On Popular Random Assignments

One of the most fundamental and ubiquitous problems in microeconomics and operations research is how to assign objects to agents based on their individual preferences. An assignment is called popular if there is no other assignment that is preferred by a majority of the agents. Popular assignments need not exist, but the minimax theorem implies the existence of a popular random assignment. In this paper, we study the compatibility of popularity with other properties that have been considered in the literature on random assignments, namely efficiency, equal treatment of equals, envy-freeness, and strategyproofness.

[1]  Jay Sethuraman,et al.  A solution to the random assignment problem on the full preference domain , 2006, J. Econ. Theory.

[2]  P. Fishburn Probabilistic Social Choice Based on Simple Voting Comparisons , 1984 .

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

[4]  David Manlove,et al.  Popular Matchings in the Marriage and Roommates Problems , 2010, CIAC.

[5]  Jennifer Ryan,et al.  Tournament games and positive tournaments , 1995, J. Graph Theory.

[6]  H. Peyton Young Dividing the Indivisible , 1995 .

[7]  P. Gärdenfors Match making: Assignments based on bilateral preferences , 1975 .

[8]  Kurt Mehlhorn,et al.  Popular matchings , 2005, SODA '05.

[9]  R. Rivest,et al.  An Optimal Single-Winner Preferential Voting System Based on Game Theory , 2010 .

[10]  Telikepalli Kavitha,et al.  Popular mixed matchings , 2009, Theor. Comput. Sci..

[11]  Hervé Moulin,et al.  Fair division and collective welfare , 2003 .

[12]  Felix Brandt,et al.  On the tradeoff between economic efficiency and strategy proofness in randomized social choice , 2013, AAMAS.

[13]  Mihai Manea Serial dictatorship and Pareto optimality , 2007, Games Econ. Behav..

[14]  M. Breton,et al.  The Bipartisan Set of a Tournament Game , 1993 .

[15]  Herbert S. Wilf,et al.  Algorithms and Complexity , 2010, Lecture Notes in Computer Science.

[16]  Paul R. Milgrom,et al.  Designing Random Allocation Mechanisms: Theory and Applications , 2013 .

[17]  Eduardo Sany Laber,et al.  LATIN 2008: Theoretical Informatics, 8th Latin American Symposium, Búzios, Brazil, April 7-11, 2008, Proceedings , 2008, Lecture Notes in Computer Science.

[18]  W. Cho Probabilistic Assignment : A Two-fold Axiomatic Approach , 2012 .

[19]  Richard Matthew McCutchen The Least-Unpopularity-Factor and Least-Unpopularity-Margin Criteria for Matching Problems with One-Sided Preferences , 2008, LATIN.

[20]  Dan S. Felsenthal,et al.  After two centuries, should condorcet's voting procedure be implemented? , 1992 .

[21]  Telikepalli Kavitha Popularity vs maximum cardinality in the stable marriage setting , 2012, SODA.