A revealed preference analysis of solutions to simple allocation problems

A revealed preference analysis of solutions to simple allocation problems

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Article ID: iaor2012953
Volume: 72
Issue: 4
Start Page Number: 509
End Page Number: 523
Publication Date: Apr 2012
Journal: Theory and Decision
Authors:
Keywords: allocation: resources, decision: rules
Abstract:

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 (ii) transitive‐rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well‐known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other‐c monotonic rule is transitive‐rational; and (iii) every contraction independent and other‐c monotonic rule, if additionally continuous, can be represented by a numerical function.

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