Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902987 | Discrete Mathematics | 2018 | 12 Pages |
Abstract
We investigate preference profiles for a set V of voters, where each voter i has a preference order â»i on a finite set A of alternatives (that is, a linear order on A) such that for each two alternatives a,bâA, voter iprefersa to b if aâ»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 â¹sp on the alternatives such that each voter's preferences on the alternatives along the order â¹sp 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 â¹sc on the voters such that each pair of alternatives divides the order â¹sc 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 âi=2nâ1nâ1iâ1 while the number of single-crossing narcissistic profiles is 2nâ12.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jiehua Chen, Ugo P. Finnendahl,