Judgment aggregation and agenda manipulation

Dietrich, Franz (2013): Judgment aggregation and agenda manipulation.

Abstract

When individual judgments ('yes' or 'no') on some propositions are aggregated into collective judgments, the agenda setter can sometimes reverse a collective judgment by changing the set of propositions under consideration (the agenda). I define different kinds of agenda manipulation, and axiomatically characterize the aggregation rules immune to each kind. Two axioms emerge as central for preventing agenda manipulation: the familiar independence axiom, requiring propositionwise aggregation, and the axiom of implicit consensus preservation, requiring the respect of any (possibly implicit) consensus. I prove that these axioms can almost never be satisfied together by a (non-degenerate) aggregation rule.

• Item Type: MPRA Paper
• Language: English
• Keywords: judgment aggregation, agenda manipulation, impossibility theorems
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior

References

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) Scoring rules for judgment aggregation, Social Choice and Welfare

Dietrich, F., List, C. (2007a) Arrow's theorem in judgment aggregation, Social Choice and Welfare 29(1): 19-33

Dietrich, F., List, C. (2007b) Strategy-proof judgment aggregation, Economics and Philosophy 23(3): 269-300

Dietrich, F., List, C. (2007c) Judgment aggregation by quota rules: majority voting generalized, Journal of Theoretical Politics 19(4): 391-424

Dietrich, F., List, C. (2010) Majority voting on restricted domains, Journal of Economic Theory 145(2): 512-543

Dietrich, F., List, C. (2013) Propositionwise judgment aggregation: the general case, Social Choice and Welfare 40: 1067-1095

Dokow, E., Falik, D. (2012) Models of Manipulation on Aggregation of Binary Evaluations, working paper

Dokow, E., Holzman, R. (2010) Aggregation of binary evaluations, Journal of Economic Theory 145(2): 495-511

Duddy, C., Piggins, A. (2012a) A measure of distance between judgment sets, Social Choice And Welfare 39: 855-867

Duddy, C., Piggins, A. (2012b) Aggregation of binary evaluations: a Borda-like approach, working paper, London School of Economics

Duddy, C., Piggins, A. (2013) Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary, Journal of Economic Theory 148: 793-805

Eckert, D., Klamler, C. (2009) A geometric approach to paradoxes of majority voting: from Anscombe's paradox to the discursive dilemma with Saari and Nurmi, Homo Oeconomicus 26: 471-488

Konieczny, S., Pino-Perez, R. (2002) Merging information under constraints: a logical framework, Journal of Logic and Computation 12: 773-808

Kornhauser, L. A., Sager, L. G. (1986) Unpacking the Court, Yale Law Journal 96(1): 82-117

Lang, J., Pigozzi, G., Slavkovik, M., van der Torre, L. (2011) Judgment aggregation rules based on minimization. In Proceedings of the 13th Conference on the Theoretical Aspects of Rationality and Knowledge (TARK XIII), ACM, pp. 238-246

List, C. (2004) A Model of Path-Dependence in Decisions over Multiple Propositions, American Political Science Review 98(3): 495-513

List, C., Pettit, P. (2002) Aggregating sets of judgments: an impossibility result, Economics and Philosophy 18: 89-110

List, C., Polak, B. eds. (2010) Symposium on Judgment Aggregation, Journal of Economic Theory 145(2)

Miller, M. K., Osherson, D. (2009) Methods for distance-based judgment aggregation, Social Choice and Welfare 32(4): 575-601

Mongin, P. (2008) Factoring out the impossibility of logical aggregation, Journal of Economic Theory 141(1): 100-113

Nehring, K., Puppe, C. (2002) Strategy-Proof Social Choice on Single-Peaked Domains: Possibility, Impossibility and the Space Between, unpublished paper, University of California at Davis

Nehring, K. Puppe, C. (2008) Consistent judgement aggregation: the truth-functional case, Social Choice and Welfare 31: 41-57

Nehring, K., Puppe, C. (2010) Abstract Arrovian Aggregation, Journal of Economic Theory 145(2): 467-494

Nehring, K., Pivato, M., Puppe, C. (2013) The Condorcet Set -- Majority Voting over Interconnected Propositions, working paper, University of California at Davis

Pauly, M., van Hees, M. (2006) Logical Constraints on Judgment Aggregation, Journal of Philosophical Logic 35(6): 569-585

Pigozzi, G. (2006) Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation, Synthese 152(2): 285-298

Pivato, M. (2009) Geometric models of consistent judgement aggregation, Social Choice and Welfare 33(4): 559-574

Wilson R (1975) On the Theory of Aggregation, Journal of Economic Theory 10: 89-99

Zwicker, W. (2011) Towards a Borda count for judgment aggregation, extended abstract, presented at the conference Judgment Aggregation and Voting, Karlsruhe Institute of Technology