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The Most Ordinally-Efficient of Random Voting Rules

Author

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  • Anna Bogomolnaia

    (National Research University Higher School of Economics)

Abstract

Aziz and Stursberg [1] propose an “Egalitarian Simultaneous Reservation” rule (ESR), a generalization of Serial rule, one of the most discussed mechanisms in random assignment problem, to the more general random social choice domain. We provide an alternative definition, or characterization, of ESR as the unique most ordinally-egalitarian one. Specifically, given a lottery p over alternatives, for each agent i we define t pi (k) to be the total share in p of objects from her first k indifference classes. ESR is shown to be the unique one which leximin maximizes the vector of all such shares (t p i (k))i;k. Serial rule is known to be characterized by the same property (see [2]). Thus, we provide an alternative way to show that ESR, indeed, coincides with Serial rule on the assignment domain. Moreover, since both rules are defined as the unique most ordinally-egalitarian ones, out result shows that ESR is “the right way” to think about generalizing Serial rule.

Suggested Citation

  • 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.
    • Handle: RePEc:hig:wpaper:106/ec/2015
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    File URL: http://www.hse.ru/data/2015/10/22/1079135488/106EC2015.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    4. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    5. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    6. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    7. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Random Social choice; Random assignment; Serial Rule; Leximin;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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