On the structure of stable tournament solutions

Felix Brandt, Markus Brill, Hans Georg Seedig, Warut Suksompong

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (2) we completely characterize which simple choice functions give rise to stable choice functions, and (3) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament—consisting of 24 alternatives—in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature.

Original languageEnglish
Pages (from-to)483-507
Number of pages25
JournalEconomic Theory
Volume65
Issue number2
DOIs
StatePublished - 1 Mar 2018

Keywords

  • Bipartisan set
  • Choice consistency
  • Tournament equilibrium set
  • Tournament solutions

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