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Independent opinions? on the causal foundations of belief formation and jury theorems

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  • Dietrich, Franz
  • Spiekermann, Kai

Abstract

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.

Suggested Citation

  • Dietrich, Franz & Spiekermann, Kai, 2012. "Independent opinions? on the causal foundations of belief formation and jury theorems," MPRA Paper 40137, University Library of Munich, Germany, revised Oct 2010.
    • Handle: RePEc:pra:mprapa:40137
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    References listed on IDEAS

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    1. Estlund, David M. & Waldron, Jeremy & Grofman, Bernard & Feld, Scott L., 1989. "Democratic Theory and the Public Interest: Condorcet and Rousseau Revisited," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1317-1340, December.
    2. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
    3. Dietrich, F.K. & Spiekermann, K., 2010. "Epistemic democracy with defensible premises," Research Memorandum 066, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Spiekermann, Kai & Goodin, Robert E., 2012. "Courts of Many Minds," British Journal of Political Science, Cambridge University Press, vol. 42(3), pages 555-571, July.
    5. Serguei Kaniovski, 2010. "Aggregation of correlated votes and Condorcet’s Jury Theorem," Theory and Decision, Springer, vol. 69(3), pages 453-468, September.
    6. Franz Dietrich & Christian List, 2002. "A Model of Jury Decisions Where All Jurors Have the Same Evidence," Economics Papers 2002-W23, Economics Group, Nuffield College, University of Oxford.
    7. Dietrich, F.K., 2008. "The premises of condorcet's jury theorem are not simultaneously justified," Research Memorandum 012, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    2. Hyoungsik Noh, 2023. "Conservativeness in jury decision-making," Theory and Decision, Springer, vol. 95(1), pages 151-172, July.
    3. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    4. Aureli Alabert & Mercè Farré & Rubén Montes, 2023. "Optimal Decision Rules for the Discursive Dilemma," Group Decision and Negotiation, Springer, vol. 32(4), pages 889-923, August.
    5. Aureli Alabert & Mercè Farré, 2022. "The doctrinal paradox: comparison of decision rules in a probabilistic framework," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(4), pages 863-895, May.
    6. Nehring, Klaus & Pivato, Marcus, 2019. "Majority rule in the absence of a majority," Journal of Economic Theory, Elsevier, vol. 183(C), pages 213-257.

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    More about this item

    Keywords

    Condorcet Jury Theorem; dependence between voters; probabilistic dependence; causal dependence;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • C0 - Mathematical and Quantitative Methods - - General
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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