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Unanimity overruled: Majority voting and the burden of history

  • Nehring, Klaus
  • Pivato, Marcus
  • Puppe, Clemens

Sequential majority voting over interconnected binary propositions can lead to the overruling of unanimous consensus. We characterize, within the general framework of judgement aggregation, under what circumstances this happens for some sequence of the voting process. It turns out that the class of aggregation spaces for which this difficulty arises is very large, including the aggregation of preference orderings over at least four alternatives, the aggregation of equivalence relations over at least four objects, resource allocation problems, and most committee selection problems. We also ask whether it is possible to design respect for unanimity by choosing appropriate decision sequences. Remarkably, while this is not possible in general, it can be accomplished in interesting special cases. Adapting and generalizing a classic result by Shepsle and Weingast, we show that respect for unanimity can indeed be thus guaranteed in case of the aggregation of weak orderings, strict orderings and equivalence relations.

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Paper provided by Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering in its series Working Paper Series in Economics with number 50.

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Date of creation: 2013
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Handle: RePEc:zbw:kitwps:50
Contact details of provider: Web page: http://www.wiwi.kit.edu/

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  1. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  2. Klaus Nehring, 2005. "The (Im)Possibility of a Paretian Rational," Economics Working Papers 0068, Institute for Advanced Study, School of Social Science.
  3. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
  4. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
  5. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2013. "The Condorcet set: Majority voting over interconnected propositions," Working Paper Series in Economics 51, .
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