# Is majority consistency possible?

## Author Info

Listed author(s):

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• 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

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File URL: http://hdl.handle.net/10.1007/s00355-015-0913-4

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## Bibliographic Info

Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 46 (2016)
Issue (Month): 2 (February)
Pages: 287-299

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 Handle: RePEc:spr:sochwe:v:46:y:2016:i:2:p:287-299 DOI: 10.1007/s00355-015-0913-4 Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/economics/economic+theory/journal/355

## References

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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.
2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
3. Biung-Ghi Ju, 2005. "An efficiency characterization of plurality social choice on simple preference domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 115-128, July.
4. repec:cup:apsrev:v:96:y:2002:i:04:p:745-754_00 is not listed on IDEAS
5. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
6. 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.
7. Mueller,Dennis C., 2003. "Public Choice III," Cambridge Books, Cambridge University Press, number 9780521894753, December.
8. repec:cup:apsrev:v:72:y:1978:i:03:p:831-847_15 is not listed on IDEAS
9. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
10. Mathias Risse, 2005. "Why the count de Borda cannot beat the Marquis de Condorcet," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 95-113, October.
11. repec:cup:apsrev:v:95:y:2001:i:02:p:415-433_00 is not listed on IDEAS
12. Eyal Baharad & Shmuel Nitzan, 2003. "The Borda rule, Condorcet consistency and Condorcet stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 685-688, October.
13. 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.
14. repec:cup:apsrev:v:68:y:1974:i:02:p:537-546_11 is not listed on IDEAS
15. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
16. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
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