Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-20T12:46:41.863Z Has data issue: false hasContentIssue false

STRATEGY-PROOF JUDGMENT AGGREGATION*

Published online by Cambridge University Press:  01 November 2007

FRANZ DIETRICH
Affiliation:
University of Maastricht
CHRISTIAN LIST
Affiliation:
London School of Economics

Abstract

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.

Type
Essay
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barberà, S., Gul, F. and Stacchetti, E.. 1993. Generalized Median Voter Schemes and Committees. Journal of Economic Theory 61: 262–89.Google Scholar
Barberà, S., Massóa, J. and Nemeb, A.. 1997. Voting under constraints. Journal of Economic Theory 76 (2): 298321.CrossRefGoogle Scholar
Baigent, N. 1987. Preference proximity and anonymous social choice. Quarterly Journal of Economics 102 (1): 161–70.Google Scholar
Bossert, W., and Storcken, T.. 1992. Strategy-proofness of social welfare functions: the use of the Kemeny distance between preference orderings. Social Choice and Welfare 9: 345–60.Google Scholar
Bovens, L., and Rabinowicz, W.. 2006. Democratic answers to complex questions–an epistemic perspective. Synthese 150: 131–53.Google Scholar
Brams, S. J., Kilgour, D. M. and Zwicker, W. S.. 1997. Voting on referenda: the separability problem and possible solutions. Electoral Studies 16 (3): 359–7.CrossRefGoogle Scholar
Brams, S. J., Kilgour, D. M. and Zwicker, W. S.. 1998. The paradox of multiple elections. Social Choice and Welfare 15: 211–36.CrossRefGoogle Scholar
Brennan, G. 2001. Collective Coherence? International Review of Law and Economics 21: 197211.Google Scholar
Chapman, B. 1998. More easily done than said: Rules, reason and rational social choice. Oxford Journal of Legal Studies 18: 293330.Google Scholar
Chapman, B. 2002. Rational Aggregation. Politics, Philosophy and Economics 1: 337–54.CrossRefGoogle Scholar
Dietrich, F. 2006. Judgment Aggregation: (Im)Possibility Theorems. Journal of Economic Theory 126: 286–98.CrossRefGoogle Scholar
Dietrich, F. 2007. A generalised model of judgment aggregation. Social Choice and Welfare 28 (4): 529–65.Google Scholar
Dietrich, F. Forthcoming. The possibility of judgment aggregation on agendas with subjunctive implications. Journal of Economic Theory.Google Scholar
Dietrich, F., and List, C.. 2007a. Arrow's theorem in judgment aggregation. Social Choice and Welfare 29 (1): 1933.Google Scholar
Dietrich, F., and List, C.. 2007b. Judgment aggregation by quota rules. Journal of Theoretical Politics 19 (4), in press).Google Scholar
Dokow, E., and Holzman, R.. 2005. Aggregation of binary evaluations. Working paper, Technion Israel Institute of Technology.Google Scholar
Dryzek, J., and List, C.. 2003. Social choice theory and deliberative democracy: A reconciliation. British Journal of Political Science 33: 128.CrossRefGoogle Scholar
Elster, J. 1986. The Market and the forum. In Foundations of Social Choice Theory, ed. Elster, J. and Hylland, A.. Cambridge, Cambridge University Press, 103–32.Google Scholar
Ferejohn, J. 2003. Conversability and collective intention. Paper presented at the Common Minds Conference, Australian National University, 24–25 July 2003.Google Scholar
Gärdenfors, P. 2006. An Arrow-like theorem for voting with logical consequences. Economics and Philosophy 22 (2): 181–90.Google Scholar
Gibbard, A. 1973. Manipulation of voting schemes: a general result. Econometrica 41 (July): 587601.Google Scholar
Goodin, R. E. 1986. Laundering preferences. In Foundations of Social Choice Theory, ed. Elster, J. and Hylland, A.. Cambridge, Cambridge University Press, 75101.Google Scholar
Grofman, B. 1985. Research note: The accuracy of group majorities for disjunctive and conjunctive decision tasks. Organizational Behavior and Human Decision Processes 35: 119–23.Google Scholar
van Hees, M. 2007. The limits of epistemic democracy. Social Choice and Welfare 28 (4): 649–66.CrossRefGoogle Scholar
Kelly, J. S. 1989. The Ostrogorski Paradox. Social Choice and Welfare 6: 71–6.Google Scholar
Konieczny, S. and Pino-Perez, R.. 2002. Merging information under constraints: a logical framework. Journal of Logic and Computation 12: 773808.CrossRefGoogle Scholar
Kornhauser, L. A. and Sager, L. G.. 1986. Unpacking the Court. Yale Law Journal 96: 82117.Google Scholar
List, C. 2002a. Two concepts of agreement. The Good Society 11 (1): 72–9.Google Scholar
List, C. 2002b. Discursive path-dependencies. Nuffield College Working Paper in Politics 2002-W15 (9 May 2002).Google Scholar
List, C. 2003. A Possibility Theorem on Aggregation over Multiple Interconnected Propositions. Mathematical Social Sciences 45: 1–13 (with Corrigendum in Mathematical Social Sciences 52: 109–10).Google Scholar
List, C. 2004. A model of path dependence in decisions over multiple propositions. American Political Science Review 98: 495513.Google Scholar
List, C. 2005. The probability of inconsistencies in complex collective decisions. Social Choice and Welfare 24: 332.CrossRefGoogle Scholar
List, C. 2006. The discursive dilemma and public reason. Ethics 116: 362402.Google Scholar
List, C. and Pettit, P.. 2002. Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18: 89110.Google Scholar
List, C. and Pettit, P.. 2004. Aggregating sets of judgments: Two impossibility results compared. Synthese 140 (1–2): 207–35.Google Scholar
Miller, D. 1992. Deliberative democracy and social choice. Political Studies 40: 5467.Google Scholar
Nehring, K. 2003. Arrow's theorem as a corollary. Economics Letters 80: 379–82.Google Scholar
Nehring, K. and Puppe, C.. 2002. Strategyproof social choice on single-peaked domains: Possibility, impossibility and the space between. Working paper, University of California at Davis.Google Scholar
Nehring, K. and Puppe, C.. 2005. Consistent judgement aggregation: A characterization. Working paper, University of Karlsruhe.Google Scholar
Osherson, D. and Vardi, M.. Forthcoming. Aggregating disparate estimates of chance. Games and Economic Behavior.Google Scholar
Pauly, M. and Hees, M. van. 2006. Logical constraints on judgment aggregation. Journal of Philosophical Logic 35: 569–85.Google Scholar
Pettit, P. 2001. Deliberative democracy and the discursive dilemma. Philosophical Issues 11: 268–99.Google Scholar
Pigozzi, G. 2006. Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152 (2): 285–98.Google Scholar
Saporiti, A. and Thomé, F.. 2005. Strategy-proofness and single-crossing. Working paper, Queen Mary, University of London.Google Scholar
Satterthwaite, M. 1975. Strategyproofness and Arrow's conditions: existence and correspondences for voting procedures and social welfare functions. Journal of Economic Theory 10:. Working paper, Queen Mary, University of London.CrossRefGoogle Scholar
Satterthwaite, M. 1975. Strategyproofness and Arrow's conditions: existence and correspondences for voting procedures and social welfare functions. Journal of Economic Theory 10: 187217.Google Scholar
Schulte, O. 2005. Minimal belief change, Pareto-optimality and logical consequence. Economic Theory 19 (1): 105–44.CrossRefGoogle Scholar
Sunstein, C. 1994. Political Conflict and Legal Agreement. Tanner Lectures on Human Values Harvard.Google Scholar
Taylor, A. D. 2002. The Manipulability of Voting Systems. American Mathematical Monthy. 109: 321–37.Google Scholar
Taylor, A. D. 2005. Social Choice and the Mathematics of Manipulation. Cambridge, Cambridge University Press.Google Scholar
Wilson, R. 1975. On the theory of aggregation. Journal of Economic Theory 10: 8999.Google Scholar