Academic Journal
On anonymous and weighted voting systems
| Title: | On anonymous and weighted voting systems |
|---|---|
| Authors: | Freixas Bosch, Josep, Pons Vallès, Montserrat |
| Contributors: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs |
| Source: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Publisher Information: | Springer Science and Business Media LLC, 2021. |
| Publication Year: | 2021 |
| Subject Terms: | Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics, social and behavioral sciences::91B Mathematical economics, 05 social sciences, Classificació AMS::91 Game theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs, economics, 91 Game theory, economics, social and behavioral sciences::91A Game theory [Classificació AMS], Anonymous decision systems, Decision making -- Mathematical models, Multichoice games, Enumerations, social and behavioral sciences::91A Game theory, 0502 economics and business, 91 Game theory, economics, social and behavioral sciences::91B Mathematical economics [Classificació AMS], Presa de -- Models matemàtics, Weighted decision systems, Vot -- Models matemàtics, Decisió, Voting -- Mathematical models, Decisió, Presa de -- Models matemàtics, Matemàtiques i estadística::Investigació operativa::Teoria de jocs [Àrees temàtiques de la UPC], Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory, Decision-making, Pseudo-Boolean functions |
| Description: | Many bodies around the world make their decisions through voting systems in which voters have several options and the collective result also has several options. Many of these voting systems are anonymous, i.e., all voters have an identical role in voting. Anonymous simple voting games, a binary vote for voters and a binary collective decision, can be represented by an easy weighted game, i.e., by means of a quota and an identical weight for the voters. Widely used voting systems of this type are the majority and the unanimity decision rules. In this article, we analyze the case in which voters have two or more voting options and the collective result of the vote has also two or more options. We prove that anonymity implies being representable through a weighted game if and only if the voting options for voters are binary. As a consequence of this result, several significant enumerations are obtained. This research was partially supported by funds from the Spanish Ministry of Science and Innovation grant PID2019-I04987GB-I00. We are grateful to the associate editor and two anonymous referees whose interesting comments allowed us to improve the paper. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1573-7187 0040-5833 |
| DOI: | 10.1007/s11238-021-09814-3 |
| DOI: | 10.13039/501100011033 |
| Access URL: | https://upcommons.upc.edu/handle/2117/351964 https://link.springer.com/article/10.1007/s11238-021-09814-3 https://hdl.handle.net/2117/351964 https://doi.org/10.1007/s11238-021-09814-3 |
| Rights: | Springer TDM |
| Accession Number: | edsair.doi.dedup.....1e789e979e3198c35587a481f9cbeedd |
| Database: | OpenAIRE |
| ISSN: | 15737187 00405833 |
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| DOI: | 10.1007/s11238-021-09814-3 |