Abstract
In this article we deal with multi-criteria simple games which constitute an extension of the basic framework of voting systems and related social-choice situations. We generalize two closely related solution concepts for these games, the stable sets and the core. A relationship between stable sets and minimal winning coalitions is established. Two generalizations of the core for multi-criteria simple games are characterized in terms of veto players. In addition, extended multi-criteria simple games obtained from different aggregation operations, such as union, intersection, marginalization, and composition, are introduced. It is shown that a voting system can be established when these operations are applied to complex voting systems.
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Monroy, L., Fernández, F.R. Stable sets and cores for multi-criteria simple games and for their extensions. Soc Choice Welf 39, 1–22 (2012). https://doi.org/10.1007/s00355-011-0543-4
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DOI: https://doi.org/10.1007/s00355-011-0543-4