Abstract
Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda conditions are tight. When applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial.
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Dietrich F. (2006) Judgment aggregation: (Im)Possibility theorems. Journal of Economic Theory 126(1): 286–298
Dietrich F. (2007) A generalised model of judgment aggregation. Social Choice and Welfare 28(4): 529–565
Dietrich, F. (forthcoming). The possibility of judgment aggregation on agendas with subjunctive implications. Journal of Economic Theory.
Dietrich F., List C. (2007a) Arrow’s theorem in judgment aggregation. Social Choice and Welfare 29(1): 19–33
Dietrich F., List C. (2007b) Judgment aggregation by quota rules: Majority voting generalized. Journal of Theoretical Politics 19(4): 391–424
Dietrich F., List C. (2008) Judgment aggregation without full rationality. Social Choice and Welfare 31: 15–39
Dokow, E., & Holman, R. (forthcoming). Aggregation of binary evaluations. Journal of Economic Theory.
Gärdenfors P. (2006) An Arrow-like theorem for voting with logical consequences. Economics and Philosophy 22(2): 181–190
Konieczny S., Pino-Perez R. (2002) Merging information under constraints: A logical framework. Journal of Logic and Computation 12(5): 773–808
List C., Pettit P. (2002) Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18: 89–110
List C., Pettit P. (2004) Aggregating sets of judgments: Two impossibility results compared. Synthese 140(1–2): 207–235
List C., Puppe C. (2009) Judgment aggregation: A survey. In: Anand P., Puppe C., Pattanaik P. (eds) Oxford handbook of rational and social choice. Oxford University Press, Oxford
May K. O. (1952) A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica 20: 680–684
Mongin P. (2008) Factoring out the impossibility of logical aggregation. Journal of Economic Theory 141: 100–113
Nehring, K., & Puppe, C. (2002). Strategy-proof social choice on single-peaked domains: Possibility, impossibility and the space between. Working paper, University of California at Davies.
Nehring, K., & Puppe, C. (2005). The sructure of strategy-proof social choice. Part II: Non-dictatorship, anonymity and neutrality. Working paper, University of Karlsruhe.
Nehring K., Puppe C. (2008) Consistent judgement aggregation: The truth-functional case. Social Choice and Welfare 31: 41–57
Pauly M., van Hees M. (2006) Logical constraints on judgment aggregation. Journal of Philosophical Logic 35: 569–585
Pettit P. (2001) Deliberative democracy and the discursive dilemma. Philosophical Issues 11: 268–299
van Hees M. (2007) The limits of epistemic democracy. Social Choice and Welfare 28(4): 649–666
Wilson R. (1972) Social choice theory without the Pareto principle. Journal of Economic Theory 5: 478–486
Wilson R. (1975) On the theory of aggregation. Journal of Economic Theory 10: 89–99
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Dietrich, F., List, C. The impossibility of unbiased judgment aggregation. Theory Decis 68, 281–299 (2010). https://doi.org/10.1007/s11238-009-9186-7
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DOI: https://doi.org/10.1007/s11238-009-9186-7