedure, that we call path-revised approval choice, is based on interpreting the approval and paired-comparison scores as degrees of collective belief, revising them in the light of the existing implications by means of the so-called Theophrastus rule, and deciding about every option on the basis of the balance of revised degrees of belief for and against its approval. The computations rely on the path scores, which are used also in a method that was introduced by Markus Schulze in the spirit of looking for the best option. Besides dealing with the confidence in the respective results of both methods, we also establish several other properties of them, including a property of upper semicontinuity of the choice set with respect to the profile and a property of Pareto consistency (in a certain weak sense).

Studies in Choice and Welfare, 2010

I owe the ideas expressed in this paper to my collaboration with Steven Brams to whom I am very grateful. I am also grateful to Jean-Francois Laslier for his thoughtful comments on the initial version of the paper. The first formal presentation of these ideas occurred at the workshop on "New Approaches to Voting and Social Choice", 25-26 May 2009, Tilburg University. We thank Harrie de Swart and the participants.

Advanced Studies in Contemporary Mathematics (Kyungshang)

The goal of this paper is to show that neither mean-based voting systems nor median-based ones can fulfill requirements of an ideal democracy. We then work out an original voting function obtained by hydrizing Borda Majority Count (mean-based) and Majority Judgment (median-based). The so-called "Mean-Median Compromise Method" slices between mean and average values. It proposes, moreover, a new tiebreaking method computing intermedian grades mean.

Theory and Decision, 1992

The formal framework of social choice theory is generalized through the introduction of separate representations of preferences and choices. This makes it possible to treat voting as a procedure in which decisions are actually made by interacting participants, rather than as a mere mechanism for aggregation. The extended framework also allows for non-consequentialist preferences that take procedural factors into account. Concepts such as decisiveness, anonymity, neutrality, and stability are redefined for use in the new context. The formal results obtained confirm the universality of strategic voting.

Journal of Mathematical Economics, 2011

Collective rationality of voting rules, requiring transitivity of social preferences (or quasi-transitivity, acyclicity for weaker notions), has been known to be incompatible with other standard conditions for voting rules when there is no prior information, thus no restriction, on individual preferences Sen, 1970). proposes two restricted domains of individual preferences where majority voting generates transitive social preferences; they are the domain consisting of preferences that have at most two indifference classes, and the domain where any set of three alternatives is partitioned into two non-empty subsets and alternatives in one set are strictly preferred to alternatives in the other set. On these two domains, we investigate whether majority voting is the unique way of generating transitive, quasi-transitive, or acyclic social preferences. First of all, we rule out non-standard voting rules by imposing monotonicity, anonymity, and neutrality. Our main results show that majority rule is the unique voting rule satisfying transitivity, yet all other voting rules satisfy acyclicity (also quasi-transitivity on the second domain). Thus we find a very thin border dividing majority and other voting rules, namely, the gap between transitivity and acyclicity.

Scandinavian Political Studies, 1981

The article focuses on the problem of choosing the ‘best’ voting procedure for making collective decisions. The procedures discussed are simple majority rule, Borda count, approval voting, and maximin method. The first three have been axiomatized while the maximin method has not yet been given an axiomatic characterization. The properties, in terms of which the goodness of the procedures is assessed, are dictatorship, consistency, path independence, weak axiom of revealed preference, Pareto optimality, and manipulability. It turns out that the picture emerging from the comparison of the procedures in terms of these properties is most favorable to the approval voting.

Social Choice and Welfare, 1996

This paper considers the construction of sets of preferences that give consistent outcomes under majority voting. Fishburn [7] shows that by combining the concepts of single-peaked and single-troughed preferences (which are themselves examples of value restriction) it is possible to provide a simple description of the extent of agreement between individuals that allows the construction of sets that are as large as those previously known (for fewer than 7 alternatives) and larger than those previously known (for 7 or more alternatives). This paper gives a characterisation of the preferences generated through these agreements and makes observations on the relation between the sizes of such sets as the number of alternatives increases.