Probabilistic power indices for voting rules with abstention

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 ex...

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Detalles Bibliográficos
Autor: Freixas Bosch, Josep|||0000-0002-9033-9432
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/16144
Acceso en línea:https://hdl.handle.net/2117/16144
https://dx.doi.org/10.1016/j.mathsocsci.2012.01.005
Access Level:acceso abierto
Palabra clave:Game theory
Probability
Voting -- Mathematical models
Voting -- Abstention
Decision making -- Mathematical models
Jocs, Teoria de
Probabilitats
Vot -- Models matemàtics
Decisió, Presa de -- Models matemàtics
Abstencionisme electoral
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
Descripción
Sumario: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.