Hostname: page-component-7b9c58cd5d-hpxsc Total loading time: 0 Render date: 2025-03-17T05:28:33.496Z Has data issue: false hasContentIssue false
  • English
  • Français

Axiomatic Characterization of the Quadratic Scoring Rule

Published online by Cambridge University Press:  14 March 2025

Reinhard Selten
Reinhard Selten*
Affiliation:
University of Bonn, Laboratorium für experimentelle Wirtschaftsforschung, Adenauerallee 24-42, D-53113 Bonn
*
email: selten@lab.econl.uni-bonn.de
Get access Rights & Permissions [Opens in a new window]

Abstract

In the evaluation of experiments often the problem arises of how to compare the predictive success of competing probabilistic theories. The quadratic scoring rule can be used for this purpose. Originally, this rule was proposed as an incentive compatible elicitation method for probabilistic expert judgments. It is shown that up to a positive linear transformation, the quadratic scoring rule is characterized by four desirable properties.

Keywords

scoring rulesdescriptive statistics

JEL classification

C4: Econometric and Statistical Methods: Special Topics
Type
Research Article
Information
Experimental Economics , Volume 1 , Issue 1 , June 1998 , pp. 43 - 62
Copyright
Copyright © 1998 Economic 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.)

References

Brier, Glenn W. (1950). “Verification of Forecasts Expressed in Terms of Probability.” Monthly Weather Review. 78(1), 1–3.2.0.CO;2>CrossRefGoogle Scholar
Friedman, Daniel (1983). “Effective Scoring Rules for Probabilistic Forecasts.” Management Science. 29, 447454.CrossRefGoogle Scholar
Hey, I.D. and Orme, Ch. (1994). “Investigating Generalisations of Expected Utility Theory Using Experimental Data.” Econometrica. 62, 1261–1326.CrossRefGoogle Scholar
Matheson, J.E. and Winkler, R.L. (1976). “Scoring Rules for Continuous Probability Distributions.” Management Science. 22, 1078–1096.CrossRefGoogle Scholar
Murphy, A.H. and Winkler, R.L. (1970). “Scoring Rules in Probability Assessment and Evaluation.” Acta Psych. 34, 273–286.CrossRefGoogle Scholar
Ostrowski, A. (1965). VorlesungenüberDifferential und Integralrechnung. 2. Auflage. Basel-Stuttgart: BirkhauserVerlag.Google Scholar
Roby, T.B. (1965). Belief States: A Preliminary Empirical Study. Decision Science Laboratory, L.G. Hascom Field.Google Scholar
Selten, R. (1991). “Properties of a Measure of Predictive Success.” Mathematical Social Sciences. 21, 153–167.CrossRefGoogle Scholar
Stael von Holstein, C.-A.S. (1970). “Measurement of Subjective Probability.” Acta Psych. 34, 146–159.CrossRefGoogle Scholar
Toda, Masanao (1963). “Measurement of Subjective Probability Distribution.” Report 3, State College, Pennsylvania, Institute for Research, Division of Mathematical Psychology.Google Scholar
Winkler, R.L. (1969). “Scoring Rules and the Evaluation of Probability Assessors.” Journal of the American Statistical Association. 64, 1073–1078.CrossRefGoogle Scholar