12 research outputs found

    The minimal quota for a complete and transitive majority relation

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    Vidu L. The minimal quota for a complete and transitive majority relation. Working Papers. Institute of Mathematical Economics. Vol 316. Bielefeld: Center for Mathematical Economics; 1999

    Calcul par simulations du pouvoir des électeurs dans le cas de la loi électorale du 29 juin 1820

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    International audienceCet article détaille les résultats de simulations informatiques effectuées en appoint d’un travail théorique mené par Le Breton et Lepelley [2011]. On s’efforce, en particulier, de mettre en évidence des résultats auxquels l’exercice analytique ne peut aboutir

    Majority cycles in a multi-dimensional setting

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    An extension of a theorem on the aggregation of separable preferences

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    An Excess-Voting Function relative to a profile assigns to each pair of alternatives (x,y), the number of voters who prefer x to y minus the number of voters who prefer y to x. It is shown that any non-binary separable Excess-Voting Function can be achieved from a preferences profile when individuals are endowed with separable preferences. This result is an extension of Hollard and Le Breton (1996).

    Majority cycles in a multi-dimensional setting

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    We consider a set of alternatives (electoral platforms, bills, etc. ...) defined as a Cartesian product of k finite discrete sets. We assume that the preferences of the individuals (voters) are marginally single-peaked and separable. The main result of this paper states that the pairwise majority relation satisfies these two properties but that it might exhibit several cycles. This result is important when related to classical problems of multi-dimensional decisions such as logrolling and vote trading. We relate our result with a continuous version of it (McKelvey, 1976).Majority cycles, Multi-dimensionnal vote, Logrolling and vote trading, McGarvey's theorem.

    Measurement of Voting Power: a Preliminary Analysis of an Historical French Electoral Episode Through Simulations

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    In this article we employ the theory of power indices to evaluate the respective influence of the two classes of electors in the polling method introduced by the electoral law of 29 June 1820, a method know as the law of "double vote". After reviewing some of the main theoretical notions underlying the use of the Banzhaf index, we use simulations to evaluate the voting power of the two types of electors

    Regles positionnelles iteratives, principe majoritaire et preferences unimodales

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    Sequential scoring rules are multi-stage social choice tules that work as follows: at each stage of the process, a score is computed for each alternative by taking into account its position in the individual preference rankings, and the alternative with the lowest score is eliminated. The current paper studies the ability of these rules for choosing the Condorcet winner (or the strong Condorcet winner) when individual preferences are single-peaked

    Referendum paradox in a federal union with unequal populations: the three state case

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    International audienceIn a federal union, a referendum paradox occurs each time a decision taken by representatives elected in separate jurisdictions (districts, states, regions) conflicts with the decision that would have been adopted if the voters had directly given their opinion via a referendum (Nurmi 1999). Assuming that the population is split into three jurisdictions of respective size n1, n2 and n3, we derive exact formulas for the probability of the referendum paradox under the Impartial Culture model. Then we use these results to show that, in our model, allocating seats to the juridictions proportionally to the square root of their size is an apportionment rule that fails to minimize the probability of the referendum paradox in some federations
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