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Lebesgue Measure and Social Choice Trade-offs

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  • Campbell, Donald E
  • Kelly, Jerry S

Abstract

An Arrovian social choice rule is a social welfare function satisfying independence of irrelevant alternatives and transitivity of social preference. Assume a measurable outcome space X with its (Lebesgue) measure normalized to unity. For any Arrovian rule and any fraction t, either some individual dictates over a subset of X of measure t or more, or at least a fraction 1 - t of the pairs of distinct alternatives have their social ordering fixed independently of individual preferences. Also, for any positive integer "Beta" (less than the total number of individuals), there is some subset H of society consisting of all but "Beta" persons such that the fraction of outcome pairs (x,y) that are social ranked without consulting the preferences of anyone in H, whenever no individual is indifferent between x and y, is at least 1 - 1/4("Beta").

Suggested Citation

  • Campbell, Donald E & Kelly, Jerry S, 1995. "Lebesgue Measure and Social Choice Trade-offs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 445-459, May.
    • Handle: RePEc:spr:joecth:v:5:y:1995:i:3:p:445-59
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    Cited by:

    1. Campbell, Donald E. & Kelly, Jerry S., 1996. "Social choice trade-offs for an arbitrary measure: With application to uncertain or fuzzy agenda," Economics Letters, Elsevier, vol. 50(1), pages 99-104, January.
    2. Campbell, Donald E. & Kelly, Jerry S., 1996. "Trade-offs in the spatial model of resource allocation," Journal of Public Economics, Elsevier, vol. 60(1), pages 1-19, April.
    3. Campbell, Donald E. & Kelly, Jerry S., 2015. "Social choice trade-off results for conditions on triples of alternatives," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 42-45.
    4. Campbell, Donald E. & Kelly, Jerry S., 1995. "Asymptotic density and social choice trade-offs," Mathematical Social Sciences, Elsevier, vol. 29(3), pages 181-194, June.

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