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 $P_2(A)$. |
Keywords
multiset, additive linear order, expected utility structure
Math Review Classification
Primary 91B16
; Secondary 91B12
Last Updated
22 June 2002
Length
28 pages
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