Abstract
In this paper we consider choice correspondences which may be empty-valued. We study conditions under which such choice correspondences are rational, transitively rational, partially rational, partially almost transitive rational, partially almost quasi-transitive rational. This provides fresh impetus and understanding of multi-criteria decision making.
Highlights
In economics the conventional method adopted to model a decision making problem is to list the set of alternatives from which the decision maker makes his choice
We provide an example of a choice correspondence that satisfies Base Domain Property (BD), Chernoff Axiom (CA) and E but is not transitively rational
There exist partially rational choice correspondences which satisfy Weak Base Domain property (WBD) and E but which do not satisfy this stronger version of our CA
Summary
In economics the conventional method adopted to model a decision making problem is to list the set of alternatives from which the decision maker makes his choice. This property is very similar to the one by the same name introduced by Bossert, Sprumont and Suzumura (2006), where it was assumed that the domain of a choice correspondence includes all one and two element subsets of the universal set of alternatives. We are able to show that if a choice correspondence satisfies (weak) base domain property satisfaction of Chernoff and Expansion is equivalent to it being (partially) rational.
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