Dominique Lepelley
University of La Réunion
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Featured researches published by Dominique Lepelley.
Social Choice and Welfare | 2008
Dominique Lepelley; Ahmed Louichi; Hatem Smaoui
In 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.
Social Choice and Welfare | 1994
Dominique Lepelley; Boniface Mbih
The vulnerability of a social choice function to coalitional manipulation of preferences is defined as the proportion of voting situations in which the social choice function can be manipulated by a coalition of individuals. In this paper, we provide exact relations giving the vulnerability of four specific social choice functions (plurality rule, anti-plurality rule, plurality with runoff, anti-plurality with runoff) in three-alternative elections. Plurality with runoff appears to be less vulnerable than the other three rules.
Social Choice and Welfare | 2006
Pierre Favardin; Dominique Lepelley
A typology of electoral environments in which strategic manipulation of voting rules can occur is proposed. From this typology, six different concepts of equilibria (or quasi-equilibria) are defined, including the usual ones. Then, focusing on three alternative elections, we derive some analytical representations for the vulnerability of a large number of voting rules to strategic manipulation by considering successively each type of equilibrium. Our results show that the hierarchy of the rules changes when the voting framework is modified. However, some rules are clearly dominated and some others (among which the Borda and the Nanson rules) appear to be uniquely the best in some specific contexts.
Economics Letters | 1987
Dominique Lepelley; Boniface Mbih
Abstract This paper provides, by an analytical approach, formulas which allow to calculate the proportion of coalitionally unstable situations under the plurality rule for a set of three social states. Computer enumeration and simulation techniques are used to obtain the same proportion for four and five social states.
Mathematical Social Sciences | 2001
Dominique Lepelley
Abstract The Condorcet winner in an election is the candidate that would be able to defeat each of the other candidates in a series of pairwise elections. The Condorcet efficiency of a voting rule is the conditional probability that it would elect the Condorcet winner, given that a Condorcet winner exists. A closed form representation is obtained for the Condorcet efficiency of Borda Rule in three candidate elections under the impartial anonymous culture condition.
Economic Theory | 2001
Dominique Lepelley; Vincent Merlin
Summary. A no-show paradox occurs each time a single voter or a group of voters can manipulate the outcome by not participating to the election process. Among other voting procedures, the scoring run-off methods, which eliminate progressively the alternatives on the basis of scoring rules, suffer from this flaw. We here estimate how frequent this paradox is for three candidate elections under the classical Impartial Culture and Impartial Anonymous Culture assumptions, for different population sizes. The conditions under which this paradox occurs are also described, as well as the relationships with manipulations for a fixed number of voters.
Social Choice and Welfare | 2007
M. R. Feix; Dominique Lepelley; Vincent Merlin; Jean-Louis Rouet
Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union.
Journal of Mathematical Economics | 1998
Dominique Lepelley
Abstract The Condorcet winner in an election is an alternative that would defeat each of the other alternatives in a series of pairwise elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that a Condorcet winner exists. The paper assumes the impartial culture condition for large electorates and shows that approval voting has greater Condorcet efficiency than plurality rule, and that it has smaller Condorcet efficiency than the voting rule in which voters must vote for half of the available alternatives. The likelihood that election rules select the Condorcet loser is also considered.
Review of Economic Design | 1994
Dominique Lepelley
Consider a three-alternative election with n voters and assume that preferences are single-peaked. LetC(λ,n) be the Condorcet efficiency of the rule that assigns 1,λ and 0 points (respectively) to each first, second and third place vote. An exact representation is obtained forC(λ,∞). This relation shows that Borda rule (λ=1/2) is not the most efficient rule. In addition to this result, exact closed form relations are provided forC(0,n),C(1/2,n) andC(1,n). All these relations are obtained by assuming that every admissible configuration of preferences is equally likely to occur.
European Journal of Political Economy | 2001
Dominique Lepelley; Mathieu Martin
Abstract We provide in this note some analytical representations for the probability of the Condorcet paradox when voter indifference between alternatives is allowed. The probability of having a Condorcet winner is also considered. Our results show that indifference reduces the likelihood of the paradox, thus improving the ability of the majority rule to aggregate individual preferences. However, indifference also decreases the probability of having a strict Condorcet winner and, for small electorates, the probability of having a Condorcet winner.