A core of voting games with improved foresight

✍ Scribed by Lawrence Diffo Lambo; Bertrand Tchantcho; Joël Moulen

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 646 KB
• Volume: 58
• Category: Article
• ISSN: 0165-4896
• DOI: 10.1016/j.mathsocsci.2009.04.003

✦ Synopsis

This paper considers voting situations in which the vote takes place iteratively. If a coalition replaces the status quo a with a contestant b, then b becomes the new status quo, and the vote goes on until a candidate is reached that no winning coalition is willing to replace. It is well known that the core, that is, the set of undominated alternatives, may be empty. To alleviate this problem, Rubinstein [Rubinstein, A., 1980. Stability of decision systems under majority rule. Journal of Economic Theory 23, 150-159] assumes that voters look forward one vote before deciding to replace an alternative by a new one. They will not do so if the new status quo is going to be replaced by a third that is less interesting than the first. The stability set, that is, the set of undominated alternatives under this behavior, is always non-empty when preferences are strict. However, this is not necessarily the case when voters' indifference is allowed. Le Breton and Salles [Le Breton, M., Salles, M., 1990. The stability set of voting games: Classification and generecity results.