FEEM working papers "Note di lavoro" series
2002 .050

Ranking Committees, Words or Multisets


Authors: Arkadii Slinko, Murat Sertel
Series: Climate Change and Sustainable Development
Editor: Carlo Carraro
Type: Journal
Keywords: Multiset,additive linear orders,expected utility structure
JEL n.: D71
JEL: Forthcoming in Economic Theory

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 Pk(A) of multisets on A of fixed cardinality k. We show that for card(A) = 3 all linear orders on Pk(A) are additive and classify them by means of Farey fractions. For card(A) minor/equal 4 we show that there are non-additive consistent linear orders of Pk(A), we prove that they cannot be extended to a linear order of Pk(A) for K sufficiently large. We give the lower bounds for the number of additive linear orders in P2(A) and the total number of consistent linear orders in P2(A).
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