Nota di Lavoro, Fondazione Eni Enrico Mattei 50.2002
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).
Multiset additive linear orders expected utility structure