Extending tournament solutions

Felix Brandt, Markus Brill, Paul Harrenstein

Research output: Contribution to conferencePaperpeer-review

Abstract

An important subclass of social choice functions, so-called C1 functions, only take into account the pairwise majority relation between alternatives. In the absence of majority ties—e.g., when there is an odd number of agents with linear preferences—the majority relation is antisymmetric and complete and can thus conveniently be represented by a tournament. Tournaments have a rich mathematical theory and many formal results for C1 functions assume that the majority relation constitutes a tournament. Moreover, most C1 functions have only been defined for tournaments and allow for a variety of generalizations to unrestricted preference profiles, none of which can be seen as the unequivocal extension of the original function. In this paper, we argue that restricting attention to tournaments is justified by the existence of a conservative extension, which inherits most of the commonly considered properties from its underlying tournament solution.

Original languageEnglish
StatePublished - 2014
Event2014 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2014 - Fort Lauderdale, United States
Duration: 6 Jan 20148 Jan 2014

Conference

Conference2014 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2014
Country/TerritoryUnited States
CityFort Lauderdale
Period6/01/148/01/14

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