Synthese

, Volume 194, Issue 6, pp 2025–2051 | Cite as

On the preference for more specific reference classes

Article

Abstract

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon (i) relatively precise-valued frequency information for a broad reference class, R, or upon (ii) relatively imprecise-valued frequency information for a more specific reference class, \(\hbox {R}^{\prime }\) (\(\hbox {R}^{\prime }\subset \hbox {R}\)). I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding \(\hbox {R}^{\prime }\) based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between (i) and (ii) is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference.

Keywords

Direct inference Statistical syllogism Specificity Scoring rules  The reference class problem Imprecise probabilities The principle of indifference 

References

  1. Bacchus, F. (1990). Representing and reasoning with probabilistic knowledge. Cambridge, MA: MIT Press.Google Scholar
  2. Bradley, S., & Steele, K. (2014). Uncertainty, learning, and the “Problem” of dilation. Erkenntnis, 79(6), 1287–1303.CrossRefGoogle Scholar
  3. Brier, G. (1950). Verification of forecasts expressed in terms of probability. Monthly Weather Review, 78, 1–3.CrossRefGoogle Scholar
  4. Carnap, R. (1962). Logical foundations of probability. Chicago: University of Chicago Press.Google Scholar
  5. de Finetti, B. (1974). Theory of probability (vol. 1). New York: Wiley.Google Scholar
  6. Easwaran, K. (2013). Expected accuracy supports conditionalization and conglomerability and reflection. Philosophy of Science, 80(1), 119–142.CrossRefGoogle Scholar
  7. Gould, H. (2010). Combinatorial identities: Table I: Intermediate techniques for summing finite series. In J. Quaintance (Ed.), http://www.math.wvu.edu/~gould/Vol.4.PDF. Accessed 3 Feb 2016.
  8. Greaves, H., & Wallace, D. (2006). Justifying conditionalization: Conditionalization maximizes expected epistemic utility. Mind, 114, 607–632.CrossRefGoogle Scholar
  9. Joyce, J. (1998). A nonpragmatic vindication of probabilism. Philosophy of Science, 65(4), 575–603.CrossRefGoogle Scholar
  10. Kyburg, H. (1974). The logical foundations of statistical inference. Dordrecht: Reidel Publishing Company.CrossRefGoogle Scholar
  11. Kyburg, H., & Teng, C. (2001). Uncertain inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  12. Leitgeb, H., & Pettigrew, R. (2010a). An objective justification of Bayesianism I: Measuring inaccuracy. Philosophy of Science, 77(2), 201–235.CrossRefGoogle Scholar
  13. Leitgeb, H., & Pettigrew, R. (2010b). An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy. Philosophy of Science, 77(2), 236–272.CrossRefGoogle Scholar
  14. Levinstein, B. (2012). Leitgeb and Pettigrew on accuracy and updating. Philosophy of Science, 79(3), 413–424.CrossRefGoogle Scholar
  15. Pollock, J. (1990). Nomic probability and the foundations of induction. Oxford: Oxford University Press.Google Scholar
  16. Reichenbach, H. (1949). A theory of probability. Berkeley: Berkeley University Press.Google Scholar
  17. Selten, R. (1998). Axiomatic characterization of the quadratic scoring rule. Experimental Economics, 1, 43–62.CrossRefGoogle Scholar
  18. Stone, M. (1987). Kyburg, Levi, and Petersen. Philosophy of Science, 54(2), 244–255.CrossRefGoogle Scholar
  19. Thorn, P. (2012). Two problems of direct inference. Erkenntnis, 76, 299–318.CrossRefGoogle Scholar
  20. Thorn, P. (2014). Defeasible conditionalization. Journal of Philosophical Logic, 43, 283–302.CrossRefGoogle Scholar
  21. Venn, J. (1866). The logic of chance. New York: Chelsea Publishing Company.Google Scholar
  22. White, R. (2009). Evidential symmetry and mushy credence. In T. Szabo Gendler & J. Hawthorne (Eds.), Oxford studies in epistemology (Vol. 3, pp. 161–186). Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of DuesseldorfDuesseldorfGermany

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