An approval-voting polytope for linear orders

Jean Paul Doignon, Michel Regenwetter

Research output: Contribution to journalArticlepeer-review


A probabilistic model of approval voting onnalternatives generates a collection of probability distributions on the family of all subsets of the set of alternatives. Focusing on thesize-independent modelproposed by Falmagne and Regenwetter, we recast the problem of characterizing these distributions as the search for a minimal system of linear equations and inequalities for a specific convex polytope. This approval-voting polytope, withn! vertices in a space of dimension 2n, is proved to be of dimension 2n-n-1. Several families of facet-defining linear inequalities are exhibited, each of which has a probabilistic interpretation. Some proofs rely on special sequences of rankings of the alternatives. Although the equations and facet-defining inequalities found so far yield a complete minimal description whenn≤4 (as indicated by the PORTA software), the problem remains open for larger values ofn.

Original languageEnglish (US)
Pages (from-to)171-188
Number of pages18
JournalJournal of Mathematical Psychology
Issue number2
StatePublished - Jun 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Psychology
  • Applied Mathematics


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