Abstract
Generalizing the celebrated “discursive dilemma”, we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions (the “conclusions”) and on a set of “premises” by which the conclusions are truth-functionally determined. We show that for conclusion- and premise-based aggregation rules to be mutually consistent, the aggregation must always be “oligarchic”, that is: unanimous within a subset of agents, and typically even be dictatorial. We characterize exactly when consistent non-dictatorial (or anonymous) aggregation rules exist, allowing for arbitrary conclusions and arbitrary interdependencies among premises.
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References
Claussen CA, Røisland Ø (2005) Collective economic decisions and the discursive dilemma. Mimeographed
Dietrich F (2006a) Judgement aggregation: (Im)Possibility theorems. J Econ Theory 126:286–298
Dietrich F (2006b) The possibility of judgement aggregation under subjunctive implications. Mimeographed
Dietrich F (2007) A generalized model of judgement aggregation. Soc Choice Welf 28:529–565
Dietrich F, List C (2004) Strategy-proof judgement aggregation. Mimeographed
Dietrich F, List C (2005) Arrow’s theorem in judgement aggregation. Forthcoming in Soc Choice Welf
Dietrich F, List C (2006) Judgement aggregation without full rationality. Mimeographed
Dokow E, Holzman R (2005) Aggregation of binary evaluations. Mimeographed
Dokow E, Holzman R (2006) Aggregation of binary evaluations with abstentions. Mimeographed
Gärdenfors P (2006) An arrow-like theorem for voting with logical consequences. Econ Phil 22:181–190
Kornhauser L, Sager L (1986) Unpacking the court. Yale Law J 96:82–117
List C (2003) A possibility theorem on aggregation over multiple interconnected propositions. Math Soc Sci 45:1–13
List C (2004) A model of path dependence in decisions over multiple propositions. Am Polit Sci Rev 98:495–513
List C, Pettit P (2002) Aggregating sets of judgements: an impossibility result. Econ Phil 18:89–110
List C, Pettit P (2004) Aggregating sets of judgements: two impossibility results compared. Synthese 140:207–235
Mongin P (2005) Factoring out the impossibility of logical aggregation. Mimeographed
Nehring K (2003) Arrow’s theorem as a corollary. Econ Lett 80:379–382
Nehring K (2005) The impossibility of a Paretian rational. Mimeographed
Nehring K, Puppe C (2002) Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between. Unpublished manuscript
Nehring K, Puppe C (2006a) The structure of strategy-proof social choice. Part I: General characterization and possibility results on median spaces. Forthcoming in J Econ Theory
Nehring K, Puppe C (2006b) The structure of strategy-proof social choice. Part II: Non-dictatorship, anonymity and neutrality. Mimeographed
Pauly M, van Hees M (2006) Logical constraints on judgement aggregation. J Philos Logic 35:569–585
Pettit P (2001) Deliberative democracy and the discursive dilemma. Philos Issues 11:268–299
Rubinstein A, Fishburn P (1986) Algebraic aggregation theory. J Econ Theory 38:63–77
van Hees M (2007) The limits of epistemic democracy. Soc Choice Welf 28:649–666
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Nehring, K., Puppe, C. Consistent judgement aggregation: the truth-functional case. Soc Choice Welfare 31, 41–57 (2008). https://doi.org/10.1007/s00355-007-0261-0
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DOI: https://doi.org/10.1007/s00355-007-0261-0