Three contrasts between two senses of coherence

Teddy Seidenfeld (CMU) gives a talk in the talk series "MCMP & Statistics Department" titled "Three contrasts between two senses of coherence" (Joint work with M. J. Schervish and J. B. Kadane – Statistics, CMU). Abstract: B. de Finetti defended two senses of coherence in providing foundations for his theory of subjective probabilities. Coherence 1 requires that when a decision maker announces fair prices for random variables these are immune to a uniform sure-loss - no Book is possible using finitely many fair contracts! Coherence 2 requires that when a decision maker's forecasts for a finite set of random variables are evaluated by Brier Score - squared error loss - there is no rival set of forecasts that dominate with a uniformly better score for sure. De Finetti established these two concepts are equivalent: fair prices are coherent 1 if and only if they constitute a coherent 2 set of forecasts if and only if they are the expected values for the variables under some common (finitely additive) personal probability. I report three additional contrasts between these two senses of coherence. One contrast (relating to finitely additive probabilities) favors coherence 2. One contrast (relating to decisions with moral hazard) favors coherence 1. The third contrast relates to the challenge of state-dependent utilities.