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Metric rationalization of social welfare functions

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  • Andjiga, Nicolas G.
  • Mekuko, Aurelien Y.
  • Moyouwou, Issofa

Abstract

Metric rationalization of social decision rules has been intensively investigated when the social outcome is a nonempty subset of alternatives. The present paper proposes a similar framework for social welfare functions (SWFs)—that is when each social outcome is a ranking of alternatives. A metric rationalizable SWF reports as an approximation of the unanimity consensus the relative ranking of any pair of alternatives as in the closest profile where individuals all agree on those alternatives, the closeness being measured with respect to a metric on profiles. Two notions of unanimity are in consideration: top unanimity on an alternative holds when individuals all agree that it is top ranked while pairwise unanimity on a pair occurs when individuals all prefer an alternative to another. Without strong requirements on metrics, characterizations provided in both cases show that metric rationalizations of SWFs are essentially equivalent to the Pareto principle for SWFs. Furthermore, two interesting classes of metric rationalizable SWFs–multi-valued scoring SWFs and pairwise scoring SWFs–are each uniquely identified by means of some appropriate and appealing properties on metrics among which decomposability, neutrality and monotonicity are known.

Suggested Citation

  • Andjiga, Nicolas G. & Mekuko, Aurelien Y. & Moyouwou, Issofa, 2014. "Metric rationalization of social welfare functions," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 14-23.
    • Handle: RePEc:eee:matsoc:v:72:y:2014:i:c:p:14-23
    DOI: 10.1016/j.mathsocsci.2014.10.001
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    References listed on IDEAS

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    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Tommi Meskanen & Hannu Nurmi, 2008. "Closeness Counts in Social Choice," Springer Books, in: Matthew Braham & Frank Steffen (ed.), Power, Freedom, and Voting, chapter 15, pages 289-306, Springer.
    3. Lerer, Ehud & Nitzan, Shmuel, 1985. "Some general results on the metric rationalization for social decision rules," Journal of Economic Theory, Elsevier, vol. 37(1), pages 191-201, October.
    4. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
    5. Baigent, Nick, 1987. "Metric rationalisation of social choice functions according to principles of social choice," Mathematical Social Sciences, Elsevier, vol. 13(1), pages 59-65, February.
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