A Theorem on Aggregating Classifications
Mathematical Social Sciences, Forthcoming
11 Pages Posted: 5 Nov 2015 Last revised: 16 Dec 2015
Date Written: October 26, 2015
Suppose that a group of individuals must classify objects into three or more categories, and does so by aggregating the individual classifications. We show that if the classifications, both individual and collective, are required to put at least one object in each category, then no aggregation rule can satisfy a unanimity and an independence condition without being dictatorial. This impossibility theorem extends a result that Kasher and Rubinstein (1997) proved for two categories and complements another that Dokow and Holzman (2010) obtained for three or more categories under the condition that classifications put at most one object in each category. The paper discusses an interpretation of its result both in terms of Kasher and Rubinstein's group identification problem and in terms of Dokow and Holzman's task assignment problem.
Keywords: Aggregation of classifications, Group identification problem, Task assignment problem, Nonbinary evaluations
JEL Classification: C65, D71
Suggested Citation: Suggested Citation