Weights in stable marriage problems increase manipulation opportunities

Abstract

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, rang-ing from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided mar-ket. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with weighted preferences: each man (resp., woman) provides a score for each woman (resp., man). In this context, we consider the manipulability prop-erties of the procedures that return stable marriages. While we know that all procedures are manipulable by modifying the preference lists or by truncating them, here we consider if manipulation can occur also by just modifying the weights while preserving the ordering and avoiding truncation. It turns out that, by adding weights, we indeed increase the possibility of manipulating and this cannot be avoided by any reasonable restriction on the weights

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Last time updated on 12/04/2017

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