Notions of anonymity for object assignment: impossibility theorems

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.

[1]  Atila Abdulkadiroglu,et al.  HOUSE ALLOCATION WITH EXISTING TENANTS , 1999 .

[2]  Hidekazu Anno.  A short proof for the characterization of the core in housing markets , 2015 .

[3]  S. Pápai,et al.  Strategyproof Assignment by Hierarchical Exchange , 2000 .

[4]  L. Shapley,et al.  On cores and indivisibility , 1974 .

[5]  Lin Zhou.  On a conjecture by gale about one-sided matching problems , 1990 .

[6]  S. Pápai,et al.  Strategyproof multiple assignment using quotas , 2000 .

[7]  Eiichi Miyagawa,et al.  Strategy-Proofness and the Core in House Allocation Problems , 2002, Games Econ. Behav..

[8]  Koji Takamiya,et al.  Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets , 2001, Math. Soc. Sci..

[9]  Hervé Moulin,et al.  A New Solution to the Random Assignment Problem , 2001, J. Econ. Theory.

[10]  Jinpeng Ma.  Strategy-proofness and the strict core in a market with indivisibilities , 1994 .

[11]  William Thomson,et al.  ON THE AXIOMATICS OF RESOURCE ALLOCATION: INTERPRETING THE CONSISTENCY PRINCIPLE , 2012, Economics and Philosophy.

[12]  Lars Ehlers,et al.  Coalitional Strategy-Proof House Allocation , 2002, J. Econ. Theory.

[13]  Lars-Gunnar Svensson.  Strategy-proof allocation of indivisible goods , 1999 .

[14]  Yoichi Kasajima,et al.  Probabilistic assignment of indivisible goods with single-peaked preferences , 2013, Soc. Choice Welf..

[15]  John William Hatfield,et al.  Strategy-proof, efficient, and nonbossy quota allocations , 2009, Soc. Choice Welf..

[16]  Onur Kesten.  The Pareto Dominant Strategy-Proof and Equitable Rule for Problems with Indivisible Goods , 2015 .

[17]  Onur Kesten,et al.  The Pareto-dominant strategy-proof and fair rule for problems with indivisible goods , 2012 .