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)

Constructive Decision Theory

Contemporary approaches to decision making describe a decision problem by sets of states and outcomes, and a rich set of acts: functions from states to outcomes over which the decision maker (DM) has preferences. Real problems do not come so equipped. It is often unclear what the state and outcome spaces would be. We present an alternative foundation for decision making, in which the primitive objects of choice are syntactic programs. We show that if the DM's preference relation on objects of choice satisfies appropriate axioms, then we can find states, outcomes, and an embedding of the programs into Savage acts such that preferences can be represented by EU in the Savage framework. A modeler can test for SEU behavior without having access to the subjective states and outcomes. We illustrate the power of our approach by showing that it can represent DMs who are subject to framing effects.Decision theory, subjective expected utility, behavioral anomalies

Quantum Probability from Decision Theory?

In a recent paper (quant-ph/9906015), Deutsch claims to derive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." We show that his derivation fails because it includes hidden probabilistic assumptions.Comment: LaTeX, 8 pages, no figure

Decision theory under uncertainty

We review recent advances in the field of decision making under uncertainty or ambiguity.Ambiguity ; ambiguity aversion ; uncertainty ; decision

Sequential Extensions of Causal and Evidential Decision Theory

Moving beyond the dualistic view in AI where agent and environment are separated incurs new challenges for decision making, as calculation of expected utility is no longer straightforward. The non-dualistic decision theory literature is split between causal decision theory and evidential decision theory. We extend these decision algorithms to the sequential setting where the agent alternates between taking actions and observing their consequences. We find that evidential decision theory has two natural extensions while causal decision theory only has one.Comment: ADT 201

Belief gambles in epistemic decision theory

Don’t form beliefs on the basis of coin flips or random guesses. More generally, don’t take belief gambles: if a proposition is no more likely to be true than false given your total body of evidence, don’t go ahead and believe that proposition. Few would deny this seemingly innocuous piece of epistemic advice. But what, exactly, is wrong with taking belief gambles? Philosophers have debated versions of this question at least since the classic dispute between William Clifford and William James near the end of the nineteenth century. Here I reassess the normative standing of belief gambles from the perspective of epistemic decision theory. The main lesson of the paper is a negative one: it turns out that we need to make some surprisingly strong and hard-to-motivate assumptions to establish a general norm against belief gambles within a decision-theoretic framework. I take this to pose a dilemma for epistemic decision theory: it forces us to either make seemingly unmotivated assumptions to secure a norm against belief gambles, or concede that belief gambles can be rational after all

Preference reversal in quantum decision theory

We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain lottery because of uncertainty aversion. But when people evaluate lottery prices, e.g. for selling to others the right to play them, they do this more rationally, being less subject to behavioral biases. This difference can be explained by the presence of the attraction factors entering the expression of quantum probabilities. Only the existence of attraction factors can explain why, considering two lotteries with close utility factors, a decision maker prefers one of them when choosing, but evaluates higher the other one when pricing. We derive a general quantitative criterion for the preference reversal to occur that relates the utilities of the two lotteries to the attraction factors under choosing versus pricing and test successfully its application on experiments by Tversky et al. We also show that the planning paradox can be treated as a kind of preference reversal.Comment: Latex file, 15 page