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Removal independent consensus methods for closed [beta]-systems of sets

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Listed:
  • Crown, Gary D.
  • Janowitz, Melvin F.
  • Powers, Robert C.

Abstract

Let [beta] be a positive integer and let E be a finite nonempty set. A closed [beta]-system of sets on E is a collection H of subsets of E such that A[set membership, variant]H implies A>=[beta], E[set membership, variant]H, and A[intersection]B[set membership, variant]H whenever A,B[set membership, variant]H with A[intersection]B>=[beta]. If is a class of closed [beta]-systems of sets and n is a positive integer, then is a consensus method. In this paper we study consensus methods that satisfy a structure preserving condition called removal independence. The basic idea behind removal independence is that if two input profiles P,P* in agree when restricted to a subset A of E, then their consensus outputs C(P),C(P*) agree when restricted to A. By working with the axiom of removal independence and classes of closed [beta]-systems of sets we obtain a result for consensus methods that is in the same spirit as Arrow's Impossibility Theorem for social welfare functions.

Suggested Citation

  • Crown, Gary D. & Janowitz, Melvin F. & Powers, Robert C., 2009. "Removal independent consensus methods for closed [beta]-systems of sets," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 325-332, May.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:3:p:325-332
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    References listed on IDEAS

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    1. Aleskerov, Fuad, 1995. "Locality in Voting Models," Mathematical Social Sciences, Elsevier, vol. 30(3), pages 320-321, December.
    2. Barthelemy, Jean-Pierre & McMorris, F. R. & Powers, R. C., 1992. "Dictatorial consensus functions on n-trees," Mathematical Social Sciences, Elsevier, vol. 25(1), pages 59-64, December.
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