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...
| Autor: | |
|---|---|
| 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 |
| 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. |
|---|