A New Solution to the Random Assignment Problem

A random assignment is ordinally efficient if it is not stochastically dominated with respect to individual preferences over sure objects. Ordinal efficiency implies (is implied by) ex post (ex ante) efficiency. A simple algorithm characterizes ordinally efficient assignments: our solution, probabilistic serial (PS), is a central element within their set. Random priority (RP) orders agents from the uniform distribution, then lets them choose successively their best remaining object. RP is ex post, but not always ordinally, efficient. PS is envy-free, RP is not; RP is strategy-proof, PS is not. Ordinal efficiency, Strategyproofness, and equal treatment of equals are incompatible. Journal of Economic Literature Classification Numbers: C78, D61, D63.

[1]  R. Zeckhauser,et al.  The Efficient Allocation of Individuals to Positions , 1979, Journal of Political Economy.

[2]  Janet L. Johnson.  Sex Differentials in Unemployment Rates: A Case for No Concern , 1983, Journal of Political Economy.

[3]  Allan Gibbard,et al.  Straightforwardness of Game Forms with Lotteries as Outcomes , 1978 .

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

[5]  H. Varian,et al.  Theories of Justice Based on Symmetry , 1984 .

[6]  U. Rothblum,et al.  Truncation Strategies in Matching Markets-in Search of Advice for Participants , 1999 .

[7]  J. Kagel,et al.  Handbook of Experimental Economics , 1997 .

[8]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[9]  Atila Abdulkadiroglu,et al.  RANDOM SERIAL DICTATORSHIP AND THE CORE FROM RANDOM ENDOWMENTS IN HOUSE ALLOCATION PROBLEMS , 1998 .

[10]  H. Varian.  Equity, Envy and Efficiency , 1974 .

[11]  L. Hurwicz,et al.  Social Goals and Social Organization , 1986 .

[12]  H. Moulin,et al.  A simple random assignment problem with a unique solution , 2002 .

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

[14]  H. Leonard.  Elicitation of Honest Preferences for the Assignment of Individuals to Positions , 1983, Journal of Political Economy.

[15]  Andrew McLennan,et al.  Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem , 2002, J. Econ. Theory.

[16]  Hervé Moulin,et al.  Scheduling with Opting Out: Improving upon Random Priority , 2001, Oper. Res..

[17]  Tayfun Sönmez,et al.  Ordinal efficiency and dominated sets of assignments , 2003, J. Econ. Theory.

[18]  W. Hofstee,et al.  Allocation by lot: a conceptual and empirical analysis , 1990 .