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The Sum of the Parts Can Violate the Whole

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  • Saari, Donald G.

Abstract

We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives and to offer new interpretations for pairwise voting. The source of the problems—an unanticipated loss of available information—also explains a variety of other phenomena, such as Simpson’s paradox (a statistical paradox in which the behavior of the “parts” disagrees with that of the “whole”) and Arrow’s theorem from social choice.

Suggested Citation

  • Saari, Donald G., 2001. "The Sum of the Parts Can Violate the Whole," American Political Science Review, Cambridge University Press, vol. 95(2), pages 415-433, June.
    • Handle: RePEc:cup:apsrev:v:95:y:2001:i:02:p:415-433_00
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    Cited by:

    1. Gennaro Amendola & Luigi Marengo & Simona Settepanella, 2012. "Decidability and manipulability in social choice," LEM Papers Series 2012/11, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. Donald G. Saari, 2015. "Voting mysteries: a picture is worth a thousand words," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 16, pages 284-302, Edward Elgar Publishing.
    3. Simon Hug & George Tsebelis, 2002. "Veto Players and Referendums Around the World," Journal of Theoretical Politics, , vol. 14(4), pages 465-515, October.
    4. Shanti P. Chakravarty, 2018. "Democratic Participation," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(3), pages 235-254, September.
    5. Amihai Glazer & Anthony McGann, 2005. "Direct Democracy and the Stability of State Policy," Working Papers 050615, University of California-Irvine, Department of Economics.
    6. Antoinette Baujard, 2022. "Ethics and Technique in Welfare Economics: How Welfarism Evolves in the Making," Revue économique, Presses de Sciences-Po, vol. 73(6), pages 1039-1053.
    7. Luigi Marengo & Davide Pirino & Simona Settepanella & Akimichi Takemura, 2012. "Decidability in complex social choices," LEM Papers Series 2012/12, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    8. Luigi Marengo & Simona Settepanella, 2010. "Social choice among complex objects," LEM Papers Series 2010/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    9. Nurmi, Hannu, 2005. "Aggregation problems in policy evaluation: an overview," European Journal of Political Economy, Elsevier, vol. 21(2), pages 287-300, June.
    10. Douglas D. Roscoe, 2014. "Yes, Raise My Taxes: Property Tax Cap Override Elections," Social Science Quarterly, Southwestern Social Science Association, vol. 95(1), pages 145-164, March.
    11. Lang, Jrme & Xia, Lirong, 2009. "Sequential composition of voting rules in multi-issue domains," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 304-324, May.
    12. Lingfang (Ivy) Li & Donald Saari, 2008. "Sen’s theorem: geometric proof, new interpretations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(3), pages 393-413, October.
    13. 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.

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