Andy Egan's Smoking Lesion and Psycho Button cases are supposed to be counterexamples to Causal Decision Theory. This paper argues that they are not: more precisely, it argues that if CDT makes the right call in Newcomb's problem then it makes the right call in Egan cases too.

Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem (...) in terms of a psychological effect: ambiguity aversion . The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis. (shrink)

According to decision theory, the rational initial action in a sequential decision-problem may be found by backward induction or folding back. But the reasoning which underwrites this claim appeals to the agent's beliefs about what she will later believe, about what she will later believe she will still later believe, and so forth. There are limits to the depth of people's beliefs. Do these limits pose a threat to the standard theory of rational sequential choice? It is argued, first, that (...) the traditional solutions of certain games depend on knowledge which exceeds depth limits, and that these solutions therefore cannot be shown rational in the usual sense. Then, for that related reason even folding back solutions of one-person problems cannot be! A revision of our notion of rational choice is proposed, analogous to the reliabilist account of knowledge of Goldman and others, by which this paradox is resolved. (shrink)

I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such (...) at every point for that would be to require the impossible. (shrink)

Abstract I analyse the relationship between the Ramsey Test (RT) for the acceptance of indicative conditionals and the so-called problem of decision-instability. In particular, I argue that the situations which allegedly bring about this problem are troublesome just in case the relevant conditionals are evaluated by non-suppositional versions, e.g. causal/evidential, of the test. In contrast, a suppositional RT, by highlighting the metacognitive nature of the evaluation of indicative conditionals, allows an agent to run a simulation of such evaluation, without yet (...) committing her to the acceptance of such conditionals. I conclude that a suppositional interpretation of RT is superior to its nonsuppositional counterparts and by briefly showing that a suppositional RT is compatible with a deliberational decision theory. (shrink)

Fine has shown that assigning any value to the Pasadena game is consistent with a certain standard set of axioms for decision theory. However, I suggest that it might be reasonable to believe that the value of an individual game is constrained by the long-run payout of repeated plays of the game. Although there is no value that repeated plays of the Pasadena game converges to in the standard strong sense, I show that there is a weaker sort of convergence (...) it exhibits, and use this to define a notion of ‘weak expectation’ that can give values to the Pasadena game and many others, though not to all games that fail to have a strong expectation in the standard sense. CiteULike Connotea Del.icio.us What's this? (shrink)

We show that, as a consequence of the Arrow Impossibility Theorem, a sufficiently knowledgeable teacher can design a completely fair test—any reasonable way one might define that so long as it depends on a sample of the material covered and not /all/ of it—and mark it perfectly, yet with the strange but true result that the resultant marks may well be unfair.

Andy Egan argues that neither evidential nor causal decision theory gives the intuitively right recommendation in the cases The Smoking Lesion, The Psychopath Button, and The Three-Option Smoking Lesion. Furthermore, Egan argues that we cannot avoid these problems by any kind of ratificationism. This paper develops a new version of ratificationism that gives the right recommendations. Thus, the new proposal has an advantage over evidential and casual decision theory and standard ratificationist evidential decision theory.

David Lewis [1988; 1996] canvases an anti-Humean thesis about mental states: that the rational agent desires something to the extent that he or she believes it to be good. Lewis offers and refutes a decision-theoretic formulation of it, the 'Desire-as-Belief Thesis'. Other authors have since added further negative results in the spirit of Lewis's. We explore ways of being anti-Humean that evade all these negative results. We begin by providing background on evidential decision theory and on Lewis's negative results. We (...) then introduce what we call the indexicality loophole: if the goodness of a proposition is indexical, partly a function of an agent's mental state, then the negative results have no purchase. Thus we propose a variant of Desire-as-Belief that exploits this loophole. We argue that a number of meta-ethical positions are committed to just such indexicality. Indeed, we show that with one central sort of evaluative belief--the belief that an option is right--the indexicality loophole can be exploited in various interesting ways. Moreover, on some accounts, 'good' is indexical in the same way. Thus, it seems that the anti-Humean can dodge the negative results. (shrink)

An association between a pair of variables can consistently be inverted in each subpopulation of a population when the population is partitioned. E.g., a medical treatment can be associated with a higher recovery rate for treated patients compared with the recovery rate for untreated patients; yet, treated male patients and treated female patients can each have lower recovery rates when compared with untreated male patients and untreated female patients. Conversely, higher recovery rates for treated patients in each subpopulation are consistent (...) with a lower recovery rate in the total population when data are aggregated. The arithmetical structures that underlie facts like these support surprising applications of them that invalidate a cluster of arguments that many people, at least initially, take to be intuitively valid. E.g., despite intuitions to the contrary, the following argument is invalid. (shrink)

In discussions surrounding epistemology and rationality, it is often useful to assume an agent is rational or ideally rational. Often, this ideal rationality assumption is spelled out along the following lines: -/- 1. The agent believes everything about a situation which the evidence entitles her to believe and nothing which it does not. -/- 2. The agent believes all the logical consequences of any of her beliefs. -/- 3. The agent knows her own mind: if she believes P, she believes (...) that she believes P; and if she doesn't believe P, she believes that she doesn't believe P. -/- 4. The agent believes nothing of the form 'P and it is not the case that P.' -/- 5. If an agent's background belief-set satisfies 1-4 and if rationality requires the agent to add P to her belief-set, then the resulting belief-set will also satisfy 1-4. -/- While individually plausible, there are cases in which holding on to 1-5 generates paradox. Some resolve such paradoxical cases by granting 1-5 but arguing while ideally rational agents can exist, they can't possibly ever find themselves in such a situation: such case descriptions are epistemically incoherent. Others allow that rational agents can coherently find themselves in such odd circumstances, and argue that it's more reasonable to weaken our concept of ideal rationality and give up premise (2) above. However, this strategy has also been rejected. My aim in this paper is to defend the utility of positing an ideally rational agent in such paradoxical circumstances. I argue in such cases we should give up (2), in particular the assumption that (necessarily) if an ideally rational agent believes both P and the conditional, if P then Q, then she believes Q.. What's important is to hold on to the goal of positing ideal rationality: to maximize the amount of true or probably true information a thinker can justifiably believe in a given circumstance. Normally that will mean holding on to (2), but these unusual paradoxical cases are best handled by giving up (2). (shrink)

This paper looks at a dispute decision theory about how best to characterize expected utility maximization and express the logic of rational choice. Where A1, … , An are actions open to some particular agent, and S1, … , Sn are mutually exclusive states of the world such that the agent knows at least one of which obtains, does the logic of rational choice require an agent to consider the conditional probability of choice Ai given that some state Si obtains, (...) Prob(Ai/Si). Or, is the logic of choice better represented by considering the probability of the counterfactual if Ai then Si, Prob(Ai ⟥-> Si). Causal decision theory, developed by Allan Gibbard, William Harper, and David Lewis defend the counterfactual analysis; whereas, Richard Jeffrey and others defend the conditional probability analysis, evidential decision theory. I argue that the problems posed by cases of decision instability favor evidential decision theory. (shrink)

Hájek has recently presented the following paradox. You are certain that a cable guy will visit you tomorrow between 8 a.m. and 4 p.m. but you have no further information about when. And you agree to a bet on whether he will come in the morning interval (8, 12] or in the afternoon interval (12, 4). At first, you have no reason to prefer one possibility rather than the other. But you soon realise that there will definitely be a future (...) time at which you will (rationally) assign higher probability to an afternoon arrival than a morning one, due to time elapsing. You are also sure there may not be a future time at which you will (rationally) assign a higher probability to a morning arrival than an afternoon one. It would therefore appear that you ought to bet on an afternoon arrival. The paradox is based on the apparent incompatibility of the principle of expected utility and principles of diachronic rationality which are prima facie plausible. Hájek concludes that the latter are false, but doesn't provide a clear diagnosis as to why. We endeavour to further our understanding of the paradox by providing such a diagnosis. (shrink)