Dietrich, Franz and Spiekermann, Kai (2012): Independent opinions? on the causal foundations of belief formation and jury theorems.
Download (303kB) | Preview
It is often claimed that opinions are more likely to be correct if they are held independently by many individuals. But what does it mean to hold independent opinions? To clarify this condition, we distinguish four notions of probabilistic opinion independence. Which notion applies depends on environmental factors such as commonly perceived evidence, or, more formally, on the causal network in which people interact and form their opinions. In a general theorem, we identify conditions on this network that guarantee opinion independence in each sense. Our results have implications for `wisdom of crowds' arguments, as we illustrate by providing old and new jury theorems.
|Item Type:||MPRA Paper|
|Original Title:||Independent opinions? on the causal foundations of belief formation and jury theorems|
|Keywords:||Condorcet Jury Theorem, dependence between voters, probabilistic dependence, causal dependence|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making
C - Mathematical and Quantitative Methods > C0 - General
D - Microeconomics > D8 - Information, Knowledge, and Uncertainty
|Depositing User:||Franz Dietrich|
|Date Deposited:||18. Jul 2012 20:54|
|Last Modified:||24. Oct 2015 20:10|
Anderson, E. (2006), 'The Epistemology of Democracy', Episteme 3(1-2), 8-22.
Berg, S. (1993), 'Condorcet's jury theorem, dependency among voters:', Social Choice and Welfare 10, 87--95.
Boland, P. J. (1989), `Majority systems and the Condorcet jury theorem', Journal of the Royal Statistical Society. Series D (The Statistician) 38(3), 181--189.
Boland, P. J.; Proschan, F. & Tong, Y. (1989), `Modelling dependence in simple and indirect majority systems', Journal of Applied Probability 26(1), 81--88.
Bovens, L. & Rabinowicz, W. (2006), `Democratic Answers to Complex Questions - an Epistemic Perpective', Synthese 150, 131--153.
Dietrich, F. (2008), `The premises of Condorcet's jury theorem are not simultaneously justified', Episteme 58(1), 56--73.
Dietrich, F. & List, C. (2004), `A model of jury decisions where all jurors have the same evidence', Synthese 142, 175--202.
Dietrich, F. and Spiekermann, K. (2010), `Epistemic Democracy with Defensible Premises', Unpublished manuscript.
Estlund, D. M. (1994), `Opinion leaders, independence, and Condorcet's Jury Theorem', Theory and Decision 36(2), 131--162.
Estlund, D. M. (2008), Democratic Authority: A Philosophical Framework, Princeton University Press, Princeton.
Estlund, D.; Jeremy, W.; Grofman, B. & Feld, S. L. (1989), 'Democratic Theory and the Public Interest: Condorcet and Rousseau Revisited', American Political Science Review 83(4), 1317--1340.
Goldman, A. I. (2004), 'Group Knowledge versus Group Rationality: Two Approaches to Social Epistemology', Episteme 1, 11--22.
Goldman, A. I. (1999), Knowledge in a Social World, Clarendon, Oxford.
Grofman, B. & Feld, S. L. (1988), 'Rousseau's General Will: A Condorcetian Perspective', American Political Science Review 82(2), 567-576.
Grofman, B.; Owen, G. & Feld, S. L. (1983), `Thirteen Theorems in Search of the Truth', Theory and Decision 15, 261--278.
Hawthorne, J. (unpublished) Voting in Search of the Public Good: the Probabilistic Logic of Majority Judgments, University of Oklahoma.
Kaniovski, S. (2010), 'Aggregation of correlated votes and Condorcet's Jury Theorem', Theory and Decision 69(3), 453-468.
Ladha, K. K. (1995), 'Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes', Journal of Economic Behavior & Organization 26(3), 353--372.
Ladha, K. K. (1993), 'Condorcet's jury theorem in light of de Finetti's theorem', Social Choice and Welfare 10(1), 69--85.
Ladha, K. K. (1992), 'The Condorcet Jury Theorem, Free Speech, and Correlated Votes', American Journal of Political Science 36(3), 617--634.
List, C. & Goodin, R. E. (2001), 'Epistemic Democracy: Generalizing the Condorcet Jury Theorem', Journal of Political Philosophy 9(3), 277--306.
Nitzan, S. & Paroush, J. (1984), 'The significance of independent decisions in uncertain dichotomous choice situations', Theory and Decision 17(1), 47--60.
Pearl, J. (2000), Causality: models, reasoning and inference, Cambridge University Press, Cambridge.
Reichenbach, H. (1956), The direction of time, University of California Press, Berkeley.
Romeijn, J. & Atkinson D. (2011), `A Condorcet jury theorem for unknown juror competence', Politics, Philosophy, and Economics, 10(3), 237--262.
Spiekermann, K., Goodin, R. E. (2012), `Courts of Many Minds', British Journal of Political Science, 12, 555-571.
Surowiecki, J. (2004) The Wisdom of Crowds, New York, Doubleday/Anchor
Vermeule, A. (2009), Law and the Limits of Reason, Oxford University Press, Oxford.