In this paper we say that a preference over opportunity sets is justifiable if there exists a reflexive and complete binary relation on the set of alternatives, such that one opportunity set is at least as good as a second, if and only if the there is at least one alternative from the first set which is no worse than any alternative of the two sets combined together, with respect to the binary relation on the alternatives. In keeping with the revered tradition set by von Neumann and Morgenstern we call a reflexive and complete binary relation, an abstract game (note: strictly speaking von Neumann and Morgenstern refer to the asymmetric part of a reflexive and complete binary relation as an abstract game; hence our terminology though analytically equivalent, leads to a harmless corruption of the original meaning). In this paper we obtain a necessary and sufficient condition for the justifiability of transitive and quasi transitive preferences over opportunity sets.
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