Arrow’s Independence Condition

  • David J. Mayston
Chapter
Part of the Macmillan Studies in Economics book series

Abstract

Arrow’s IIA condition requires that every subset S of A be independent in the sense that whenever the individual preference relations between alternatives in S are known, the social choice set C(S) is unaffected by individual rankings of alternatives not in S. The rank-order (or ‘finite ranking’ or ‘Borda’) method (ROM) is an example of a form of SCR which breaks the IIA condition when applied over the whole of A. For a finite number m of alternatives and strict preference orderings, it requires individuals to assign m points to the highest alternative in their ranking, m − 1 points to the next most preferred, and so on down to one point for their least preferred alternative. The social ranking over the m alternatives is determined by summing individual points for each alternative and ranking them according to this total. For the particular case of m = 3, n = 2 with A = {x1, x2, x3}, and under the orderings x1P1x3P1x2; x2P2x1P2x3, we have socially x1Px2. However, if we consider the social ordering taken from the subset S = {x1, x2} of the initial A, the SCR then generates x1Ix2. Hence under this procedure the social preference relation between the pair x1 and x2 is not independent of individual orderings of x3 outside of S, and Arrow’s IIA condition would be broken here.

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Copyright information

© David J. Mayston 1974

Authors and Affiliations

  • David J. Mayston
    • 1
  1. 1.University of EssexUK

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