Abstract
A preference defined on a set of alternatives can be extended to a preference on the subsets of alternatives (named opportunity sets) in different ways. We specifically consider the application of the indirect-utility (IU) criterion in various stages, when both the alternatives and the preferences can change over time. In other words, we maintain the symmetry over time as far as criteria are concerned, but neither in the preferences, nor in the alternatives. We characterize this criterion by three testable axioms. Our study bears comparison with Krause (Economic Theory, 2008) for the two-period model.
Highlights
In many decision problems, the final choice is made after a sequential process
We do not aim at characterization of lexicographic preferences, but we focus on a specific criterion with a lexicographic nature instead; nor are we concerned with ranking opportunity sets by the lexicographic application of different criteria, but with ranking opportunity sets in different stages by an overall IU criterion associated with the corresponding preference on the alternatives in each period
Let us prove that if < is a complete preorder on D satisfying Axioms Axiom 1 (A1), Axiom 2 (A2), and Axiom 3 (A3), there exist complete preorders Ri on Xi, i = 1, . . . , n, and such that
Summary
The final choice is made after a sequential process. A selection of a subset of the alternatives from the universal set of options precedes the final decision. The notation there is slightly different from ours, and it is supposed that for all the subsets, “it is natural” to assume its equivalence with a two-element subset (the subset containing the best elements of the set in each period), because he was concerned only with the indirect utility context. For this reason, Krause only expressed the axioms for the two-element sets and used a complete quasi-ordering defined over the set of alternatives.
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