On the number of single-peaked narcissistic or single-crossing narcissistic preference profiles

Jiehua Chen, Ugo P. Finnendahl

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We investigate preference profiles for a set V of voters, where each voter i has a preference order ≻i on a finite set A of alternatives (that is, a linear order on A) such that for each two alternatives a,b∈A, voter i prefers a to b if a≻ib. Such a profile is narcissistic if each alternative a is preferred the most by at least one voter. It is single-peaked if there is a linear order ▹sp on the alternatives such that each voter's preferences on the alternatives along the order ▹sp are either strictly increasing, or strictly decreasing, or first strictly increasing and then strictly decreasing. It is single-crossing if there is a linear order ▹sc on the voters such that each pair of alternatives divides the order ▹sc into at most two suborders, where in each suborder, all voters have the same linear order on this pair. We show that for n voters and n alternatives, the number of single-peaked narcissistic profiles is ∏i=2n−1[Formula presented] while the number of single-crossing narcissistic profiles is 2[Formula presented].

Original languageEnglish
Pages (from-to)1225-1236
Number of pages12
JournalDiscrete Mathematics
Volume341
Issue number5
DOIs
StatePublished - 1 May 2018

Keywords

  • Narcissistic preferences
  • Semi-standard Young tableaux
  • Single-crossing preferences
  • Single-peaked preferences

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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