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A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")

Author

Listed:
  • Yasuhito Tanaka

    (Doshisha University)

Abstract

Recently Eliaz(2004) has presented a unified framework to study (Arrovian) social welfare functions and non-binary social choice functions based on the concept of 'preference reversal'. He showed that social choice rules which satisfy the property of preference reversal and a variant of the Pareto principle are dictatorial. This result includes the Arrow impossibility theorem and the Gibbard-Satterthwaite theorem as its special cases. We present a concise proof of his theorem using elementary concepts of algebraic topology such as homomorphisms of homology groups of simplicial complexes induced by simplicial mappings.

Suggested Citation

  • Yasuhito Tanaka, 2005. "A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")," Public Economics 0510021, University Library of Munich, Germany, revised 26 Oct 2005.
  • Handle: RePEc:wpa:wuwppe:0510021
    Note: Type of Document - pdf; pages: 11
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/pe/papers/0510/0510021.pdf
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    References listed on IDEAS

    as
    1. Candeal, Juan Carlos & Indurain, Esteban, 1994. "The Moebius strip and a social choice paradox," Economics Letters, Elsevier, vol. 45(3), pages 407-412.
    2. Weinberger, Shmuel, 2004. "On the topological social choice model," Journal of Economic Theory, Elsevier, vol. 115(2), pages 377-384, April.
    3. Yuliy M. Baryshnikov, 1997. "Topological and discrete social choice: in a search of a theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 199-209.
    4. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March.
    5. 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.
    6. Kfir Eliaz, 2004. "Social aggregators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 317-330, April.
    7. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    8. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
    9. Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 295-302.
    10. Luc Lauwers, 2004. "Topological manipulators form an ultrafilter," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 437-445, June.
    11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    12. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 233-243.
    Full references (including those not matched with items on IDEAS)

    More about this item

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • H - Public Economics

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