Decision Theory

A book chapter (about 4,000 words, plus references) on decision theory in moral philosophy, with particular attention to uses of decision theory in specifying the contents of moral principles (e.g., expected-value forms of act and rule utilitarianism), uses of decision theory in arguing in support of moral principles (e.g., the hypothetical-choice arguments of Harsanyi and Rawls), and attempts to derive morality from rationality (e.g., the views of Gauthier and McClennen)

Risk, ambiguity and quantum decision theory

In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do not follow the classic laws of probability theory. In particular, we show that it is possible to use consistently the classic expected utility formula, where the probability associated to the events are computed with the equation of quantum interference. Thus we show that the correct utility of a lottery can be simply computed by adding to the classic expected utility a new corrective term, the uncertainty utility, directly connected with the quantum interference term.Comment: 1 figur

Expected utility theory, Jeffrey’s decision theory, and the paradoxes

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested

Bayesian Decision Theory and Stochastic Independence

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