A Theorem on Aggregating Classifications

Mathematical Social Sciences, Forthcoming

HEC Paris Research Paper No. ECO/SCD-2015-1116

11 Pages Posted: 5 Nov 2015 Last revised: 16 Dec 2015

See all articles by Francois Maniquet

Francois Maniquet

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Philippe Mongin

GREGHEC; CNRS & HEC Paris - Economics & Decision Sciences

Date Written: October 26, 2015

Abstract

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

Maniquet, Francois and Mongin, Philippe, A Theorem on Aggregating Classifications (October 26, 2015). Mathematical Social Sciences, Forthcoming; HEC Paris Research Paper No. ECO/SCD-2015-1116. Available at SSRN: https://ssrn.com/abstract=2686037

Francois Maniquet

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium
+32 10 474328 (Phone)
+32 10 474301 (Fax)

HOME PAGE: http://www.core.ucl.ac.be/staff/maniquetcore.htm

Philippe Mongin (Contact Author)

GREGHEC ( email )

1 rue de la Libération
Jouy-en-Josas, 78350
France

CNRS & HEC Paris - Economics & Decision Sciences ( email )

Paris
France

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