Stability set, Pareto-optimality and single-peaked preferences

نویسندگان

  • Issofa Moyouwou
  • Nicolas Gabriel Andjiga
چکیده

The emptiness of the core of a voting game can be viewed as the failure of a society to select a stable alternative : every alternative can be vetoed by a winning coalition. To solve this problem, also known as the paradox of voting, Rubinstein (1980) introduces the stability set by a clause of prudence in the core dominance relation which amounts to assume that individuals are aware of possible future developments while voting for a change. Unfortunately, the stability set may contain a Pareto dominated alternative; that is an alternative less preferred to another by every voter. Instead of speci…c illustrations as done in the literature, the present paper provides an exhaustive study of this issue. It is shown that the stability set of a proper voting game does not contain a Pareto dominated alternative at any pro…le of linear orders given any set of at least …ve alternatives if and only if the game is oligarchic, meaning that there exists a single minimal winning coalition for the game. In contrast to this disappointing behavior of the stability set over the universal domain, a positive result is proved : the stability set of any proper voting game selects only Pareto-optimal alternatives when individual preferences are single-peaked. Correspondences to Issofa Moyouwou, Visiting Professor, Université de Caen, BasseNormandie, email: [email protected]

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تاریخ انتشار 2011