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On the structure of stable tournament solutions

Felix Brandt (), Markus Brill, Hans Georg Seedig and Warut Suksompong
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Felix Brandt: Technical University of Munich
Markus Brill: Oxford University
Hans Georg Seedig: Technical University of Munich
Warut Suksompong: Stanford University

Economic Theory, 2018, vol. 65, issue 2, 483-507

Abstract: 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.

Keywords: Choice consistency; Tournament solutions; Bipartisan set; Tournament equilibrium set (search for similar items in EconPapers)
JEL-codes: D7 C6 (search for similar items in EconPapers)
Date: 2018
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