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Divide-and-choose with nonmonotonic preferences

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  • Laurence Kranich

    (University at Albany)

Abstract

I consider the divide-and-choose method for allocating fixed quantities of infinitely divisible commodities among two agents when their preferences are commonly known but need not be monotonic. First, I show that with single-dipped preferences, the outcome may not be envy-free (or efficient). Also, it may be advantageous to be the chooser rather than the divider. I then show that if preferences are single-peaked, the divide-and-choose outcome is envy-free. This establishes a significantly weaker sufficient condition for no-envy than monotonicity. Moreover, it shows that it is not the lack of monotonicity per se that may cause the divide-and-choose outcome to be envious but rather a particular type.

Suggested Citation

  • Laurence Kranich, 2019. "Divide-and-choose with nonmonotonic preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 271-276, December.
    • Handle: RePEc:spr:etbull:v:7:y:2019:i:2:d:10.1007_s40505-018-0160-9
    DOI: 10.1007/s40505-018-0160-9
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    References listed on IDEAS

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    1. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 335-352, July.
    2. Öztürk, Murat & Peters, Hans & Storcken, Ton, 2013. "Strategy-proof location of a public bad on a disc," Economics Letters, Elsevier, vol. 119(1), pages 14-16.
    3. Vikram Manjunath, 2014. "Efficient and strategy-proof social choice when preferences are single-dipped," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 579-597, August.
    4. William V. Gehrlein & Dominique Lepelley, 2017. "Elections, Voting Rules and Paradoxical Outcomes," Studies in Choice and Welfare, Springer, number 978-3-319-64659-6, December.
    5. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
    6. Vincent P. Crawford, 1977. "A Game of Fair Division," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 235-247.
    7. Crawford, V. P. & Heller, W. P., 1979. "Fair division with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 21(1), pages 10-27, August.
    8. Klaus, Bettina, 2001. "Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object," Games and Economic Behavior, Elsevier, vol. 34(1), pages 64-82, January.
    9. Lars Ehlers, 2002. "Probabilistic allocation rules and single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 325-348.
    10. William Vickrey, 1960. "Utility, Strategy, and Social Decision Rules," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 74(4), pages 507-535.
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    Cited by:

    1. Dietzenbacher, Bas & Tamura, Yuki, 2023. "Fair and efficient allocations when preferences are single-dipped," Research Memorandum 009, Maastricht University, Graduate School of Business and Economics (GSBE).

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    More about this item

    Keywords

    Divide-and-choose; Envy-free; Divider’s advantage; Nonmonotonic preferences; Single-peaked; Single-dipped;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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