Pivato, Marcus and Nehring, Klaus (2010): The McGarvey problem in judgement aggregation.
Download (293kB) | Preview
`Judgement aggregation' is a model of social choice where the space of social alternatives is the set of consistent truth-valuations (`judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. We show that, for a variety of spaces, propositionwise majority voting can yield any possible judgement. By considering the geometry of sub-polytopes of the Hamming cube, we also estimate the number of voters required to achieve all possible judgements. These results generalize the classic results of McGarvey (1953) and Stearns (1959).
|Item Type:||MPRA Paper|
|Original Title:||The McGarvey problem in judgement aggregation|
|Keywords:||judgement aggregation; majority vote; McGarvey; Stearns; 0/1 polytope; Hamming cube;|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General|
|Depositing User:||Marcus Pivato|
|Date Deposited:||11. May 2010 10:40|
|Last Modified:||31. Dec 2015 00:12|
 G.-T. Guilbaud, Les theories de l'interet general et le probleme logique de l'aggregation, Economie Appliquee V (4) (1952)
 R. Wilson, On the theory of aggregation, J. Econom. Theory 10 (1) (1975) 89-99.
 A. Rubinstein, P. C. Fishburn, Algebraic aggregation theory, J. Econom. Theory 38 (1) (1986) 63-77.
 J.-P. Barthelemy, M. F. Janowitz, A formal theory of consensus, SIAM J. Discrete Math. 4 (3) (1991) 305-322. ee  C. List, P. Pettit, Aggregating sets of judgements: an impossibility result, Economics and Philosophy 18 (2002) 89-110.
 C. List, C. Puppe, Judgement aggregation: a survey, in: Oxford handbook of rational and social choice, Oxford University Press, Oxford, UK, 2009.
 Condorcet, Marquis de, Essai sur l'application de l'analyse a la probabilite des decisions rendues a la pluralite des voix, Paris (1785).
 D. C. McGarvey, A theorem on the construction of voting paradoxes, Econometrica 21 (1953) 608-610.
 K. Nehring, C. Puppe, The structure of strategy-proof social choice I: General characterization and possibility results on median spaces, J.Econ.Theory 135 (2007) 269-305.
 K. Nehring, C. Puppe, Abstract arrowian aggregation, J.Econ.Theory 145 (2010) 467-494.
 F. R. McMorris, H. M. Mulder, R. C. Powers, The median function on median graphs and semilattices, Discrete Appl. Math. 101 (1-3) (2000) 221-230.
 K. Nehring, M. Pivato, C. Puppe, Condorcet efficiency and path-dependence in judgement aggregation, (preprint).
 R. Stearns, The voting problem, Amer. Math. Monthly 66 (1959) 761-763.
 N. Alon, V. H. Vu, Anti-Hadamard matrices, coin weighing, threshold gates, and indecomposable hypergraphs, J. Combin. Theory Ser. A 79 (1) (1997) 133-160.
 K. Nehring, C. Puppe, Consistent judgement aggregation: the truth-functional case, Soc. Choice Welf. 31 (1) (2008) 41-57.
 E. Dokow, R. Holzman, Aggregation of binary evaluations for truth-functional agendas, Soc. Choice Welf. 32 (2) (2009) 221-241.
 M. L. J. van de Vel, Theory of convex structures, Vol. 50 of North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, 1993.
 P. Erdos, L. Moser, On the representation of directed graphs as unions of orderings, Magyar Tud. Akad. Mat. Kutate Int.Kozl. 9 (1964) 125-132.
 N. Alon, Voting paradoxes and digraphs realizations, Adv. in Appl. Math. 29 (1) (2002) 126-135.
 G. M. Ziegler, Lectures on 0/1-polytopes, in: Polytopes ---combinatorics and computation (Oberwolfach, 1997), Vol. 29 of DMV Sem., Birkhauser, Basel, 2000, pp. 1-41.
Available Versions of this Item
- The McGarvey problem in judgement aggregation. (deposited 11. May 2010 10:40) [Currently Displayed]