The Pasadena game is an example of a decision problem which lacks an expected value, as traditionally conceived. Easwaran (2008) has shown that, if we distinguish between two different kinds of expectations, which he calls ‘strong’ and ‘weak’, the Pasadena game lacks a strong expectation but has a weak expectation. Furthermore, he argues that we should use the weak expectation as providing a measure of the value of an individual play of the Pasadena game. By considering a modified version of (...) the Pasadena game, I argue that weak expectations may provide a very poor measure of the value of an individual play of the game, and hence should not be used to value individual plays unless further information is taken into consideration. (shrink)

One of the reasons for adopting hyperbolic discounting is to explain preference reversals. Another is that this value structure suggests an elegant theory of the will. I examine the capacity of the theory to solve Newcomb's problem. In addition, I compare Ainslie's account with other procedural theories of choice that seem at least equally capable of accommodating reversals of preference.

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as ‘Trumped’ (Arntzenius and McCarthy 1997), ‘Rouble trouble’ (Arntzenius and Barrett 1999), ‘The airtight Dutch book’ (McGee 1999), and ‘The two envelopes puzzle’ (Broome 1999). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (shrink)

There are two boxes in front of you and you are asked to choose between taking only box B or taking both box A and box B. Box A contains $ 1,000. Box B will contain either nothing or $ 1,000,000. What B will contain is (or will be) determined by Predictor, who has an excellent track record of predicting your choices. There are two possibilities. Either Predictor has already made his move by predicting your choice and putting a million (...) dollars in B iff he predicted that you will take only B (like in the standard Newcomb problem); or else Predictor has not yet made his move but will wait and observe what box you choose and then put a million dollars in B iff you take only B. In cases like this, Predictor makes his move before the subject roughly half of the time. However, there is a Metapredictor, who has an excellent track record of predicting Predictor’s choices as well as your own. You know all this. Metapredictor informs you of the following truth functional: Either you choose A and B, and Predictor will make his move after you make your choice; or else you choose only B, and Predictor has already made his choice. Now, what do you choose? (shrink)

How should we update our beliefs when we learn new evidence? Bayesian confirmation theory provides a widely accepted and well understood answer – we should conditionalize. But this theory has a problem with self-locating beliefs, beliefs that tell you where you are in the world, as opposed to what the world is like. To see the problem, consider your current belief that it is January. You might be absolutely, 100%, sure that it is January. But you will soon believe it (...) is February. This type of belief change cannot be modelled by conditionalization. We need some new principles of belief change for this kind of case, which I call belief mutation. In part 1, I defend the Relevance-Limiting Thesis, which says that a change in a purely self-locating belief of the kind that results in belief mutation should not shift your degree of belief in a non-self-locating belief, which can only change by conditionalization. My method is to give detailed analyses of the puzzles which threaten this thesis: Duplication, Sleeping Beauty, and The Prisoner. This also requires giving my own theory of observation selection effects. In part 2, I argue that when self-locating evidence is learnt from a position of uncertainty, it should be conditionalized on in the normal way. I defend this position by applying it to various cases where such evidence is found. I defend the Halfer position in Sleeping Beauty, and I defend the Doomsday Argument and the Fine-Tuning Argument. (shrink)

The aim of this paper is to diagnose the so-called two envelopes paradox. Many writers have claimed that there is something genuinely paradoxical in the situation with the two envelopes, and some writers are now developing non-standards theories of expected utility. I claim that there is no paradox for expected utility theory as I understand that theory, and that contrary claims are confused. Expected utility theory is completely unaffected by the two-envelope paradox.

It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game. We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We also show a case where repeatedly opting for a higher expected value leads to a worse outcome.

This paper treats two problem cases in decision theory, the Newcomb problem and Reed Richter''s Button III. Although I argue that, contrary to Richter, the latter case does not constitute a genuine counterexample to a standard general proposition of (causal) decision theory, I agree with and undertake to amplify his solution to the decision problem in Button III. I then apply the conclusions and distinctions in the foregoing treatment of Button III to the Newcomb problem and argue that a familiar (...) version of the dominance argument for taking both boxes runs afoul of plausible general constraints on rational agency. The underlying theme of the paper is that basic considerations of epistemic coherence play an important role in dealing with problem cases in decision theory. (shrink)

One's inaccuracy for a proposition is defined as the squared difference between the truth value (1 or 0) of the proposition and the credence (or subjective probability, or degree of belief) assigned to the proposition. One should have the epistemic goal of minimizing the expected inaccuracies of one's credences. We show that the method of minimizing expected inaccuracy can be used to solve certain probability problems involving information loss and self-locating beliefs (where a self-locating belief of a temporal part of (...) an individual is a belief about where or when that temporal part is located). We analyze the Sleeping Beauty problem, the duplication version of the Sleeping Beauty problem, and various related problems. (shrink)

The square of opposition (as part of a lattice) is used as a natural way to represent different and opposite ways of who makes decisions, and in what way, in/for a group or a society. Majority logic is characterized by multiple logical squares (one for each possible majority), with the “discursive dilemma” as a consequence. Three-valued logics of majority decisions with discursive dilemma undecided, of veto, consensus, and sequential voting are analyzed from the semantic point of view. For instance, the (...) paraconsistent and paracomplete logics M3, M3veto and C3 are described. The distinction of designated and non-designated values is not used, and instead, the consequence relation is defined as a preservation of the minimum truth-value of the implying set of sentences. The consequence and opposition relations of the logics described are compared, and an ordering of the logics with respect to their opposition relations is established. (shrink)

Four variations on Two Envelope Paradox are stated and compared. The variations are employed to provide a diagnosis and an explanation of what has gone awry in the paradoxical modeling of the decision problem that the paradox poses. The canonical formulation of the paradox underdescribes the ways in which one envelope can have twice the amount that is in the other. Some ways one envelope can have twice the amount that is in the other make it rational to prefer the (...) envelope that was originally rejected. Some do not, and it is a mistake to treat them alike. The nature of the mistake is diagnosed by the different roles that rigid designators and definite descriptions play in unproblematic and in untoward formulations of decision tables that are employed in setting out the decision problem that gives rise to the paradox. The decision maker’s knowledge or ignorance of how one envelope came to have twice the amount that is in the other determines which of the different ways of modeling his decision problem is correct. Under this diagnosis, the paradoxical modeling of the Two Envelope problem is incoherent. (shrink)

The relations between rationality and optimization have been widely discussed in the wake of Herbert Simon's work, with the common conclusion that the rationality concept does not imply the optimization principle. The paper is partly concerned with adding evidence for this view, but its main, more challenging objective is to question the converse implication from optimization to rationality, which is accepted even by bounded rationality theorists. We discuss three topics in succession: (1) rationally defensible cyclical choices, (2) the revealed preference (...) theory of optimization, and (3) the infinite regress of optimization. We conclude that (1) and (2) provide evidence only for the weak thesis that rationality does not imply optimization. But (3) is seen to deliver a significant argument for the strong thesis that optimization does not imply rationality. (shrink)

Suppose that a very large number of people, say one billion, will suffer a moderately severe headache for the next twenty-four hours. For these billion people, the next twenty-four hours will be fairly unpleasant, though by no means unbearable. However, there will be no side-effects from these headaches; no drop in productivity in the work-place, no lapses in concentration leading to accidents, no unkind words spoken to loved ones that will later fester. Nonetheless, it is clearly desirable that these billion (...) people avoid the headaches. Even though the headaches are moderate, they are impervious to pain-killing drugs, acupuncture, transcendental meditation, and just about any other remedy. In fact, there is only one way in which the headaches can be avoided. In a remote South American village, a young woman, Agnes, is suffering from a fever. A simple dose of antibiotics will save her life, otherwise she will die. If, and only if, she dies, the billion headaches will be prevented. You just happen to be passing through the village, in full knowledge of the circumstances. Although not a doctor (and therefore not bound by codes of professional ethics, Hippocratic oaths, etc.), you possess the requisite dose of antibiotics, for which you have no other use, and which will become useless, if not used in the next two hours. (shrink)

In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.

Piccione and Rubinstein (1997) present and analyse the sequential decision problem of an “absentminded driver”. The driver's absentmindedness (imperfect recall) leads him to time-inconsistent strategy evaluations. His original evaluation gets replaced by a new one under impact of the information that the circumstances have changed, notwithstanding the fact that this change in circumstances has been expected by him all along. The time inconsistency in strategy evaluation suggests that such an agent might have reason to renege on his adopted strategy. As (...) we shall see, however, this danger is only apparent. There is no serious problem of dynamic inconsistency in this case. My diagnosis of the case under consideration is in many respects similar to the one provided by Aumann, Hart and Perry (1997), but the analysis leading to this diagnosis is not quite the same. (shrink)

Simon Blackburn has claimed that on a theory of revealed preference it is tautological that any eligible player - one whose preferences are consistent - plays hawk, chooses a strategy of non-cooperation with the other prisoner. This claim is examined and rejected. A prisoner in the appropriate sense is defined not by preferences over actions (playing hawk or playing dove) but by preferences over the four possible outcomes which result from the players' actions jointly (both playing hawk, both playing dove, (...) the first playing hawk and the second dove, and vice versa). It is not inconsistent to suppose that a prisoner has the appropriate preferences over outcomes but nevertheless chooses to play dove. This can happen either if the prisoner believes for some reason that the full range of outcomes is not available, or if the prisoner is simply a bad strategic thinker. It is perhaps tautological that a player with the appropriate preferences over outcome and with suitable beliefs will if rational choose to play hawk. However, rationality would then involve an appeal to a further principle, the sure-thing principle: if a prisoner would choose hawk knowing that the other will choose hawk, and would also choose hawk knowing that the other will choose dove, then hawk should be chosen when it is uncertain what the other will choose. (shrink)

It is plausible that Newcomb problems in which causal maximizers and evidential maximizers would do different things would not be possible for ideal maximizers who are attentive to metatickles. An objection to Eells's first argument for this makes welcome a second. Against it I argue that even ideal evidential and causal maximizers would do different things in some non-dominance Newcomb problems; and that they would hope for different things in some third-person and non-action problems, which is relevant if a good (...) theory of rational choices of acts should fit smoothly into a good theory of rational desires for facts. (shrink)

I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief (as opposed to “imprecise” belief), such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an (...) agent may come to have unique preferences for each of the Ellsberg options. Levi (1986, Hard choices: Decision making under unresolved conflict. Cambridge, New York: Cambridge University Press) holds that the extra element amounts to innocuous secondary “risk” or security considerations that are used to break ties when more than one option is rationally permissible. While I think a lexical choice rule of this kind is very plausible, I argue that it involves a greater break with xpected utility theory than mere violation of the ordering axiom. (shrink)

Examples involving common causes — most prominently, examples involving genetically influenced choices — are analytically equivalent not to standard Newcomb Problems — in which the Predictor genuinely predicts the agent's decision — but to non-standard Newcomb Problems — in which the Predictor guarantees the truth of her predictions by interfering with the agent's decision to make the agent choose as it was predicted she would. When properly qualified, causal and epistemic decision theories diverge only on standard — not on non-standard (...) — Newcomb Problems, and thus not on examples involving common causes. (shrink)

In Newcomb’s paradox you can choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to accurately deduce your choice, and uses that deduction to fill the two boxes. The way they do this guarantees that you made the wrong choice. Newcomb’s paradox is that game theory’s expected utility and dominance principles appear to provide conflicting recommendations for what (...) you should choose. Here we show that the conflicting recommendations assume different probabilistic structures relating your choice and the algorithm’s prediction. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the probabilistic structure relating the problem’s random variables is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb’s paradox, the focus of much previous work, is irrelevant. We end by showing that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its ‘prediction’ after you make your choice rather than before. (shrink)

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)

If the task of theoretical reason is to discover truth or reasons for belief, then theoretical reason is impossible. Attempts to circumvent this by appeal to probabilities are self-defeating. If the task of practical reason is to discover what we ought to do or what actions are desirable or valuable, then practical reason is impossible. Appeal to the subjective ought is self-defeating and often gives either a wrong answer or a self-contradictory one. I argue that the task of theoretical reason (...) is to decide which propositions to instate; and that the task of practical reason is to decide which ought-propositions to act on. As a consequence theoretical reason is seen as a branch of practical reason. This approach makes both theoretical and practical reason practicable and free of the defects of the usual accounts. (shrink)

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)

This chapter argues that, under certain conditions, forming an intention makes an action rational which would otherwise not have been rational, since intentions (together with beliefs) in and of themselves provide deductive reasons for further intentions and actions, an argument which builds on previous work by R M Hare, Michael Bratman and others, It also provides an articulation and defense of the concept of "minimally constrained maximization" as a unified general solution to the well-known paradoxes of rationality, including the paradox (...) of deterrence and the prisoner's dilemma. (shrink)

The traditional form of the backward induction argument, which concludes that two initially rational agents would always defect, relies on the assumption that they believe they will be rational in later rounds. Philip Pettit and Robert Sugden have argued, however, that this assumption is unjustified. The purpose of this paper is to reconstruct the argument without using this assumption. The formulation offered concludes that two initially rational agents would decide to always defect, and relies only on the weaker assumption that (...) they do not believe they will not be rational in later rounds. The argument employs the idea that decisions justify revocable presumptions about behaviour. (shrink)

In their attempt to provide a reason to be moral, contractarians such as David Gauthier are concerned with situations allowing a group of agents the chance of mutual benefit, so long as at least some of them are prepared to constrain their maximising behaviour. But what justifies this constraint? Gauthier argues that it could be rational (because maximising) to intend to constrain one's behaviour, and in certain circumstances to act on this intention. The purpose of this paper is to examine (...) the conditions under which it is rational to form, and to act on, intentions. I introduce and examine in detail what Gauthier has to say on these issues, argue that it suffers from various problems, and propose an alternative account which I claim avoids them. (shrink)

To show it is sometimes rational to cooperate in the Prisoner's Dilemma, David Gauthier has claimed that if it is rational to form an intention then it is sometimes rational act on it. However, the Paradox of Deterrence and the Toxin Puzzle seem to put this general type of claim into doubt. For even if it is rational to form a deterrent intention, it is not rational act on it (if it is not successful); and even if it is rational (...) to form an intention to drink a toxin, it is not rational to act on it (come the time for drinking). This article employs an extended version of Michael Bratman's theory of intention to show how to argue systematically that it can be rational to act on rationally formed cooperative intentions, while not being committed to the rationality of apocalyptic retaliation, or pointless toxin drinking. (shrink)

David Gauthier has argued that, under certain conditions, cooperation in the Prisoner's Dilemma is rational. A crucial principle he employs in this argument, however, also implies the pointless retaliation after a failed threat could also be rational. In this paper, I introduce one possible reformulation of the Cooperation Argument, by replacing its second premise with a principle connecting rationally adopted intentions, rational action, and rational reconsideration, and a specific theory of rational reconsideration. I then argue that this reformulated Cooperation Argument (...) is not susceptible to any form of the Deterrence Objection, and conclude that the Deterrence Objection may be circumvented if proper attention is paid to the role of rational reconsideration. (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)

This paper presents a number of apparent anomalies in rational choice scenarios, and their translation into the logic of everyday reasoning. Three classes of examples that have been discussed in the context of probabilistic choice since the 1960s (by Debreu, Tversky and others) are analyzed in a non-probabilistic setting. It is shown how they can at the same time be regarded as logical problems that concern the drawing of defeasible inferences from a given information base. I argue that initial appearances (...) notwithstanding, these cases should not be classed as instances of irrationality in choice or reasoning. One way of explaining away their apparent oddity is to view certain aspects of these examples as making particular options salient. The decision problems in point can then be solved by ‘picking’ these options, although they could not have been ‘chosen’ in a principled way, due to ties or incomparabilities with alternative options. (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)

Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...) insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)

This paper aims to make three contributions to decision theory. First there is the hope that it will help to re-establish the legitimacy of the problem, pace various recent analyses provided by Maitzen and Wilson, Slezak and Priest. Second, after pointing out that analyses of the problem have generally relied upon evidence that is conditional on the taking of one particular option, this paper argues that certain assumptions implicit in those analyses are subtly flawed. As a third contribution, the piece (...) aims to draw attention to an important similarity between Newcomb’s problem and the toxin puzzle. In short, both problems illustrate the fact that you can have a reason to intend to φ without having a reason to actually φ. (shrink)

The Newcomb problem is analysed here as a type of common cause problem. In relation to such problems, if you take the dominated option your expected outcome will be good and if you take the dominant option your expected outcome will be not so good. As is explained, however, these arenot conventional conditional expected outcomes but `conditional evidence expected outcomes' and while in the deliberation process, the evidence on which they are based is only hypothetical evidence.Conventional conditional expected outcomes are (...) more sensitive to your current epistemic state in that they are based purely on actual evidence which is available to you during the deliberation process. So although they are conditional on a certain act being performed, they are not based on evidence that you would have only if that act is performed. Moreover, for any given epistemic state during the deliberation process, your conventional conditional expected outcome for the dominant option will be better than that for the dominated option. The principle of dominance is thus in perfect harmony with the conventional conditional expected outcomes. In relation to the Newcomb problem then, the evidence unequivocally supports two-boxing as the rational option. Yet what is advanced here is not simply a two-boxing strategy. To see why, two stages to the problem need to be recognised. The first stage is that which occurs before the information used by the predictor in making his predictions has been gained. The second stage is after this point. Provided that you are still in the first stage, you have an opportunity to influence whether or not the predictor places the $1m in the opaque box. To maximise the probability that it is, you need to commit yourself to one-boxing. (shrink)

1 Background for the Uninitiated RICHMOND CAMPBELL Paradoxes are intrinsically fascinating. They are also distinctively ...

I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations (...) underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. (shrink)

Certain paradoxes set us reeling endlessly. In surprise examination paradoxes, pupils' reasonings lead them to reel between expecting an examination and expecting none. With Newcomb's puzzle, choosers reel between reasoning in favour of choosing just one box and choosing two. The paradoxes demand an answer to what it is rational to believe or do. Highlighting other reelings and puzzles, this paper shows that the paradoxes should come as no surprise. The paradoxes demand an end to our reasoning when the conditions (...) they set ensure no end. They equivocate between, so to speak, reasoning in heaven and reasoning on earth; and, on the conditions set, not even an infinite god could reach a conclusion. (shrink)

Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to be (...) independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments. (shrink)

Newcomb’s problem is a decision puzzle whose difficulty and interest stem from the fact that the possible outcomes are probabilistically dependent on, yet causally independent of, the agent’s options. The problem is named for its inventor, the physicist William Newcomb, but first appeared in print in a 1969 paper by Robert Nozick [12]. Closely related to, though less well-known than, the Prisoners’ Dilemma, it has been the subject of intense debate in the philosophical literature. After three decades, the issues remain (...) unresolved. Newcomb’s problem is of genuine importance because it poses a challenge to the theoretical adequacy of orthodox Bayesian decision theory. It has led both to the development of causal decision theory and to efforts aimed at defending the adequacy of the orthodox theory. (shrink)

Doris Olin's Paradox is a very helpful book for those who want to be introduced to the philosophical treatment of paradoxes, or for those who already have knowledge of the general area and would like to have a helpful resource book.

Newcomb's Paradox thus serves as an illustrative vindication of the compatibility of divine foreknowledge and human freedom. A proper understanding of the counterfactual conditionals involved enables us to see that the pastness of God's knowledge serves neither to make God's beliefs counterfactually closed nor to rob us of genuine freedom. It is evident that our decisions determine God's past beliefs about those decisions and do so without invoking an objectionable backward causation. It is also clear that in the context of (...) foreknowledge, backtracking counterfactuals are entirely appropriate and that no alteration of the past occurs. With the justification of the one box strategy, the death of theological fatalism seems ensured. *** DIRECT SUPPORT *** A0985044 00003. (shrink)

• What’s essential to Newcomb’s problem? 1. You must choose between two particular acts: A1 = you take just the opaque box; A2 = you take both boxes, where the two states of nature are: S 1 = there’s $1M in the opaque box, S2 = there’s $0 in the opaque box.

Should we act only for the sake of what we might bring about (causal decision theory); or is it enough for a decent motive that our action is highly correlated with something desirable (evidential decision theory)? The conflict between these points of view is embodied in Newcomb's problem. It is argued here that intuitive evidence from familiar decision contexts does not enable us to settle the issue, since the two theories dictate the same results in normal circumstances. Nevertheless, there are (...) several reasons to reject the causal approach: (1) its relative complexity; (2) its commitment to the existence of situations in which every possible act would be irrational; (3) its incorporation of an arbitrary time bias; and (4) its implicit distinction between what ought to be done and what ought to be hoped for. (shrink)

In their development of causal decision theory, Allan Gibbard and William Harper advocate a particular method for calculating the expected utility of an action, a method based upon the probabilities of certain counterfactuals. Gibbard and Harper then employ their method to support a two-box solution to Newcomb’s paradox. This paper argues against some of Gibbard and Harper’s key claims concerning the truth-values and probabilities of counterfactuals involved in expected utility calculations, thereby disputing their analysis of Newcomb’s Paradox. If we are (...) right, then Gibbard and Harper’s method of calculating expected utility does not adequately represent rational choice. (shrink)

Among various cases that equally admit of evidentialist reasoning, the supposedly evidentialist solution has varying degrees of intuitive attractiveness. I suggest that cooperative reasoning may account for the appeal of apparently evidentialist behavior in the cases in which it is intuitively attractive, while the inapplicability of cooperative reasoning may account for the unattractiveness of evidentialist behaviour in other cases. A collective causal power with respect to agreed outcomes, not evidentialist reasoning, makes cooperation attractive in the Prisoners' Dilemma. And a natural (...) though unwarranted assumption of such a power may account for the intuitive appeal of the one-box response in Newcomb's Problem. (shrink)

Abstract Newcomb's problem is regularly described as a problem arising from equally defensible yet contradictory models of rationality. Braess? paradox is regularly described as nothing more than the existence of non?intuitive (but ultimately non?contradictory) equilibrium points within physical networks of various kinds. Yet it can be shown that Newcomb's problem is structurally identical to Braess? paradox. Both are instances of a well?known result in game theory, namely that equilibria of non?cooperative games are generally Pareto?inefficient. Newcomb's problem is simply a limiting (...) case in which the number of players equals one. Braess? paradox is another limiting case in which the ?players? need not be assumed to be discrete individuals. The result is that Newcomb's problem is no more difficult to solve than (the easy to solve) Braess? paradox. (shrink)

Richard Jeffrey long held that decision theory should be formulated without recourse to explicitly causal notions. Newcomb problems stand out as putative counterexamples to this ‘evidential’ decision theory. Jeffrey initially sought to defuse Newcomb problems via recourse to the doctrine of ratificationism, but later came to see this as problematic. We will see that Jeffrey’s worries about ratificationism were not compelling, but that valid ratificationist arguments implicitly presuppose causal decision theory. In later work, Jeffrey argued that Newcomb problems are not (...) decisions at all because agents who face them possess so much evidence about correlations between their actions and states of the world that they are unable to regard their deliberate choices as causes of outcomes, and so cannot see themselves as making free choices. Jeffrey’s reasoning goes wrong because it fails to recognize that an agent’s beliefs about her immediately available acts are so closely tied to the immediate causes of these actions that she can create evidence that outweighs any antecedent correlations between acts and states. Once we recognize that deliberating agents are free to believe what they want about their own actions, it will be clear that Newcomb problems are indeed counterexamples to evidential decision theory. (shrink)

Newcomb's problem supposedly involves your choosing one or else two boxes in circumstances in which a predictor has made a prediction of how many boxes you will choose. We argue that the circumstances which allegedly define Newcomb's problem generate a previously unnoticed regress which shows that Newcomb's problem is insoluble because it is ill-formed. Those who favor, as we do, a ``no-box'' reply to Newcomb's problem typically claim either that the problem's solution is underdetermined or else that it is overdetermined. (...) We are no-boxers of the first kind, but the underdetermination we identify is more radical than any previously identified: it blocks the very set-up of the problem and not just potential solutions to the problem once it has been set up. The defect is subtle, but it cripples every genuine version of the problem, regardless of variations in such things as the predictor's degree of reliability, the basis on which the prediction is made, or the amount of money in each box. The regress shows that, surprisingly enough, no one can understand Newcomb's problem, and so no one can possibly solve it. (shrink)

Abstract In an engaging and ingenious paper, Irvine (1993) purports to show how the resolution of Braess? paradox can be applied to Newcomb's problem. To accomplish this end, Irvine forges three links. First, he couples Braess? paradox to the Cohen?Kelly queuing paradox. Second, he couples the Cohen?Kelly queuing paradox to the Prisoner's Dilemma (PD). Third, in accord with received literature, he couples the PD to Newcomb's problem itself. Claiming that the linked models are ?structurally identical?, he argues that Braess solves (...) Newcomb's problem. This paper shows that Irvine's linkage depends on structural similarities?rather than identities?between and among the models. The elucidation of functional disanalogies illuminates structural dissimilarities which sever that linkage. I claim that the Cohen?Kelly queuing paradox cloaks a fine structure that decouples it from both Braess? paradox and the PD (Marinoff, 1996a). I further assert that the putative reduction of the PD to a Newcomb problem (e.g. Brams, 1975; Lewis, 1979) is seriously flawed. It follows that Braess? paradox does not solve Newcomb's problem via the foregoing and herein sundered chain. I conclude by substantiating a stronger claim, namely that Braess'paradox cannot solve Newcomb's problem at all. (shrink)

In “Bayesianism, Infinite Decisions, and Binding”, Arntzenius et al. (Mind 113:251–283, 2004 ) present cases in which agents who cannot bind themselves are driven by standard decision theory to choose sequences of actions with disastrous consequences. They defend standard decision theory by arguing that if a decision rule leads agents to disaster only when they cannot bind themselves, this should not be taken to be a mark against the decision rule. I show that this claim has surprising implications for a (...) number of other debates in decision theory. I then assess the plausibility of this claim, and suggest that it should be rejected. (shrink)