Choice on the simplex domain

Walter Bossert, Hans Peters

Research output: Working paper / PreprintWorking paper

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One unit of a good has to be divided among a group N of individuals who each
are entitled to a minimal share and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic. The resulting rules are what we refer to as N-path choice functions. If there are only three individuals, the monotonicity property can be weakened. We also consider the issue of rationalizability and show that, for the threeagent
case, excluding cycles of length three in the revealed preference relation implies the strong axiom of revealed preference, that is, the exclusion of cycles of any length.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
Publication statusPublished - 5 Dec 2017

Publication series

SeriesGSBE Research Memoranda

JEL classifications

  • d11 - Consumer Economics: Theory
  • d71 - "Social Choice; Clubs; Committees; Associations"


  • choice functions
  • simplex domain
  • rationalizability

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