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As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage's postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. [ABSTRACT FROM AUTHOR]

I have claimed that risk-weighted expected utility (REU) maximizers are rational, and that their preferences cannot be captured by expected utility (EU) theory. Richard Pettigrew and Rachael Briggs have recently challenged these claims. Both authors argue that only EU-maximizers are rational. In addition, Pettigrew argues that the preferences of REU-maximizers can indeed be captured by EU theory, and Briggs argues that REU-maximizers lose a valuable tool for simplifying their decision problems. I hold that their arguments do not succeed and that my original claims still stand. However, their arguments do highlight some costs of REU theory. [ABSTRACT FROM PUBLISHER]

Risk-weighted expected utility theory (REU theory for short) permits preferences which violate the Sure-Thing Principle (STP for short). But preferences that violate the STP can lead to bad decisions in sequential choice problems. In particular, they can lead decision-makers to adopt a strategy that is dominated – i.e. a strategy such that some available alternative leads to a better outcome in every possible state of the world. [ABSTRACT FROM PUBLISHER]

This paper provides a novel interpretation of focal point responses (0, 50, 100 percent) in terms of ambiguous beliefs dynamics that arise in new developments of decision theory such as Choquet expected utility theory. In particular, focal point responses that have been updated from nonfocal responses can be interpreted as non-additive beliefs that account for psychological bias. A focal point response of 100 that has been updated from a nonfocal response can be represented by a non-additive belief that has been updated according to the Overestimating Update Rule. A focal point response of zero that has been updated from a nonfocal response can be represented by a non-additive belief that has been updated according to the Underestimating Update Rule. Focal point responses given consistently over time are not subject to psychological bias, and can be represented by additive probability distributions. Estimation results show such a model to be a very good fit to the data. [ABSTRACT FROM AUTHOR]