Ranking Committees, Words or Multisets

Sertel, Murat; Slinko, Arkadii

Ranking Committees, Words or Multisets

Sertel, Murat

Slinko, Arkadii

Reference

Department of Mathematics - Research Reports-482 (2002)

Abstract

We investigate the ways in which a linear order on a finite set $A$ can be consistently extended to a linear order on a set $P k (A)$ of multisets on $A$ of cardinality $k$ . We show that, when $c a r d (A)=3$ , all linear orders on $P k (A)$ are additive and classify them by means of Farey fractions. For $c a r d (A) g e 4$ we show that there are non-additive consistent linear orders on $P k (A)$ , we prove that they cannot be extended to a consistent linear order on $P K (A)$ for sufficiently large $K$ . We give the lower bounds for the number of consistent linear orders on $P 2(A)$ and for the total number of consistent linear orders on $P 2(A)$ .