Intermediate notions of rationality for simple allocation problems

Abstract

In this study, we interpret solution rules on a class of simple allocation problems as data on the choices of a policy-maker. We analyze conditions under which the policy maker's choices are (i) rational on a partition (ii) transitiverational on a partition. In addition we introduce two new rationaltiy notions: (i) Constant Proportion rationality,(ii) Constant Distance Rationality. Our main results are as follows: (i) if the elements of a partition is closed under coordinate-wise minimum or coordinate-wise maximum operatation, then a well known property in the literature, contraction independence (a.k.a. IIA) is equivalent to rationality on that partition; (ii) if the characteristics vectors falling into the same element of a partition is ordered Weak Axiom of Revealed Preferences (WARP) is equivalent to transitive rationality.