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Probabilistic power indices for voting rules with abstention
Freixas Bosch, Josep
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
In this paper, we introduce eight power indices that admit a probabilistic interpretation for voting rules with abstention or with three levels of approval in the input, briefly (3, 2) games.Weanalyze the analogies and discrepancies between standard known indices for simple games and the proposed extensions for this more general context. A remarkable difference is that for (3, 2) games the proposed extensions of the Banzhaf index, Coleman index to prevent action and Coleman index to initiate action become non-proportional notions, contrarily to what succeeds for simple games. We conclude the work by providing procedures based on generating functions for weighted (3, 2) games, and extensible to (j,k) games, to efficiently compute them.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Aspectes socials
Game theory
Voting--Mathematical models
Decision making--Mathematical models
Jocs, Teoria de
Vot -- Models matemàtics
Decisió, Presa de--Models matemàtics
Abstencionisme electoral
North Holland Mathematical Library

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