An axiomatic model of non bayesian updating

Johann Pfanzagl completed the Theory of Games and Economic Behavior by providing an axiomatization of subjective probability and utility, a task left uncompleted by von Neumann and Oskar Morgenstern: their original theory supposed that all the agents had the same probability distribution, as a convenience. We did not carry this out; it was demonstrated by Pfanzagl ... Ramsey and Savage noted that the individual agent's probability distribution could be objectively studied in experiments.

A representation theorem generalizes (the dynamic version of) Anscombe-Aumanns theorem so that both the prior and the way in which it is updated are subjective.

The model can generate updating biases analogous to those observed by psychologists.

This paper models an agent in a three-period setting who does not update according to Bayes’ Rule, and who is self-aware and anticipates her updating behavior when formulating plans.

Salt could lose its savour." In fact, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "probability kinematics" A decision-theoretic justification of the use of Bayesian inference (and hence of Bayesian probabilities) was given by Abraham Wald, who proved that every admissible statistical procedure is either a Bayesian procedure or a limit of Bayesian procedures.

Following the work on expected utility theory of Ramsey and von Neumann, decision-theorists have accounted for rational behavior using a probability distribution for the agent.

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