Preference structures I: Distances between transitive preference relations†
- 1 July 1973
- journal article
- research article
- Published by Informa UK Limited in The Journal of Mathematical Sociology
- Vol. 3 (1), 49-67
- https://doi.org/10.1080/0022250x.1973.9989823
Abstract
This paper generalizes the Kemeny‐Snell distance function for distances between weak orderings to a distance function for the collection of all partial orderings of a set. This generalization explains some of the seemingly strange properties of the Kemeny‐Snell distance, and extends it to such important classes of orderings as semiorders and interval orders. In section four I consider possible applications of the distance function and describe a number of problems that arise in attempts to apply the distance function. In section 3 I discuss the concept of a distance function in more general terms and introduce a new distance function defined by a set of axioms different from those given in Section 2.Keywords
This publication has 1 reference indexed in Scilit:
- Social Welfare Functions Based on Individual RankingsAmerican Journal of Sociology, 1952