Corrigendum to “Resource-monotonicity for house allocation problems”

Abstract

Ehlers and Klaus (Int J Game Theory 32:545–560, 2003) study so-called allocation problems and claim to characterize all rules satisfying efficiency, independence of irrelevant objects, and resource-monotonicity on two preference domains (Ehlers and Klaus 2003, Theorem 1). They explicitly prove Theorem 1 for preference domain \({\mathcal{R}_0}\) which requires that the null object is always the worst object and mention that the corresponding proofs for the larger domain \({\mathcal{R}}\) of unrestricted preferences “are completely analogous.” In Example 1 and Lemma 1, this corrigendum provides a counterexample to Ehlers and Klaus (2003, Theorem 1) on the general domain \({\mathcal{R}}\) . We also propose a way of correcting the result on the general domain \({\mathcal{R}}\) by strengthening independence of irrelevant objects: in addition to requiring that the chosen allocation should depend only on preferences over the set of available objects (which always includes the null object), we add a situation in which the allocation should also be invariant when preferences over the null object change. Finally, we offer a short proof of the corrected result that uses the established result of Theorem 1 for the restricted domain \({\mathcal{R}_0}\).