Propositionwise judgment aggregation: the general case

Abstract

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or extended unanimity preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between, 2002), Nehring (Oligarchies in judgment aggregation: a characterization, 2006), Dietrich and List (Soc Choice Welf 29(1):19–33, 2007a) and Dokow and Holzman (J Econ Theory 145(2):495–511, 2010a).

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Acknowledgments

Although the authors are jointly responsible for this paper, Christian List wishes to note that Franz Dietrich should be considered the primary author, who deserves the credit for the present mathematical proofs. We are grateful to Ben Polak, the anonymous referees, and an anonymous associate editor for comments on this article.

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Correspondence to Franz Dietrich.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Dietrich, F., List, C. Propositionwise judgment aggregation: the general case. Soc Choice Welf 40, 1067–1095 (2013). https://doi.org/10.1007/s00355-012-0661-7

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Keywords

  • Econ Theory
  • Aggregation Rule
  • Agenda Condition
  • Veto Power
  • Material Implication