Abstract
Similar to Arrow’s impossibility theorem for preference aggregation, judgment aggregation has also an intrinsic impossibility for generating consistent group judgment from individual judgments. Removing some of the pre-assumed conditions would mitigate the problem but may still lead to too restrictive solutions. It was proved that if completeness is removed but other plausible conditions are kept, the only possible aggregation functions are oligarchic, which means that the group judgment is purely determined by a certain subset of participating judges. Instead of further challenging the other conditions, this paper investigates how the judgment from each individual judge affects the group judgment in an oligarchic environment. We explore a set of intuitively demanded conditions under abstentions and design a feasible judgment aggregation rule based on the agents’ hierarchy. We show this proposed aggregation rule satisfies the desirable conditions. More importantly, this rule is oligarchic with respect to a subset of agenda instead of the whole agenda due to its literal-based characteristics.
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References
Dietrich, F., List, C.: Arrow’s theorem in judgment aggregation. Social Choice and Welfare 29(1), 19–33 (2007)
Mongin, P.: Consistent bayesian aggregation. Journal of Economic Theory 66(2), 313–351 (1995)
Pigozzi, G.: Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152(2), 285–298 (2006)
Wilson, R.: On the theory of aggregation. Journal of Economic Theory 10(1), 89–99 (1975)
Konieczny, S., Pérez, R.P.: Merging information under constraints: a logical framework. Journal of Logic and Computation 12(5), 773–808 (2002)
Kornhauser, L.A., Sager, L.G.: Unpacking the court. The Yale Law Journal 96(1), 82–117 (1986)
List, C.: The theory of judgment aggregation: an introductory review. Synthese 187(1), 179–207 (2012)
Pettit, P.: Deliberative democracy and the discursive dilemma. Philosophical Issues 11(1), 268–299 (2001)
Pivato, M.: The discursive dilemma and probabilistic judgement aggregation. Munich Personal RePEc Archive (2008)
Arrow, K.J.: A difficulty in the concept of social welfare. Journal of Political Economy 58, 328–346 (1950)
List, C., Pettit, P.: Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18(01), 89–110 (2002)
Dietrich, F.: Judgment aggregation (im)possibility theorems. Journal of Economic Theory 126(1), 286–298 (2006)
List, C., Pettit, P.: Aggregating sets of judgments: Two impossibility results compared. Synthese 140(1-2), 207–235 (2004)
Mongin, P.: Factoring out the impossibility of logical aggregation. Journal of Economic Theory 141(1), 100–113 (2008)
Pauly, M., Van Hees, M.: Logical constraints on judgement aggregation. Journal of Philosophical logic 35(6), 569–585 (2006)
Van Hees, M.: The limits of epistemic democracy. Social Choice and Welfare 28(4), 649–666 (2007)
Dietrich, F., List, C.: Judgment aggregation with consistency alone. London School of Economics, Government Department, London, UK (2007)
Dietrich, F., List, C.: Judgment aggregation without full rationality. Social Choice and Welfare 31(1), 15–39 (2008)
Dokow, E., Holzman, R.: Aggregation of binary evaluations with abstentions. Journal of Economic Theory 145(2), 544–561 (2010)
Gärdenfors, P.: A representation theorem for voting with logical consequences. Economics and Philosophy 22(2), 181–190 (2006)
Jiang, G., Zhang, D., Tang, X.: Judgment aggregation with abstentions: A hierarchical approach. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI. LNCS, vol. 8196, pp. 321–325. Springer, Heidelberg (2013)
Dietrich, F., List, C.: A liberal paradox for judgment aggregation. Social Choice and Welfare 31(1), 59–78 (2008)
Mongin, P.: Factoring out the impossibility of logical aggregation. Journal of Economic Theory 141(1), 100–113 (2008)
Dietrich, F.: A generalised model of judgment aggregation. Social Choice and Welfare 28(4), 529–565 (2007)
Arrow, K.J.: Social Choice and Individual Values. Cowles Foundation Monographs. Wiley, New York (1953, 1964)
Nehring, K., Puppe, C.: Consistent judgement aggregation: the truth-functional case. Social Choice and Welfare 31(1), 41–57 (2008)
Dietrich, F., Mongin, P.: The premiss-based approach to judgment aggregation. Journal of Economic Theory 145(2), 562–582 (2010)
Andréka, H., Ryan, M., Schobbens, P.Y.: Operators and laws for combining preference relations. Journal of Logic and Computation 12(1), 13–53 (2002)
Rossi, F., Venable, K.B., Walsh, T.: Aggregating preferences cannot be fair. Intelligenza Artificiale 2(1), 30–38 (2005)
Dietrich, F., List, C.: Propositionwise judgment aggregation: the general case. Social Choice and Welfare 40(4), 1067–1095 (2013)
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Jiang, G., Zhang, D., Perrussel, L. (2014). Judgment Aggregation with Abstentions under Voters’ Hierarchy. In: Dam, H.K., Pitt, J., Xu, Y., Governatori, G., Ito, T. (eds) PRIMA 2014: Principles and Practice of Multi-Agent Systems. PRIMA 2014. Lecture Notes in Computer Science(), vol 8861. Springer, Cham. https://doi.org/10.1007/978-3-319-13191-7_28
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DOI: https://doi.org/10.1007/978-3-319-13191-7_28
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