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Synthese

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The joint aggregation of beliefs and degrees of belief

  • Paul D. Thorn
Article
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Abstract

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: (1) consistency and deductive closure for belief sets, (2) conformity to the axioms of probability for degrees of belief, and (3) the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on the aggregation of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief.

Keywords

Belief aggregation Opinion pooling Discursive dilemma Full and partial belief The Lockean thesis 

Notes

Acknowledgements

Work on this paper was supported by the DFG Grant SCHU1566/9-1 as part of the priority program New Frameworks of Rationality (SPP 1516), and by the DFG Collaborative Research Centre 991: The Structure of Representations in Language, Cognition, and Science. For valuable comments and suggestions I am thankful to Peter Brössel, Ludwig Fahrbach, Theo Kuipers, Olivier Roy, Gerhard Schurz, and two anonymous reviewers for Synthese. I particularly indebted to the contributions of Christian Feldbacher-Escamilla, who came up with the idea to investigate the synchronized aggregation of beliefs and degrees of belief, and provided many valuable suggestions during conversations of this topic.

References

  1. Arló-Costa, H., & Pedersen, A. (2012). Belief and probability: A general theory of probability cores. International Journal of Approximate Reasoning, 53, 293–315.CrossRefGoogle Scholar
  2. Briggs, R., Cariani, F., Easwaran, K., & Fitelson, B. (2014). Individual coherence and group coherence. In J. Lackey (Ed.), Essays in collective epistemology (pp. 215–249). Oxford: Oxford University Press.CrossRefGoogle Scholar
  3. Brössel, P., & Eder, A. (2014). How to resolve doxastic disagreement. Synthese, 191, 2359–2381.CrossRefGoogle Scholar
  4. Buchak, L. (2014). Belief, credence, and norms. Philosophical Studies, 169, 1–27.CrossRefGoogle Scholar
  5. Cariani, F. (2016). Local supermajorities. Erkenntnis, 81, 391–406.CrossRefGoogle Scholar
  6. Chandler, J. (2013). Acceptance, aggregation and scoring rules. Erkenntnis, 78, 201–217.CrossRefGoogle Scholar
  7. Dietrich, F. (2010). Bayesian group belief. Social Choice and Welfare, 35, 595–626.CrossRefGoogle Scholar
  8. Dietrich, F., & List, C. (2016). Probabilistic opinion pooling. In C. Hitchcock & A. Hajek (Eds.), Oxford handbook of probability and philosophy. Oxford: Oxford University Press.Google Scholar
  9. Dietrich, F., & List, C. (2018). From degrees of belief to binary beliefs: Lessons from judgment-aggregation theory. Journal of Philosophy, 115, 225–270.CrossRefGoogle Scholar
  10. Douven, I., & Romeijn, J. (2007). The discursive dilemma as a lottery paradox. Economics and Philosophy, 23, 301–319.CrossRefGoogle Scholar
  11. Douven, I., & Williamson, T. (2006). Generalizing the lottery paradox. British Journal for the Philosophy of Science, 57, 755–779.CrossRefGoogle Scholar
  12. Elkin, L., & Wheeler, G. (2018). Resolving peer disagreements through imprecise probabilities. Noûs, 52, 260–278.CrossRefGoogle Scholar
  13. Fantl, J., & McGrath, M. (2002). Evidence, pragmatics, and justification. Philosophical Review, 111, 67–94.CrossRefGoogle Scholar
  14. Foley, R. (1993). Working without a net. Oxford: Oxford University Press.Google Scholar
  15. Foley, R. (2009). Beliefs, degrees of belief, and the lockean thesis. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief (pp. 37–47). Dordrecht: Springer.CrossRefGoogle Scholar
  16. Ganson, D. (2008). Evidentialism and pragmatic constraints on outright belief. Philosophical Studies, 139, 441–458.CrossRefGoogle Scholar
  17. Genest, C. (1984a). A conflict between two axioms for combining subjective distributions. Journal of the Royal Statistical Society: Series B, 46, 403–405.Google Scholar
  18. Genest, C. (1984b). A characterization theorem for externally Bayesian groups. The Annals of Statistics, 12, 1100–1105.CrossRefGoogle Scholar
  19. Genest, C., & Wagner, C. (1984). Further evidence against independence preservation in expert judgement synthesis. Technical Report No. 84-10. Department of Statistics and Actuarial Science, University of Waterloo.Google Scholar
  20. Genest, C., & Wagner, C. (1987). Further evidence against independence preservation in expert judgement synthesis. Aequationes Mathematicae, 32, 74–86.CrossRefGoogle Scholar
  21. Genest, C., & Zidek, J. (1986). Combining probability distributions: A critique and annotated bibliography. Statistical Science, 1, 114–135.CrossRefGoogle Scholar
  22. Hawthorne, J. (2004). Knowledge and lotteries. Oxford: Oxford University Press.Google Scholar
  23. Hawthorne, J. (2009). The Lockean thesis and the logic of belief. In F. Huber & C. Schmidt-Petri (Eds.), Degrees of belief (pp. 49–74). Dordrecht: Springer.CrossRefGoogle Scholar
  24. Kyburg, H. (1961). Probability and the logic of rational belief. Middletown, CT: Wesleyan University Press.Google Scholar
  25. Laddaga, R. (1977). Lehrer and the consensus proposal. Synthese, 36, 473–477.CrossRefGoogle Scholar
  26. Lehrer, K., & Wagner, C. (1981). Rational consensus in science and society. Dordrecht: Reidel.CrossRefGoogle Scholar
  27. Lehrer, K., & Wagner, C. (1983). Probability amalgamation and the independence issue: A reply to Laddaga. Synthese, 55, 339–346.CrossRefGoogle Scholar
  28. Leitgeb, H. (2013). Reducing belief simpliciter to degrees of belief. Annals of Pure and Applied Logic, 164, 1338–1389.CrossRefGoogle Scholar
  29. Leitgeb, H. (2014). The stability theory of belief. Philosophical Review, 123, 131–171.CrossRefGoogle Scholar
  30. Levi, I. (2004). List and Pettit. Synthese, 140, 237–242.CrossRefGoogle Scholar
  31. Lin, H., & Kelly, K. (2012). A geo-logical solution to the lottery paradox. Synthese, 186, 531–575.CrossRefGoogle Scholar
  32. List, C., & Pettit, P. (2002). Aggregating sets of judgements: an impossibility result. Economics and Philosophy, 18, 89–110.CrossRefGoogle Scholar
  33. Pauly, M., & Van Hees, M. (2006). Logical constraints on judgement aggregation. Journal of Philosophical Logic, 35, 569–585.CrossRefGoogle Scholar
  34. Pigozzi, G. (2015). Belief merging and judgment aggregation. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy, Fall 2015 edn. http://plato.stanford.edu/archives/fall2015/entries/belief-merging/. Accessed 1 Mar 2017.
  35. Russell, J., Hawthorne, J., & Buchak, L. (2015). Groupthink. Philosophical Studies, 172, 1287–1309.CrossRefGoogle Scholar
  36. Schurz, G. (2017). Impossibility results for rational belief. Noûs.  https://doi.org/10.1111/nous.12214.
  37. Staffel, J. (2016). Beliefs, buses and lotteries: Why rational belief can’t be stably high credence. Philosophical Studies, 173, 1721–1734.CrossRefGoogle Scholar
  38. Thorn, P. (2017). Against deductive closure. Theoria, 83, 103–119.CrossRefGoogle Scholar
  39. Wagner, C. (2010). Jeffrey conditioning and external Bayesianity. Logic Journal of the IGPL, 18, 336–345.CrossRefGoogle Scholar
  40. Weatherson, B. (2005). Can we do without pragmatic encroachment? Philosophical Studies, 19, 417–443.Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Heinrich Heine Universitaet DuesseldorfDuesseldorfGermany

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