Notions of Anonymity for Object Assignment: Impossibility Theorems

14 Pages Posted: 6 Mar 2015

See all articles by Hikaru Kondo

Hikaru Kondo

Osaka University - Graduate School of Economics

Shigehiro Serizawa

Osaka University - Institute of Social and Economic Research (ISER)

Date Written: February 27, 2015

Abstract

We search for impartiality in the allocation of objects when monetary transfers are not possible. Our main focus is anonymity. The standard definition requires that if agents' names are permuted, their assignments should be permuted in the same way. Since no rule satisfies this definition in this model, we introduce weaker variants, “anonymity on distinct preferences,” “pairwise-anonymity on distinct preferences,” “pairwise-anonymity on distinct profiles,” and “independence of others' permutations.” We show that for more than two agents and two objects, no rule is pairwise-anonymous on distinct preferences and Pareto-efficient (Theorem 1), no rule is pairwise-anonymous on distinct preferences and independent of others' permutations (Theorem 2), and no rule is pairwise-anonymous on distinct profiles and strategy-proof (Theorem 3). These results suggest that introducing randomization to object allocation problems is almost inevitable for achieving impartiality.

Keywords: impartiality, anonymity, indivisible goods

Suggested Citation

Kondo, Hikaru and Serizawa, Shigehiro, Notions of Anonymity for Object Assignment: Impossibility Theorems (February 27, 2015). ISER Discussion Paper No. 927, Available at SSRN: https://ssrn.com/abstract=2574525

Hikaru Kondo (Contact Author)

Osaka University - Graduate School of Economics ( email )

1-7 Machikaneyama
Toyonaka, Osaka, 560-0043
Japan

Shigehiro Serizawa

Osaka University - Institute of Social and Economic Research (ISER) ( email )

6-1 Mihogaoka
Ibaraki, Osaka 567-0047
Japan
+81 6 6879 8558 (Phone)
+81 6 6878 2766 (Fax)

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