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Deliberation, Single-Peakedness, and Coherent Aggregation

Published online by Cambridge University Press:  22 February 2021

Bayreuth University
Bayreuth University
Soroush Rafiee Rad, Postdoctoral Researcher, Department of Philosophy, Bayreuth University,
Olivier Roy, Professor, Department of Philosophy, Bayreuth University,


Rational deliberation helps to avoid cyclic or intransitive group preferences by fostering meta-agreements, which in turn ensures single-peaked profiles. This is the received view, but this paper argues that it should be qualified. On one hand we provide evidence from computational simulations that rational deliberation tends to increase proximity to so-called single-plateaued preferences. This evidence is important to the extent that, as we argue, the idea that rational deliberation fosters the creation of meta-agreement and, in turn, single-peaked profiles does not carry over to single-plateaued ones, and the latter but not the former makes coherent aggregation possible when the participants are allowed to express indifference between options. On the other hand, however, our computational results show, against the received view, that when the participants are strongly biased towards their own opinions, rational deliberation tends to create irrational group preferences, instead of eliminating them. These results are independent of whether the participants reach meta-agreements in the process, and as such they highlight the importance of rational preference change and biases towards one’s own opinion in understanding the effects of rational deliberation.

Research Article
© The Author(s), 2021. Published by Cambridge University Press on behalf of the American Political Science Association

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We would like to thank the editors and reviewers of the APSR for their careful consideration of the paper, especially in the midst of the 2020 pandemic lockdown, and their valuable comments that improved the paper significantly. The paper has also benefited immensely from comments by Alexandru Baltag, Christian List, Stefan Napel, Clemens Puppe, Jan-Willem Romeijn, and the participants in Philosophy Breakfast meeting at Bayreuth University and the ColAForm meetings in London, Paris, and Copenhagen.

Both authors’ work is in part supported by the Deutsche Forschungsgemeinschaft (DFG) and Agence Nationale de la Recherche (ANR) as part of the joint project Collective Attitude Formation [RO 4548/8-1].


Allport, Alan, and Wylie, Glenn. 2000. “Task Switching, Stimulus Response Bindings, and Negative Priming.” Control of Cognitive Processes: Attention and Performance 18: 3570.Google Scholar
Arrow, Kenneth J. 1963. Social Choice and Individual Values. New Haven, CT: Yale University Press.Google Scholar
Black, Duncan. 1948. “On the Rationale of Group Decision-Making.” Journal of Political Economy 56 (1): 2334.CrossRefGoogle Scholar
Bohman, James. 1997. Deliberative Democracy: Essays on Reason and Politics. Cambridge, MA: MIT press.CrossRefGoogle Scholar
Bramson, Aaron, Grim, Patrick, Singer, Daniel J., Berger, William J., Sack, Graham, Fisher, Steven, Flocken, Carissa, and Holman, Bennett. 2017. “Understanding Polarization: Meanings, Measures, and Model Evaluation.” Philosophy of Science 84 (1): 115159.CrossRefGoogle Scholar
Cook, Wade D. 2006. “Distance-Based and Ad Hoc Consensus Models in Ordinal Preference Ranking.” European Journal of Operational Research 172 (2): 369385.CrossRefGoogle Scholar
Cook, Wade D., and Seiford, Lawrence M.. 1978. “Priority Ranking and Consensus Formation.” Management Science 24 (16): 17211732.CrossRefGoogle Scholar
Dryzek, John S., and List, Christian. 2003. “Social Choice Theory and Deliberative Democracy: A Reconciliation.” British Journal of Political Science 33 (1): 128.CrossRefGoogle Scholar
Duddy, Conal, and Piggins, Ashley. 2012. “A Measure of Distance between Judgment Sets.” Social Choice and Welfare 39 (4): 855867.CrossRefGoogle Scholar
Estlund, David. 1997. Beyond Fairness and Deliberation: The Epistemic Dimension of Democratic Authority. Cambridge, MA: MIT Press.Google Scholar
Farrar, Cynthia, Fishkin, James S., Green, Donald P., List, Christian, Luskin, Robert C., and Paluck, Elizabeth L.. 2010. “Disaggregating Deliberation’s Effects: An Experiment within a Deliberative Poll.” British Journal of Political Science 40 (2): 333347.CrossRefGoogle Scholar
Feld, Scott L., and Grofman, Bernard. 1992. “Who’s Afraid of the Big Bad Cycle? Evidence from 36 Elections.” Journal of Theoretical Politics 4 (2): 231237.CrossRefGoogle Scholar
Fishburn, Peter C., and Gehrlein, William V.. 1980. “The Paradox of Voting: Effects of Individual Indifference and Intransitivity.” Journal of Public Economics 14 (1): 8394.CrossRefGoogle Scholar
Frigg, Roman, and Hartmann, Stephan. 2020. “Models in Science.” In The Stanford Encyclopedia of Philosophy, ed. Zelta, Edward N.. Stanford. Google Scholar
Gaertner, Wulf. 2001. Domain Conditions in Social Choice Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Gehrlein, William V. 2004. “Consistency in Measures of Social Homogeneity: A Connection with Proximity to Single Peaked Preferences.” Quality and Quantity 38 (2): 147171.CrossRefGoogle Scholar
Grüne-Yanoff, Till. 2009. “Learning from Minimal Economic Models.” Erkenntnis 70 (1): 8199.CrossRefGoogle Scholar
Habermas, Jurgen. 1984. The Theory of Communicative Action. Boston: Beacon Press.Google Scholar
Hartmann, Stephan, and Rad, Soroush Rafiee. 2020. “Anchoring in Deliberation.” Erkenntnis 85: 10411069.CrossRefGoogle Scholar
Hegselmann, Rainer, and Krause, Ulrich. 2002. “Opinion Dynamics and Bounded Confidence Models, Analysis, and Simulation.” Journal of Artificial Societies and Social Simulation 5 (3).Google Scholar
Janis, Irving L. 1982. Groupthink: Psychological Studies of Policy Decisions and Fiascos. Boston: Houghton Mifflin Press.Google Scholar
Jones, Bradford, Radcliff, Benjamin, Taber, Charles, and Timpone, Richard. 1995. “Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders.” American Political Science Review 89 (1): 137144.CrossRefGoogle Scholar
Kemeny, John. 1959. “Mathematics without Numbers.” Daedalus 88 (4): 577591.Google Scholar
Kemeny, John, and Snell, James L.. 1962. “Preference Ranking: An Axiomatic Approach.” In Mathematical Models in the Social Sciences, eds. Kemeny, John G., and Snell, Laurie, 923. Cambridge, MA: MIT Press.Google Scholar
Landa, Dimitri, and Meirowitz, Adam. 2009. “Game Theory, Information, and Deliberative Democracy.” American Journal of Political Science 53 (2): 427444.CrossRefGoogle Scholar
List, C., and Goodin, Robert E.. 2001. “Epistemic Democracy: Generalizing the Condorcet Jury Theorem.” Journal of Political Philosophy 9 (3): 277306.CrossRefGoogle Scholar
List, Christian. 2002. “Two Concepts of Agreement.” The Good Society 11 (1): 7279.CrossRefGoogle Scholar
List, Christian. 2011. “Group Communication and the Transformation of Judgments: An Impossibility Result.” Journal of Political Philosophy 19 (1): 127.CrossRefGoogle Scholar
List, Christian, Luskin, Robert C., Fishkin, James S., and McLean, Iain. 2012. “Deliberation, Single-peakedness, and the Possibility of Meaningful Democracy: Evidence from Deliberative Polls.” The Journal of Politics 75 (1): 8095.CrossRefGoogle Scholar
List, Christian. 2017. “Democratic Deliberation and Social Choice: A Review.” In The Oxford Handbook of Deliberative Democracy, eds. Bächtiger, Andre, Dryzek, John S., Mansbridge, Jane, and Warren, Mark, 463–89. Oxford: Oxford University Press.Google Scholar
Martini, Carlo, Sprenger, Jan, and Colyvan, Mark. 2013. “Resolving Disagreement through Mutual Respect.” Erkenntnis 78 (4): 881898.CrossRefGoogle Scholar
Mayo-Wilson, Conor, Zollman, Kevin. J., and Danks, David. 2011. “The Independence Thesis: When Individual and Social Epistemology Diverge.” Philosophy of Science 78 (4): 653677.CrossRefGoogle Scholar
Miller, David. 1992. “Deliberative Democracy and Social Choice.” Political Studies 40: 5467.CrossRefGoogle Scholar
Moulin, Hervé. 1984. “Generalized Condorcet-Winners for Single Peaked and Single-Plateau Preferences.” Social Choice and Welfare 1 (2): 127147.CrossRefGoogle Scholar
Niemi, Richard G. 1969. “Majority Decision-Making with Partial Unidimensionality.” American Political Science Review 63 (2): 488497.CrossRefGoogle Scholar
Ottonelli, Valeria, and Porello, Daniele. 2013. “On the Elusive Notion of Meta-Agreement.” Politics, Philosophy & Economics 12 (1): 6892.CrossRefGoogle Scholar
Perote-Peña, Juan, and Piggins, Ashley. 2015. “A Model of Deliberative and Aggregative Democracy.” Economics & Philosophy 31 (1): 93121.CrossRefGoogle Scholar
Prentice, Deborah A., and Miller, Dale T.. 1993. “Pluralistic Ignorance and Alcohol Use on Campus: Some Consequences of Misperceiving the Social Norm.” Journal of Personality and Social Psychology 64 (2): 243256.CrossRefGoogle ScholarPubMed
Puppe, Clemens. 2018. “The Single-Peaked Domain Revisited: A Simple Global Characterization.” Journal of Economic Theory 176: 5580.CrossRefGoogle Scholar
Radcliff, Benjamin. 1994. “Collective Preferences in Presidential Elections.” Electoral Studies 13 (1): 5057.CrossRefGoogle Scholar
Regenwetter, Michel, Grofman, Bernard, Tsetlin, Ilia, and Marley, A. A. J.. 2006. Behavioral Social Choice: Probabilistic Models, Statistical Inference, and Applications. Cambridge: Cambridge University Press.Google Scholar
Riker, William H. 1982. Liberalism against Populism. San Francisco: W. H. Freeman.Google Scholar
Steiner, Jürg. 2012. The Foundations of Deliberative Democracy: Empirical Research and Normative Implications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Tsetlin, Ilia, Regenwetter, Michel, and Grofman, Bernard. 2003. “The Impartial Culture Maximizes the Probability of Majority Cycles.” Social Choice and Welfare 21 (3): 387398.CrossRefGoogle Scholar