All power structures are achievable in basic weighted games
A major problem in decision making is designing voting systems that are as simple as possible and able to reflect a given hierarchy of power of its members. It is known that in the class of weighted games all hierarchies are achievable except two of them. However, many weighted games are either impr...
| Autores: | , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2023 |
| 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:2117/385961 |
| Acceso en línea: | https://hdl.handle.net/2117/385961 |
| Access Level: | acceso abierto |
| Palabra clave: | Decision making -- Mathematical models Voting -- Mathematical models Hierarchies Weighted voting Recurrence relations Fibonacci sequences Decisió, Presa de -- Models matemàtics Vot -- Models matemàtics Jerarquies Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs |
| Sumario: | A major problem in decision making is designing voting systems that are as simple as possible and able to reflect a given hierarchy of power of its members. It is known that in the class of weighted games all hierarchies are achievable except two of them. However, many weighted games are either improper, or do not admit a minimum representation in integers, or do not assign a minimum weight of 1 to the weakest non-null players. These factors prevent obtaining a good representation. The purpose of the paper is to prove that for each achievable hierarchy for weighted games there is a handy weighted game fulfilling these three desirable properties. A representation of this type is ideal for the design of a weighted game with a given hierarchy. Moreover, the subclass of weighted games with these properties is considerably smaller than the class of weighted games. |
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