Proper Scoring Rules, Dominated Forecasts, and Coherence

Authors:
Mark J. Schervish;Teddy Seidenfeld;Joseph B. Kadane
Affiliations:
Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Venue:
Decision Analysis
Year:
2009

Citing 1
Cited 12

Probabilistic coherence and proper scoring rules

IEEE Transactions on Information Theory

From the Editors...

Decision Analysis
Honoring Michael H. Rothkopf's Legacy of Rigor and Relevance in Auction Theory: From the Editors

Decision Analysis
From the Editors...

Decision Analysis
Investment and Defense Strategies, Heuristics, and Games: From the Editor...

Decision Analysis
From the Editors---Deterrence, Multiattribute Utility, and Probability and Bayes' Updating

Decision Analysis
Using Bayes' Rule to Update an Event's Probabilities Based on the Outcomes of Partially Similar Events

Decision Analysis
From the Editor---Multiattribute and Intertemporal Preferences, Probability, and Stochastic Processes: Models and Assessment

Decision Analysis
From the Editors---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis

Decision Analysis
From the Editors---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics

Decision Analysis
Forecasting with imprecise probabilities

International Journal of Approximate Reasoning
From the Editors---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus

Decision Analysis
From the Editors: Probability Approximations, Anti-Terrorism Strategy, and Bull's-Eye Display for Performance Feedback

Decision Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

The concept of coherent probabilities and conditional probabilities through a gambling argument and through a parallel argument based on a quadratic scoring rule was introduced by de Finetti (de Finetti, B. 1974. The Theory of Probability. John Wiley & Sons, New York). He showed that the two arguments lead to the same concept of coherence. When dealing with events only, there is a rich class of scoring rules that might be used in place of the quadratic scoring rule. We give conditions under which a general strictly proper scoring rule can replace the quadratic scoring rule while preserving the equivalence of de Finetti's two arguments. In proving our results, we present a strengthening of the usual minimax theorem. We also present generalizations of de Finetti's fundamental theorem of probability to deal with conditional probabilities.