Generalized ultraproduct and Kirman-Sondermann correspondence for vote abstention

Geghard Bedrosian, Alessandra Palmigiano, Zhiguang Zhao

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

Abstract

The present paper refines Herzberg and Eckert’s modeltheoretic approach to aggregation. The proposed refinement is aimed at naturally accounting for vote abstention, and is technically based on a more general notion of ultraproduct than the one standardly occurring in model theory textbooks. Unlike the standard ultraproduct construction, which yields the empty model as soon as any one single coordinate features the empty model, this generalized ultraproduct construction faithfully reflects the indication of ‘large sets’. Thus, our proposed refinement naturally accounts for those situations in which e.g. a voting round is non-null if and only if a ‘large set’ of voters actually participate in the vote. In the present setting, Arrow’s impossibility theorem also covers ‘elections with only two candidates’

Original languageEnglish
Title of host publicationLogic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings
EditorsWen-Fang Wang, Wiebe van der Hoek, Wesley H. Holliday
PublisherSpringer Verlag
Pages27-39
Number of pages13
ISBN (Print)9783662485606
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes
Event5th International Workshop on Logic, Rationality, and Interaction, LORI 2015 - Taipei, Taiwan, Province of China
Duration: 28 Oct 201531 Oct 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9394
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Workshop on Logic, Rationality, and Interaction, LORI 2015
CountryTaiwan, Province of China
CityTaipei
Period28/10/1531/10/15

Keywords

  • generalized ultraproduct
  • Kirman sonderman correspondence
  • model theory
  • Social choice
  • ultrafilter
  • vote abstention

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  • Cite this

    Bedrosian, G., Palmigiano, A., & Zhao, Z. (2015). Generalized ultraproduct and Kirman-Sondermann correspondence for vote abstention. In W-F. Wang, W. van der Hoek, & W. H. Holliday (Eds.), Logic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings (pp. 27-39). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9394). Springer Verlag. https://doi.org/10.1007/978-3-662-48561-3_3