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Choosing k from m: feasible elimination procedures reconsidered

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  • Bezalel Peleg
  • Hans Peters

Abstract

We show that feasible elimination procedures (Peleg, 1978) can be used to select k from m alternatives. An important advantage of this method is the core property: no coalition can guarantee an outcome that is preferred by all its members. We also provide an axiomatic characterization for the case k = 1, using the conditions of anonymity, Maskin monotonicity, and independent blocking. Finally, we show for any k that outcomes of feasible elimination procedures can be computed in polynomial time, by showing that the problem is computationally equivalent to finding a maximal matching in a bipartite graph.

Suggested Citation

  • Bezalel Peleg & Hans Peters, 2014. "Choosing k from m: feasible elimination procedures reconsidered," Discussion Paper Series dp671, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp671
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    References listed on IDEAS

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    1. Peleg, Bezalel & Peters, Hans, 2017. "Feasible elimination procedures in social choice: An axiomatic characterization," Research in Economics, Elsevier, vol. 71(1), pages 43-50.
    2. Holzman, Ron, 1986. "On strong representations of games by social choice functions," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 39-57, February.
    3. Oren, Ishai, 1981. "The structure of exactly strongly consistent social choice functions," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 207-220, October.
    4. Bezalel Peleg & Hans Peters, 2010. "Consistent voting systems with a continuum of voters," Studies in Choice and Welfare, in: Strategic Social Choice, chapter 0, pages 123-145, Springer.
    5. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    6. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    7. Dutta, Bhaskar & Pattanaik, Prasanta K, 1978. "On Nicely Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 163-170, January.
    8. Bezalel Peleg & Hans Peters, 2010. "Strategic Social Choice," Studies in Choice and Welfare, Springer, number 978-3-642-13875-1, December.
    9. Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 4, pages 173-236, Elsevier.
    10. Peleg, Bezalel, 1978. "Consistent Voting Systems," Econometrica, Econometric Society, vol. 46(1), pages 153-161, January.
    11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

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    2. Aziz, Haris & Lee, Barton E., 2022. "A characterization of proportionally representative committees," Games and Economic Behavior, Elsevier, vol. 133(C), pages 248-255.

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    More about this item

    Keywords

    Feasible elimination procedure ; choosing k from m ; axiomatization ; computation;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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