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Is majority consistency possible?

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  • Eyal Baharad

    ()

  • Shmuel Nitzan

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Abstract

The most well-known approaches to decision rules are inspired by “majority-based” and “ranking-based” utilitarianism. The long lasting discussion on the appropriate collective decision mechanism is based on the merits of the rules consistent with these two approaches. Focusing on conformity with qualified majority, we propose single-approval multiple-rejection (SAMR) as a plausible flexible scoring rule narrowing the gap between the two approaches. Given k alternatives, such a mechanism permits approval of a single alternative and rejection of at most $$(k-2)$$ ( k - 2 ) alternatives allowing any relative significance of the approved vs. the rejected alternatives. SAMR is the unique type of rule that spans the whole spectrum of the qualified majority-based utilitarian rules, independent of k. Our first characterization result exposes the relationship between its consistency with any predetermined $$\alpha $$ α -majority based rule, $$\alpha >1/2$$ α > 1 / 2 , and the best/worst (approval/rejection) relative weight p. Our second result establishes that the plurality rule is the unique scoring rule consistent with any $$\alpha $$ α -majority, $$\alpha > 1/2$$ α > 1 / 2 . These results imply the impossibility of universal scoring-rule consistency with any ideal or real $$\alpha $$ α -majority. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Eyal Baharad & Shmuel Nitzan, 2016. "Is majority consistency possible?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 287-299, February.
  • Handle: RePEc:spr:sochwe:v:46:y:2016:i:2:p:287-299
    DOI: 10.1007/s00355-015-0913-4
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    References listed on IDEAS

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    1. Jerry S. Kelly & Donald E. Campbell, 2000. "A simple characterization of majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 689-700.
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    10. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
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    14. Eyal Baharad & Shmuel Nitzan, 2007. "The Costs of Implementing the Majority Principle: The Golden Voting Rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 69-84, April.
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    Cited by:

    1. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which "Almost" Rule is Optimal?," CESifo Working Paper Series 6851, CESifo Group Munich.
    2. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," IZA Discussion Papers 11287, Institute for the Study of Labor (IZA).
    3. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," GLO Discussion Paper Series 185, Global Labor Organization (GLO).
    4. repec:spr:grdene:v:27:y:2018:i:1:d:10.1007_s10726-017-9553-7 is not listed on IDEAS
    5. Muhammad Mahajne & Oscar Volij, 2017. "The Socially Acceptable Scoring Rule," Working Papers 1705, Ben-Gurion University of the Negev, Department of Economics.

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