Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abraham, D.K., Irving, R.W., Kavitha, T., Mehlhorn, K.: Popular matchings. SIAM Journal on Computing 37(4), 1030–1034 (2007)
Aziz, H., Brandt, F., Brill, M.: On the tradeoff between economic efficiency and strategyproofness in randomized social choice. In: Proc. of 12th AAMAS Conference, pp. 455–462. IFAAMAS (2013)
Biró, P., Irving, R.W., Manlove, D.F.: Popular matchings in the marriage and roommates problems. In: Calamoneri, T., Diaz, J. (eds.) CIAC 2010. LNCS, vol. 6078, pp. 97–108. Springer, Heidelberg (2010)
Bogomolnaia, A., Moulin, H.: A new solution to the random assignment problem. Journal of Economic Theory 100(2), 295–328 (2001)
Budish, E., Che, Y.-K., Kojima, F., Milgrom, P.: Designing random allocation mechanisms: Theory and applications. American Economic Review (forthcoming, 2013)
Cho, W.J.: Probabilistic assignment: A two-fold axiomatic approach (unpublished manuscript, 2012)
Felsenthal, D.S., Machover, M.: After two centuries should Condorcet’s voting procedure be implemented? Behavioral Science 37(4), 250–274 (1992)
Fishburn, P.C.: Probabilistic social choice based on simple voting comparisons. Review of Economic Studies 51(167), 683–692 (1984)
Fisher, D.C., Ryan, J.: Tournament games and positive tournaments. Journal of Graph Theory 19(2), 217–236 (1995)
Gärdenfors, P.: Match making: Assignments based on bilateral preferences. Behavioral Science 20(3), 166–173 (1975)
Katta, A.-K., Sethuraman, J.: A solution to the random assignment problem on the full preference domain. Journal of Economic Theory 131(1), 231–250 (2006)
Kavitha, T.: Popularity vs maximum cardinality in the stable marriage setting. In: Proc. of 23rd SODA, pp. 123–134. ACM Press (2012)
Kavitha, T., Mestre, J., Nasre, M.: Popular mixed matchings. Theoretical Computer Science 412(24), 2679–2690 (2011)
Kreweras, G.: Aggregation of preference orderings. In: Sternberg, S., Capecchi, V., Kloek, T., Leenders, C. (eds.) Mathematics and Social Sciences I: Proceedings of the Seminars of Menthon-Saint-Bernard, France (July 1-27, 1960), and of Gösing, Austria (July 3-27, 1962), pp. 73–79 (1965)
Laffond, G., Laslier, J.-F., Le Breton, M.: The bipartisan set of a tournament game. Games and Economic Behavior 5, 182–201 (1993)
Manea, M.: Serial dictatorship and Pareto optimality. Games and Economic Behavior 61, 316–330 (2007)
McCutchen, R.M.: The least-unpopularity-factor and least-unpopularity-margin criteria for matching problems with one-sided preferences. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 593–604. Springer, Heidelberg (2008)
Moulin, H.: Fair Division and Collective Welfare. The MIT Press (2003)
Rivest, R.L., Shen, E.: An optimal single-winner preferential voting system based on game theory. In: Proc. of 3rd International Workshop on Computational Social Choice, pp. 399–410 (2010)
Roth, A.E.: Repugnance as a constraint on markets. Journal of Economic Perspectives 21(3), 37–58 (2007)
Young, H.P.: Dividing the indivisible. American Behavioral Scientist 38, 904–920 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aziz, H., Brandt, F., Stursberg, P. (2013). On Popular Random Assignments. In: Vöcking, B. (eds) Algorithmic Game Theory. SAGT 2013. Lecture Notes in Computer Science, vol 8146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41392-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-41392-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41391-9
Online ISBN: 978-3-642-41392-6
eBook Packages: Computer ScienceComputer Science (R0)