In spite of its infinite expectation value, the St. Petersburg game is not only a gamble without supply in the real world, but also one without demand at apparently very reasonable asking prices. We offer a rationalizing explanation of why the St. Petersburg bargain is unattractive on both sides (to both house and player) in the mid-range of prices (finite but upwards of about $4). Our analysis – featuring (1) the already-established fact that the average of finite ensembles of the (...) St. Petersburg game grows with ensemble size but is unbounded, and (2) our own simulation data showing that the debt-to-entry fee ratio rises exponentially – explains why both house and player are quite rational in abstaining from the St. Petersburg game. The house will be unavoidably (and intentionally) exposed to very large ensembles (with very high averages, and so very costly to them), while contrariwise even the well-heeled player is not sufficiently capitalized (as our simulation data reveals) to be able to capture the potential gains from large-ensemble play. (Smaller ensembles, meanwhile, enjoy low means, as others have shown, and so are not worth paying more than $4 to play, even if a merchant were to offer them at such low prices per trial.) Both sides are consequently rational in abstaining from entry into the St. Petersburg market in the mid-range of asking prices. We utilize the concept of capitalization vis-à-vis a gamble to make this case. Classical analyses of this question have paid insufficient attention to the question of the propriety of using expected values to assess the St. Petersburg gamble. And extant analyses have not noted the average-maximum-debt-before-breaking-even figures, and so are incomplete. (shrink)

It is argued that higher-order awareness is central to one type of everyday rationality. The author starts by specifying the target notion of rationality, contrasting it with other useful notions in the neighbourhood. It is then shown that the target notion relies on first-person awareness of the unfolding of cognition. This is used to explain the kernel of truth in epistemic conservatism, the structure of defeasibility, and the root motive behind the widely accepted distinction between rational inference and trivial entailment.

According to the orthodox treatment of risk preferences in decision theory, they are to be explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for conflating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that an agent's attitudes to risk should be captured by a risk function that is independent of her utility and probability functions. The main (...) problem with that approach is that it suggests that attitudes to risk are wholly distinct from people's (non-instrumental) desires. To overcome this problem, we develop a framework where an agent's utility function is defined over chance propositions (i.e., propositions describing objective probability distributions) as well as ordinary (non-chance) ones, and argue that one should explain different risk attitudes in terms of different forms of the utility function over such propositions. (shrink)

Jim Joyce has argued that David Lewis’s formulation of causal decision theory is inadequate because it fails to apply to the “small world” decisions that people face in real life. Meanwhile, several authors have argued that causal decision theory should be developed such that it integrates the interventionist approach to causal modeling because of the expressive power afforded by the language of causal models, but, as of now, there has been little work towards this end. In this paper, I propose (...) a variant of Lewis’s causal decision theory that is intended to meet both of these demands. Specifically, I argue that Lewis’s causal decision theory can be rendered applicable to small world decisions if one analyzes his dependency hypotheses as causal hypotheses that depend on the interventionist causal modeling framework for their semantics. I then argue that this interventionist variant of Lewis’s causal decision theory is preferable to interventionist causal decision theories that purportedly generalize Lewis’s through the use of conditional probabilities. This is because Lewisian interventionist decision theory captures the causal decision theorist’s conviction that any correlation between what the agent does and cannot cause should be irrelevant to the agent’s choice, while purported generalizations do not. (shrink)

Chance Neutrality is the thesis that, conditional on some proposition being true, its chance of being true should be a matter of practical indifference. The aim of this article is to examine whether Chance Neutrality is a requirement of rationality. We prove that given Chance Neutrality, the Principal Principle entails a thesis called Linearity; the centerpiece of von Neumann and Morgenstern’s expected utility theory. With this in mind, we argue that the Principal Principle is a requirement of practical rationality but (...) that Linearity is not and, hence, that Chance Neutrality is not rationally required. (shrink)

The Bayesian maxim for rational learning could be described as conservative change from one probabilistic belief or credence function to another in response to newinformation. Roughly: ‘Hold fixed any credences that are not directly affected by the learning experience.’ This is precisely articulated for the case when we learn that some proposition that we had previously entertained is indeed true (the rule of conditionalisation). But can this conservative-change maxim be extended to revising one’s credences in response to entertaining propositions or (...) concepts of which one was previously unaware? The economists Karni and Vierø (2013, 2015) make a proposal in this spirit. Philosophers have adopted effectively the same rule: revision in response to growing awareness should not affect the relative probabilities of propositions in one’s ‘old’ epistemic state. The rule is compelling, but only under the assumptions that its advocates introduce. It is not a general requirement of rationality, or so we argue. We provide informal counterexamples. And we show that, when awareness grows, the boundary between one’s ‘old’ and ‘new’ epistemic commitments is blurred. Accordingly, there is no general notion of conservative change in this setting. (shrink)

According to our intuitions, certain generalizations are better confirmed by positive instances than others. In order to characterize the difference between these generalizations, I have proposed in [3] to investigate the generalizing behavior of living beings. Such an investigation makes it possible to classify into different categories the generalizations that are intuitively confirmed by their positive instances and those that are not intuitively confirmed by such instances. One important aspect of my treatment, however, has been shown to be unsatisfactory: sentences (...) that are logically equivalent may belong to different categories. In this paper, I shall first give a short summary of the relevant parts of my previous paper, and then I shall try to improve it in order to avoid the undesirable result. (shrink)

The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to ambiguity---which is both (...) the most commonly observed and a seemingly reasonable attitude to ambiguity---however supports a version of Egalitarianism, whose logical form is quite different from the theories defended by the aforementioned authors. Moreover, it turns out that the veil of ignorance argument neither supports standard Utilitarianism nor Prioritarianism unless we assume that rational people are insensitive to ambiguity. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...) reasoning with idealized models in science. (shrink)

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

The crucial premise of the standard argument for two-boxing in Newcomb's problem, a causal dominance principle, is false. We present some counterexamples. We then offer a metaethical explanation for why the counterexamples arise. Our explanation reveals a new and superior argument for two-boxing, one that eschews the causal dominance principle in favor of a principle linking rational choice to guidance and actual value maximization.

Consequentialists often assume rational monism: the thesis that options are always made rationally permissible by the maximization of the selfsame quantity. This essay argues that consequentialists should reject rational monism and instead accept rational pluralism: the thesis that, on different occasions, options are made rationally permissible by the maximization of different quantities. The essay then develops a systematic form of rational pluralism which, unlike its rivals, is capable of handling both the Newcomb problems that challenge evidential decision theory and the (...) unstable problems that challenge causal decision theory. (shrink)

Two partition-theorems are proved for a particular causal decision theory. One is restricted to a certain kind of partition of circumstances, and analyzes the utility of an option in terms of its utilities in conjunction with circumstances in this partition. The other analyzes an option's utility in terms of its utilities conditional on circumstances and is quite unrestricted. While the first form seems more useful for applications, the second form may be of theoretical importance in foundational exercises. Comparisons are made (...) with theorems of Richard Jeffrey, Brad Armendt, and Peter Fishburn. (shrink)

Responses to Newcomb-like challenges to evidential decision theories such as Jeffrey’s “logic of decision” range from allegations of incoherence and irrelevance; through stonewalling - “Just one box for me, thank you.“; to arguments that maintain that when properly applied by an ideal agent such theories get the right answers and, for example, prescribe the taking of both boxes, not just one; on to conservative revisions of evidential decision theories that are held to get these supposedly right answers while remaining true (...) to its evidential, Humean spirit; and finally to responses of radical revisionists who claim that only causal decision theories can get all Newcomb-like problem cases right. I discuss responses of the first sort in another paper - “Newcomb-like Problems for Jeffrey’s Logic of Decision.”. (shrink)

After maintaining in that certain cyclical preferences can be reasonable, the following questions were tabled: “in what circumstances and under what assumptions … these … preferences of George's would turn him into a ”money pump,” and in what circumstances and under what assumptions they would not do that.” Two pumps afford answers. George, who is sufficiently reasonable and well-informed to use backward induction, has, for this reason, nothing to fear from the first pump, but the second, of a nonstandard design (...) by Wlodek Rabinowicz, ruins him just because he is subject to the constraints of backward induction. Could he be helped by extending his options from actions in a single round, to courses of actions starting in that round? Possibly not. He would be safe if he were capable of resolute choices of couses of action. Even so, he is in trouble through no fault of his, if, as I think, not having that capacity, though a misfortune, is not a fault. (shrink)

Rational actions reflect beliefs and preferences in certain orderly ways. The problem of theory is to explain which beliefs and preferences are relevant to the rationality of particular actions, and exactly how they are relevant. One distinction of interest here is between an agent's beliefs and preferences just before an action's time, and his beliefs and preferences at its time. Theorists do not agree about the times of beliefs and desires that are relevant to the rationality of action. Another distinction (...) is between actions that would, in one sense or another, maximize expected utilities given relevant beliefs and desires, and actions, decisions for which would, in one sense or another, be stable. There is disagreement about the relevance of these things to the rationality of actions. Here, in the first part below, several possible positions on these issues are explained and compared. In the second part, I contrast perspectives on these issues, and comment on arguments that might be brought against the position I favor. In the third part, I restate and elaborate on this position. (shrink)

An example shows that 'pairwise preferences' (certain hypothetical choices) can cycle even when rational. General considerations entail that preferences tout court (certain relations of actual valuations) cannot cycle. A world-bayesian theory is explained that accommodates these two kinds of preference, and a theory for rational actions that would have them maximize and be objects of ratifiable choices. It is observed that choices can be unratifiable either because of troublesome credences or because of troublesome preferences. An appendix comments on a third (...) way in which efforts to maximize can be frustrated. (shrink)

Relations between conditional probabilities, revisions of probabilities in the light of new information, and conditions of ideal rationality are discussed herein. The formal character of conditional probabilities, and their significance for epistemic states of agents is taken up. Then principles are considered that would, under certain conditions, equate rationally revised probabilities on new information with probabilities reached by conditionalizing on this information. And lastly the possibility of kinds of ‘books’ against known non-conditionalizers is explored, and the question is taken up, (...) What, if anything, would be wrong with a person against whom such a book could be made?1. The standard mathematical treatment takes probability functions as basic, and conditional probabilities defined. If P(-) is a probability function, then is its conditional probability function if and only if P(h/e) is defined only for e such that P(e) > 0, and is then equal to P(e & h)/P(e). (shrink)

A de minimis risk is defined as a risk that is so small that it may be legitimately ignored when making a decision. While ignoring small risks is common in our day-to-day decision making, attempts to introduce the notion of a de minimis risk into the framework of decision theory have run up against a series of well-known difficulties. In this paper, I will develop an enriched decision theoretic framework that is capable of overcoming two major obstacles to the modelling (...) of de minimis risk. The key move is to introduce, into decision theory, a non-probabilistic conception of risk known as normic risk. (shrink)

The degrees of belief of rational agents should be guided by the evidence available to them. This paper takes as a starting point the view—argued elsewhere—that the formal model best able to capture this idea is one that represents degrees of belief using Dempster–Shafer belief functions. However degrees of belief should not only respect evidence: they also guide decision and action. Whatever formal model of degrees of belief we adopt, we need a decision theory that works with it: that takes (...) as input degrees of belief so represented. The task of this paper is to develop such a decision theory for the belief function model of degrees of belief. This is not the first paper to attempt that task, but compared to the existing literature it takes a more abstract route to its destination, via a consideration of the very idea of rational decision making in light of one’s beliefs and desires. After presenting the new decision theory and comparing it to existing views, the paper goes on to consider diachronic decision situations. (shrink)

By “Propensities” I mean the kind of probabilities that figure in laws of nature. Propensities might be (i) relative frequencies, finite or long run, de facto or modalized, or (ii) reflections of our epistemic probabilities or (iii) sui generus theoretical notions. I believe that the whole family of relative frequency proposals (i) are inadequate. As an alternative I wish to suggest (ii) an epistemic account of propensities and of nomic force in general, in the spirit of Hume, Mill, DeFinetti, Ayer, (...) Suppes and Jeffrey. Whether accounts of the third kind differ in substance or in name only from the sort of account that I am proposing is a nice question, to which. I will devote some brief closing remarks. (shrink)

Does the philosophy of Radical Probabilism have enough structure to enable it to address fundamental epistemological questions? The requirement of dynamic coherence provides the structure for radical probabilist epistemology. This structure is sufficient to establish (i) the value of knowledge and (ii) long run convergence of degrees of belief.

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of "ratifiability" is the appropriate generalization of "evolutionarily stable strategy". The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may be (...) selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected. (shrink)

There is not a unique inductive skeptical position; there are grades of inductive skepticism. There is nothing much to say about complete skepticism, but some more restricted skeptical positions may be profitably analyzed.

We show how Richard Jeffrey's The Logic of Decision provides the proper formalism for calculating expected fitness for correlated encounters in general. As an illustration, some puzzles about kin selection are resolved.

The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.

The question of diachronic coherence, coherence of degrees of belief across time, is investigated within the context of Richard Jeffrey’s radical probabilism. Diachronic coherence is taken as fundamental, and coherence results for degrees of belief at a single time, such as additivity, are recovered only with additional assumptions. Additivity of probabilities of probabilities is seen to be less problematic than additivity of first-order probabilities. Without any assumed model of belief change, diachronic coherence applied to higher-order degrees of belief yields the (...) martingale property. (shrink)

Theories in the cognitive science of religion (CSR) are sometimes seen as debunking religious or supernatural beliefs (SBs). To date, arguments have been produced by proponents on both sides, with some claiming that debunking would result and others claiming that it would not. In this paper, I depart from the approach taken by others and offer an approach based in broadly Bayesian methods of updating subjective probability assignments, including classical Bayesian formulas as well as comparative ratios and Jeffrey conditionalization. I (...) argue that debunking may take place, but only if specified conditions are met. One way to show that debunking takes place would be to show that the probability of some CSR theory naturalistically explaining SBs diminishes when it is postulated that SBs have epistemic warrant. Another alternative would be to show that CSR theories are less likely to succeed in explaining the origin of SBs if SBs have warrant than if they lack warrant. It can also be helpful to consider the role played by uncertain and even ineffable judgments. Either way, debunking SBs does not follow simply from CSR but must be considered in light of prior epistemic commitments and the role they play in evaluating probabilities. (shrink)

Professor Savage has been candid and generous in stating his interest in philosophy, and the philosophers who have heard him are surely grateful for this. His attitude is very far from that of some competent scientists and mathematicans who purport to clear up the questions which philosophers raise concerning their disciplines by means of a battery of technical results of varying relevance—a procedure which can often be appropriately described as “an abominable snow-job.” However, Professor Savage's generosity places a responsibility on (...) philosophers, since the questions he raises are difficult. (shrink)

:One view of practical reasoning is that it involves the weighing of reasons. It is not clear, however, how the weights of reasons combine, especially given the logical and substantive relations among different reasons. Nor is it clear how the weighing of reasons relates to decision theoretic maximization of expected value. This paper constructs a formal model of reasons and their weight in order to shed light on these issues. The model informs philosophical debates about reasons, such as the question (...) of whether reasons or values are more fundamental and the opposing doctrines of atomism and holism about reasons. (shrink)

Theories of subjective probability are viewed as formal languages for analyzing evidence and expressing degrees of belief. This article focuses on two probability langauges, the Bayesian language and the language of belief functions (Shafer, 1976). We describe and compare the semantics (i.e., the meaning of the scale) and the syntax (i.e., the formal calculus) of these languages. We also investigate some of the designs for probability judgment afforded by the two languages.

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than Jeffrey's examples of uncertain perception (...) might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)

Rational agents are supposed to maximize expected utility. But what are the options from which they choose? I outline some constraints on an adequate representation of an agent’s options. The options should, for example, contain no information of which the agent is unsure. But they should be sufficiently rich to distinguish all available acts from one another. These demands often come into conflict, so that there seems to be no adequate representation of the options at all. After reviewing existing proposals (...) for how to construe decision-theoretic options and finding them all wanting, I suggest that our model of rational agents should include a special domain of ‘virtual’ option propositions to serve as formal objects of deliberation and choice. (shrink)

I present a game-theoretic way to understand the situation describing Newcomb’s Problem (NP) which helps to explain the intuition of both one-boxers and two-boxers. David Lewis has shown that the NP may be modelled as a Prisoners Dilemma game (PD) in which ‘cooperating’ corresponds to ‘taking one box’. Adopting relevant results from game theory, this means that one should take just one box if the NP is repeated an indefinite number of times, but both boxes if it is a one-shot (...) game. Causal decision theorists thus give the right answer for the one-shot situation, whereas the one-boxers’ solution applies to the indefinitely iterated case. Because Nozick’s set-up of the NP is ambiguous between a one-shot and a repeated game, both of these solutions may appear plausible – depending on whether one conceives of the situation as one-off or repeated. If the players’ aim is to maximize their payoffs, the symmetric structure of the PD implies that the two players will behave alike both when the game is one-shot and when it is played repeatedly. Therefore neither the observed outcome of both players selecting the same strategy (in the PD) nor, correspondingly, the predictor’s accurate prediction of this outcome (in the NP) is at all surprising. There is no need for a supernatural predictor to explain the NP phenomena. (shrink)

I argue that none of the usual interpretations of probability provide an adequate interpretation of probabilistic theories in science. Assuming that the aim of such theories is to capture noisy relationships in the world, I suggest that we do not have to give them classical truth-conditional content at all: their probabilities can remain uninterpreted. Indirectly, this account turns out to explain what is right about the frequency interpretation, the best-systems interpretation, and the epistemic interpretation.

I critically discuss a recent innovation in the debate surrounding the plausibility of rational choice theory : the appeal to evolutionary theory. Specifically, I assess Gigerenzer and colleagues’ claim that considerations based on natural selection show that, instead of making decisions in a RCT-like way, we rely on ‘simple heuristics’. As I try to make clearer here, though, Gigerenzer and colleagues’ arguments are unconvincing: we lack the needed information about our past to determine whether the premises on which they are (...) built are true—and, hence, we cannot tell whether they, in fact, speak against RCT. (shrink)

Can there be deterministic chance? That is, can there be objective chance values other than 0 or 1, in a deterministic world? I will argue that the answer is no. In a deterministic world, the only function that can play the role of chance is one that outputs just Os and 1s. The role of chance involves connections from chance to credence, possibility, time, intrinsicness, lawhood, and causation. These connections do not allow for deterministic chance.

A knowledge-based decision theory faces what has been called the prodigality problem : given that many propositions are assigned probability 1, agents will be inclined to risk everything when betting on propositions which are known. In order to undo probability 1 assignments in high risk situations, the paper develops a theory which systematically connects higher level goods with higher-order knowledge.

This paper analyzes three contrasting strategies for modeling intentional agency in contemporary analytic philosophy of mind and action, and draws parallels between them and similar strategies of scientific model-construction. Gricean modeling involves identifying primitive building blocks of intentional agency, and building up from such building blocks to prototypically agential behaviors. Analogical modeling is based on picking out an exemplary type of intentional agency, which is used as a model for other agential types. Theoretical modeling involves reasoning about intentional agency in (...) terms of some domain-general framework of lawlike regularities, which involves no detailed reference to particular building blocks or exemplars of intentional agency. Given the contrasting procedural approaches that they employ and the different types of knowledge that they embody, the three strategies are argued to provide mutually complementary perspectives on intentional agency. (shrink)