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Choice on the simplex domain

Author

Listed:
  • Bossert, Walter
  • Peters, Hans

    (QE Math. Economics & Game Theory, RS: GSBE ETBC)

Abstract

One unit of a good has to be divided among a group N of individuals who each are entitled to a minimal share and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic. The resulting rules are what we refer to as N-path choice functions. If there are only three individuals, the monotonicity property can be weakened. We also consider the issue of rationalizability and show that, for the threeagent case, excluding cycles of length three in the revealed preference relation implies the strong axiom of revealed preference, that is, the exclusion of cycles of any length.

Suggested Citation

  • Bossert, Walter & Peters, Hans, 2017. "Choice on the simplex domain," Research Memorandum 030, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2017030
    DOI: 10.26481/umagsb.2017030
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    References listed on IDEAS

    as
    1. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 213-230, November.
    2. Stovall, John E., 2014. "Collective rationality and monotone path division rules," Journal of Economic Theory, Elsevier, vol. 154(C), pages 1-24.
    3. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
    4. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, Spring.
    5. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1995. "Multi-valued demand and rational choice in the two-commodity case," Economics Letters, Elsevier, vol. 47(1), pages 5-10, January.
    6. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 124-125.
    7. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    10. Peters Hans & Wakker Peter, 1994. "WARP Does Not Imply SARP for More Than Two Commodities," Journal of Economic Theory, Elsevier, vol. 62(1), pages 152-160, February.
    11. Özgür Kıbrıs, 2012. "A revealed preference analysis of solutions to simple allocation problems," Theory and Decision, Springer, vol. 72(4), pages 509-523, April.
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    More about this item

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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