Ranking Committees, Words or Multisets

Murat Sertel, Arkadii Slinko


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 $card(A)=3$, all linear orders on $P_k(A)$ are additive and classify them by
means of Farey fractions. For $card(A)ge 4$ 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 $P_2(A)$.

multiset, additive linear order, expected utility structure

Math Review Classification
Primary 91B16 ; Secondary 91B12

Last Updated
22 June 2002

28 pages

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