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

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  • 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.

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Bibliographic Info

Paper provided by EconWPA in its series Public Economics with number 0510021.

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Length: 11 pages
Date of creation: 26 Oct 2005
Date of revision: 26 Oct 2005
Handle: RePEc:wpa:wuwppe:0510021

Note: Type of Document - pdf; pages: 11
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  1. Weinberger, Shmuel, 2004. "On the topological social choice model," Journal of Economic Theory, Elsevier, vol. 115(2), pages 377-384, April.
  2. Kfir Eliaz, 2004. "Social aggregators," Social Choice and Welfare, Springer, vol. 22(2), pages 317-330, 04.
  3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  4. Candeal, Juan Carlos & Indurain, Esteban, 1994. "The Moebius strip and a social choice paradox," Economics Letters, Elsevier, vol. 45(3), pages 407-412.
  5. Luc Lauwers, 1999. "Topological Social Choice," Center for Economic Studies - Discussion papers ces9912, Katholieke Universiteit Leuven, Centrum voor Economische Studiƫn.
  6. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
  7. 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.
  8. Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer, vol. 14(2), pages 295-302.
  9. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer, vol. 14(2), pages 233-243.
  10. Luc Lauwers, 2004. "Topological manipulators form an ultrafilter," Social Choice and Welfare, Springer, vol. 22(3), pages 437-445, 06.
  11. 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.
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