Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T00:51:44.514Z Has data issue: false hasContentIssue false
  • English
  • Français

In Favor of Logarithmic Scoring

Published online by Cambridge University Press:  01 January 2022

Randall G. McCutcheon
Get access Rights & Permissions [Opens in a new window]

Abstract

Shuford, Albert, and Massengill proved, a half century ago, that the logarithmic scoring rule is the only proper measure of inaccuracy determined by a differentiable function of probability assigned the actual cell of a scored partition. In spite of this, the log rule has gained less traction in applied disciplines and among formal epistemologists that one might expect. In this article we show that the differentiability criterion in the Shuford et al. result is unnecessary and use the resulting simplified characterization of the logarithmic rule to give novel arguments in favor of it.

Type
Articles
Information
Philosophy of Science , Volume 86 , Issue 2 , April 2019 , pp. 286 - 303
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Thanks to Steve Kalikow and the anonymous referees and editors at Philosophy of Science.

References

Bernardo, J. M. 1979. “Expected Information as Expected Utility.” Annals of Statistics 7:686–90.CrossRefGoogle Scholar
Brier, Glenn W. 1950. “Verification of Forecasts Expressed in Terms of Probability.” Monthly Weather Review 78:1–3.2.0.CO;2>CrossRefGoogle Scholar
Fallis, Don, and Lewis, Peter J.. 2015. “The Brier Rule Is Not a Good Measure of Epistemic Utility (and Other Useful Facts about Epistemic Betterness).” Australasian Journal of Philosophy 94:576–90.Google Scholar
Good, I. J. 1952. “Rational Decisions.” Journal of the Royal Statistical Society B 14:107–14.Google Scholar
Jeffrey, R. 1965. The Logic of Decision. New York: McGraw-Hill.Google Scholar
Joyce, J. M. 1998. “A Nonpragmatic Vindication of Probabilism.” Philosophy of Science 65 (4): 575–603..CrossRefGoogle Scholar
Joyce, J. M.. 2009. “Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.” In Degrees of Belief, ed. Huber, F. and Schmidt-Petri, C.. Synthese Library: Studies in Epistemology, Logic, Methodology, and Philosophy of Science 342. Dordrecht: Springer.Google Scholar
Knab, Brian, and Schoenfield, Miriam 2015. “A Strange Thing about the Brier Score.” M-Phi, March 12. http://m-phi.blogspot.nl/2015/03/a-strange-thing-about-brier-score.html.Google Scholar
Leitgeb, H., and Pettigrew, R.. 2010. “An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy.” Philosophy of Science 77:236–72.Google Scholar
Levinstein, Benjamin Anders. 2012. “Leitgeb and Pettigrew on Accuracy and Updating.” Philosophy of Science 79:413–24.CrossRefGoogle Scholar
Predd, J., Seiringer, Robert, Lieb, Elliott H., Osherson, Daniel N., Poor, H. Vincent, and Kulkarni, Sanjeev R.. 2009. “Probabilistic Coherence and Proper Scoring Rules.” IEEE Transactions on Information Theory 55 (10): 4786–92..CrossRefGoogle Scholar
Selten, Reinhard. 1998. “Axiomatic Characterization of the Quadratic Scoring Rule.” Experimental Economics 1:43–62.CrossRefGoogle Scholar
Shuford, Emir H. Jr., Albert, Arthur, and Massengill, H. Edward. 1966. “Admissible Probability Measurement Procedures.” Psychometrika 31 (2): 125–45..CrossRefGoogle ScholarPubMed