Nehring, Klaus and Pivato, Marcus (2013): Majority rule in the absence of a majority.
There is a more recent version of this item available. 

PDF
MPRA_paper_46721.pdf Download (718kB)  Preview 
Abstract
What is the meaning of "majoritarianism" as a principle of democratic group decisionmaking in a judgement aggregation problem, when the propositionwise majority view is logically inconsistent? We argue that the majoritarian ideal is best embodied by the principle of "supermajority efficiency" (SME). SME reflects the idea that smaller supermajorities must yield to larger supermajorities. We show that in a welldemarcated class of judgement spaces, the SME outcome is generically unique. But in most spaces, it is not unique; we must make tradeoffs between the different supermajorities. We axiomatically characterize the class of "additive majority rules", which specify how such tradeoffs are made. This requires, in general, a hyperrealvalued representation.
Item Type:  MPRA Paper 

Original Title:  Majority rule in the absence of a majority 
Language:  English 
Keywords:  judgement aggregation; majority rule; majoritarian; hyperreal; Condorcet 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations 
Item ID:  46721 
Depositing User:  Marcus Pivato 
Date Deposited:  04 May 2013 17:44 
Last Modified:  03 Oct 2019 01:50 
References:  Anderson, R. M., 1991. Nonstandard analysis with applications to economics. In: Handbook of mathematical economics, Vol. IV. NorthHolland, Amsterdam, pp. 2145–2208. Arrow, K. J., 1963. Individual Values and Social Choice, 2nd Edition. John Wiley & Sons, New York. Barthelemy, J.P., 1989. Social welfare and aggregation procedures: combinatorial and algorithmic aspects. In: Applications of combinatorics and graph theory to the biological and social sciences. Vol. 17 of IMA Vol. Math. Appl. Springer, New York, pp. 39–73. Barthelemy, J.P., Janowitz, M. F., 1991. A formal theory of consensus. SIAM J. Discrete Math. 4 (3), 305–322. Barthelemy, J.P., Monjardet, B., 1981. The median procedure in cluster analysis and social choice theory. Math. Social Sci. 1 (3), 235–267. Barthelemy, J.P., Monjardet, B., 1988. The median procedure in data analysis: new results and open problems. In: Classification and related methods of data analysis (Aachen, 1987). NorthHolland, Amsterdam, pp. 309–316. Black, D. S., 1948. On the rationale of group decisionmaking. J. Political Economy 56, 23–34. Christiano, T., 2006. Democracy. In: Stanford Encylopedia of Philosophy. http:/plato.stanford.edu/archives/spr2009/entries/democracy. Clifford, A. H., 1954. Note on Hahn’s theorem on ordered abelian groups. Proc. Amer. Math. Soc. 5, 860–863. Dietrich, F., List, C., 2010. Majority voting on restricted domains. Journal of Economic Theory 145 (2), 512–543. Goldblatt, R., 1998. Lectures on the hyperreals. Vol. 188 of Graduate Texts in Mathematics. Springer Verlag, New York, an introduction to nonstandard analysis. Gravett, K. A. H., 1956. Ordered abelian groups. Quart. J. Math. Oxford Ser. (2) 7, 57–63. Guilbaud, G.T., OctobreDecembre 1952. Les theories de l’interet general et le probleme logique de l’aggregation. Economie Appliquee V (4), 501–551. Hausner, M., Wendel, J. G., 1952. Ordered vector spaces. Proc. Amer. Math. Soc. 3, 977–982. Kemeny, J. G., Fall 1959. Math without numbers. Daedalus 88, 571–591. Kornhauser, L., Sager, L., 1986. Unpacking the court. Yale Law Journal 96, 82–117. Lindner, T., Nehring, K., Puppe, C., 2010. Allocating public goods via the midpoint rule. (preprint). List, C., Pettit, P., 2002. Aggregating sets of judgements: an impossibility result. Economics and Philosophy 18, 89–110. List, C., Polak, B. e., March 2010. Symposium on judgement aggregation. Journal of Economic Theory 145 (2), 441–638. List, C., Puppe, C., 2009. Judgement aggregation: a survey. In: Oxford handbook of rational and social choice. Oxford University Press, Oxford, UK., pp. 457–482. McKelvey, R. D., 1976. Intransitivities in multidimensional voting models and some implications for agenda control. J. Econom. Theory 12 (3), 472–482. McKelvey, R. D., 1979. General conditions for global intransitivities in formal voting models. Econometrica 47 (5), 1085–1112. Myerson, R. B., 1995. Axiomatic derivation of scoring rules without the ordering assumption. Soc. Choice Welf. 12 (1), 59–74. Nehring, K., Pivato, M., 2011. Incoherent majorities: the McGarvey problem in judgement aggregation. Discrete Applied Mathematics 159, 1488–1507. Nehring, K., Pivato, M., 2012a. Additive majority rules in judgement aggregation. (preprint). Nehring, K., Pivato, M., 2012b. The median rule in judgement aggregation. (preprint). Nehring, K., Pivato, M., Puppe, C., July 2011. Condorcet admissibility: Indeterminacy and pathdependence under majority voting on interconnected decisions. (preprint). URL http://mpra.ub.unimuenchen.de/32434 Nehring, K., Puppe, C., 2007. The structure of strategyproof social choice I: General characterization and possibility results on median spaces. J.Econ.Theory 135, 269–305. Nehring, K., Puppe, C., 2010. Justifiable group choice. J. Econom. Theory 145 (2), 583–602. Pivato, M., 2009. Geometric models of consistent judgement aggregation. Soc. Choice Welf. 33 (4), 559–574. Rubinstein, A., Fishburn, P. C., 1986. Algebraic aggregation theory. J. Econom. Theory 38 (1), 63–77. Tideman, T. N., 1987. Independence of clones as a criterion for voting rules. Soc. Choice Welf. 4 (3), 185–206. Waldron, J., 1999. The Dignity of Legislation. Cambridge University Press. Wilson, R., 1975. On the theory of aggregation. J. Econom. Theory 10 (1), 89–99. Young, H. P., Levenglick, A., 1978. A consistent extension of Condorcet’s election principle. SIAM J. Appl. Math. 35 (2), 285–300. Zavist, T. M., Tideman, T. N., 1989. Complete independence of clones in the ranked pairs rule. Soc. Choice Welf. 6 (2), 167–173. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/46721 
Available Versions of this Item
 Majority rule in the absence of a majority. (deposited 04 May 2013 17:44) [Currently Displayed]