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Probabilistic assignment of objects: Characterizing the serial rule


  • Bogomolnaia, Anna
  • Heo, Eun Jeong


We study the problem of assigning a set of objects to a set of agents, when each agent receives one object and has strict preferences over the objects. In the absence of monetary transfers, we focus on the probabilistic rules, which take the ordinal preferences as input. We characterize the serial rule, proposed by Bogomolnaia and Moulin (2001) [2]: it is the only rule satisfying sd efficiency, sd no-envy, and bounded invariance. A special representation of feasible assignment matrices by means of consumption processes is the key to the simple and intuitive proof of our main result.

Suggested Citation

  • Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:2072-2082 DOI: 10.1016/j.jet.2012.05.013

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    References listed on IDEAS

    1. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    2. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    3. Zhou, Lin, 1990. "On a conjecture by gale about one-sided matching problems," Journal of Economic Theory, Elsevier, vol. 52(1), pages 123-135, October.
    4. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
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    Cited by:

    1. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    2. Heo, Eun Jeong & Yılmaz, Özgür, 2015. "A characterization of the extended serial correspondence," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 102-110.
    3. Saban, Daniela & Sethuraman, Jay, 2014. "A note on object allocation under lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 283-289.
    4. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    5. repec:eee:matsoc:v:90:y:2017:i:c:p:80-92 is not listed on IDEAS
    6. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    7. Bogomolnaia, Anna, 2015. "Random assignment: Redefining the serial rule," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 308-318.
    8. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    9. repec:eee:matsoc:v:90:y:2017:i:c:p:56-62 is not listed on IDEAS
    10. Afacan, Mustafa Oǧuz, 2013. "Alternative characterizations of Boston mechanism," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 176-179.
    11. Anna Bogomolnaia, 2015. "The Most Ordinally-Efficient of Random Voting Rules," HSE Working papers WP BRP 106/EC/2015, National Research University Higher School of Economics.
    12. repec:eee:gamebe:v:105:y:2017:i:c:p:1-8 is not listed on IDEAS

    More about this item


    Probabilistic assignment; Serial rule; Sd efficiency; Sd no-envy; Bounded invariance; Consumption process;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement


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