Workshop on Decision Theory

Wednesday 29th September

Venue: T206, Lakatos Building, Portugal Street

Please register with: c.heilmann at lse.ac.uk

Schedule

9:45 - 11:00: Jason Alexander (LSE), Why the Angels Cannot Choose

11:15 - 12:30: Richard Bradley (LSE), Counterfactual Reasoning and Causal Decision Theory

Lunch break

14:30 - 15:45 Franz Dietrich (LSE) and Christian List (LSE), Conditionalisation Unified (joint work with Richard Bradley, LSE)

16:00 - 17:15 David Etlin (Leuven), Vague Desire

Coffee break

17:45 - 19:00 James Joyce (Michigan, Ann Arbor), A Defense of Imprecise Probabilities

Workshop dinner

Abstracts

Why the Angels Cannot Choose

Jason Alexander (LSE)

The Pasadena game, first introduced by Nover and Hájek (2004), has generated a substantial amount of discussion regarding what value an ideal rational agent should assign to the game. Yet little attention has been devoted to the question of what an ideal rational agent is, and in what sense decision theory may be said to apply to one. I show that, given one arguably natural set of constraints on the preferences of an idealised rational agent, such an agent is forced to be indifferent among entire families of goods, and hence cannot choose among them. This result provides an upper bound on the kinds of idealising assumptions which can be made for rational agents, beyond which the very notion of decision theory becomes untenable.

Counterfactual Reasoning and Causal Decision Theory

Richard Bradley (LSE)

Human decision makers make their choices not just in the light of what they believe and desire to the case, but also with reference to what is or would be the case were certain conditions fulfilled or actions performed. The topic of this paper is the nature of the hypothetical reasoning that characterises such prospective agency. In particular we introduce a model in which the differences between factual and counterfactual supposition can be explored and the respective claims of evidential and causal decision theory examined.

Conditionalisation Unified

Franz Dietrich (LSE) and Christian List (LSE) (joint work with Richard Bradley, LSE)

This paper introduces a generalized framework for revising states of mind in which it gives a unified characterisation of the main probabilistic belief revision rules: Bayesian conditionalisation, Jeffrey conditionalisation, and Adams conditionalisation. These seemingly so different revision rules all turn out to follow from the same two underlying principles on how beliefs change in response to new experiences: (i) Responsiveness, whereby revised beliefs are consistent with the new experience, and (ii) Conservativeness, whereby features of beliefs on which the new experience is silent are preserved. The only difference between the three revision rules is the kind of experience allowed: Bayesian experiences are more narrow than Jeffrey experiences, and Adams experiences are altogether different. A truly general revision rule allows for all three and even other kinds of experience, whilst still revising in accordance with Responsiveness and Conservativeness.

A Defense of Imprecise Probabilities

James Joyce (Michigan, Ann Arbor)

Some Bayesians have suggested that beliefs based on ambiguous or incomplete evidence are best represented by families of probability functions. I shall defend this "imprecise model of belief" against recent objections, raised by Roger White and others, which concern the phenomenon of probabilistic dilation. Dilation occurs when learning some definite fact forces a person's beliefs about an event to shift from a sharp, point-valued subjective probability to an imprecise spread of probabilities. Some commentators find dilation disturbing, both from an epistemic and a decision-theoretic perspective, and place the blame on the use of sets of probabilities to model opinion. These reactions are based on an overly narrow conception of imprecise belief states, which assumes that we know everything there is to know about a person's doxastic attitudes once we have identified the spreads of values for her imprecise credences. Once we recognize that the imprecise model has the resources to characterize a much richer family of doxastic attitudes than this, we will see that White's charges of epistemological and decision theoretic incoherence are unfounded.

 

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