The stability set as a social choice correspondence

Abstract The stability set has been introduced in the game theory and social choice literature by Rubinstein [J. Econ. Theory 23 (1980) 150], as a possible resolution of the problem of the emptiness of the core of voting games. In this context, it models the idea that individuals may be, in some sense, prudent: a voter i will never vote for candidate a against candidate b in a pairwise comparison if a is afterwards beaten by a candidate c that is worse than a and b in her preference ordering. Most of the literature on the stability set focused on its non-existence, but almost nothing is said on its relationships with other social choice correspondences and its normative properties. This is what we intend to do here in a rather extensive study. We first prove that the stability set offers a specific way to select the best alternatives, different from many other voting rules. Secondly, we show that this prudent behavior, in the context of voting, may lead to the selection of undesired alternatives.

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