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FOURTH
INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Carnegie Mellon University

Pittsburgh, PA, USA

July 20-23 2005

#
ISIPTA'05 ELECTRONIC PROCEEDINGS

## Robert Nau

# Bayesianism Without Priors, Acts Without Consequences

### Abstract

A generalization of subjective expected utility is presented in which the primitives are a finite set of states of the world, a finite set of strategies available to the decision maker, and allocations of money. The model does not require explicit definitions of consequences ("states of the person"), nor does it rely on counterfactual preferences, nor does it emphasize the unique separation of prior probabilities from possibly-state-dependent utilities. Rather, preferences have an additively separable representation in which the valuation of outcomes of a decision or game is implicit in the state- and strategy-dependence of utility for money. This model provides an axiomatic foundation for Bayesian decision analysis and game theory in the tradition of de Finetti and Arrow-Debreu rather than Savage. The observable parameters of beliefs are risk neutral probabilities (betting rates for money) and in situations where the decision maker has no intrinsic interest or influence over an experiment given the truth or falsity of the hypothesis, her risk neutral probabilities and preferences among strategies are updated by application of Bayes' rule without the need to identify "true" prior probabilities.

** Keywords. ** Subjective probability, state-dependent utility, state-preference theory, risk neutral probabilities

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** Authors addresses: **

Fuqua School of Business

Duke University

Durham, NC 27708-0120

USA

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