The effects of closeness on the election of a pairwise majority rule winner

Some studies have recently examined the effect of closeness on the probability of observing the monotonicity paradox in three-candidate elections under Scoring Elimination Rules. It has been shown that the frequency of such paradox significantly increases as elections become more closely contested. In this paper we consider the effect of closeness on one of the most studied notions in Social Choice Theory: The election of the Condorcet winner, i.e., the candidate who defeats any other opponent in pairwise majority comparisons, when she exists. To be more concrete, we use the well known concept of the Condorcet efficiency, that is, the conditional probability that a voting rule will elect the Condorcet winner, given that such a candidate exists. Our results, based on the Impartial Anonymous Culture (IAC) assumption, show that closeness has also a significant effect on the Condorcet efficiency of different voting rules in the class of Scoring and Scoring Elimination Rules

On Ehrhart polynomials and probability calculations in voting theory

International audienceIn voting theory, analyzing the frequency of an event (e.g. a voting paradox), under some specific but widely used assumptions, is equivalent to computing the exact number of integer solutions in a system of linear constraints. Recently, some algorithms for computing this number have been proposed in social choice literature by Huang and Chua (Soc Choice Welfare 17:143–155 2000) and by Gehrlein (Soc Choice Welfare 19:503–512 2002; Rev Econ Des 9:317–336 2006). The purpose of this paper is threefold. Firstly, we want to do justice to Eugène Ehrhart, who, more than forty years ago, discovered the theoretical foundations of the above mentioned algorithms. Secondly, we present some efficient algorithms that have been recently developed by computer scientists, independently from voting theorists. Thirdly, we illustrate the use of these algorithms by providing some original results in voting theory

Some Further Results on the Manipulability of Social Choice Rules

http://www.springerlink.com/media/3846tnrxrp6xbcutmtfg/contributions/7/1/8/l/718ll43221300942.pdfInternational audienc

One-way monotonicity as a form of strategy-proofness

One-way monotonicity, Monotonicity, Participation, No-show paradox, Strategy-proofness, Manipulation, Scoring rule, Sensible virtue, Condorcet extension, D71,

An individual manipulability of positional voting rules

Manipulability, Positional voting rules, Multiple choice, Extended preferences, D7,

On the positive association of parliamentary social choice functions

International audienceIntuitively, a voting rule satisfies the condition of positive association if it guarantees that an improvement for an alternative in the preferences expressed by voters results in a change, if there is any, of the social status of that alternative in the same direction. In this article, we consider two interpretations of this notion, and for parliamentary voting procedures, we provide results showing under the impartial anonymous culture (IAC) hypothesis how often the positive association is (not) satisfied. Furthermore, our analysis also permits us to investigate the relationships between these notions