The main result of this paper is a formal argument for the principle of maximizing expected utility that does not rely on the law of large numbers. Unlike the well-known arguments by Savage and von Neumann & Morgenstern, this argument does not presuppose the sure-thing principle or the independence axiom. The principal idea is to use the concept of transformative decision rules for decomposing the principle of maximizing expected utility into a sequence of normatively reasonable subrules. It is shown that (...) this procedure provides a resolution of Allais's paradox that cannot be obtained by Savage-style or von Neumann & Morgenstern-style arguments. (shrink)

Philosophers of science have often favoured reductive approaches to how-possibly explanation. This article identifies three alternative conceptions making how-possibly explanation an interesting phenomenon in its own right. The first variety approaches “how possibly X?” by showing that X is not epistemically impossible. This can sometimes be achieved by removing misunderstandings concerning the implications of one’s current belief system but involves characteristically a modification of this belief system so that acceptance of X does not result in contradiction. The second variety offers (...) a potential how-explanation of X. It is usually followed by a range of further potential how-explanations of the same phenomenon. In recent literature the factual claims implied by the second variety have been downplayed whereas the heuristic role of mapping the space of conceptual possibilities has been emphasized. I will focus especially on this truth-bracketing sense of potentiality when looking closer at the second variety in the paper. The third variety has attracted less interest. It presents a partial how-explanation of X. Typically it aims to establish the existence of a mechanism by which X could be and was generated. The third conception stands out as the natural alternative for the advocate of ontic how-possibly explanations. This article transfers Salmon’s view that explanation-concepts can be broadly divided into epistemic, modal, and ontic to the context of how-possibly explanations. Moreover, it is argued that each of the three above-mentioned varieties of how-possibly explanation occurs in science. To recognize this may be especially relevant for philosophers. We are often misled by the promises of various why-explanation accounts, and seem to have forgotten nearly everything about the diversity of how-possibly explanations. (shrink)

In the literature there are at least two models for probabilistic belief revision: Bayesian updating and imaging [Lewis, D. K. (1973), Counterfactuals, Blackwell, Oxford; Gärdenfors, P. (1988), Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, MA]. In this paper we focus on imaging rules that can be described by the following procedure: (1) Identify every state with some real valued vector of characteristics, and accordingly identify every probabilistic belief with an expected vector of characteristics; (2) For (...) every initial belief and every piece of information, choose the revised belief which is compatible with this information and for which the expected vector of characteristics has minimal Euclidean distance to the expected vector of characteristics of the initial belief. This class of rules thus satisfies an intuitive notion of minimal belief revision. The main result in this paper is to provide an axiomatic characterization of this class of imaging rules. (shrink)

Recent criticisms of traditional understandings of risk, responsibility and the division of labour between science and politics build on the idea of the co-produced character of the natural and social orders, making a case for less ambitious and more inclusive policy processes, where questions of values and goals may be addressed together with questions of facts and means, causal liabilities and principled responsibilities. Within the neo-liberal political economy, however, the contingency of the world is depicted as a source of unprecedented (...) opportunities for human craftsmanship, rather than of possibly unmanageable surprises. Gene technologies offer a vantage point for reflecting on the consequences of the drift from discovery to invention as a master frame in the appraisal of human intermingling with the world. Biotech patenting regulations carve out a sovereign agency which, by crafting nature, also crafts the distinction between the manufactured and non-manufactured world. Difficulties in ascribing responsibility stem as a consequence. It is likely that politics and economy can be democratized and responsibilities rearranged not by ‘democratizing’ knowledge production, but rather the reverse. (shrink)

Zeckhauser’s paradox has puzzled and entertained many rationality enthusiasts for almost half a century. You are forced to play a Russian Roulette with a 6-chamber revolver containing either two bullets, or four bullets. Would you pay more to remove the two bullets in than you would to remove one in? Most would say yes, but rational considerations based on the classical utility theory suggest you should not. We discuss a possible solution within the classical framework, by explicitly stating and accounting (...) for more detailed preferences in terms of fewer bullets and smaller debt. To a large extent, the paradox arises due to a surreptitious trespassing of Savage’s Small-World utilities implied by a limited set of preferences to govern a larger world containing potentially conflicting preferences. To avoid logical issues associated with death in the roulette, we also describe a non-fatal game-show version, where you choose one box out of six that could be either empty or contain prize money. Here, the paradox arises when you pay from the prize money, but not when you pay from your own money. In summary, the paradox provides a useful lesson about the normative role of the utility function as a rational guide for our decisions and preferences. (shrink)

We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning (...) to beliefs in general contexts, including the context of animal belief , and of human belief which is expressed in language. (shrink)

This paper starts out from the proposition that case-based decision theory is an appropriate tool to explain human decision behavior in situations of structural ignorance. Although the developers of CBDT suggest its reality adequacy, CBDT has not yet been tested empirically very often, especially not in repetitive decision situations. Therefore, our main objective is to analyse the decision behavior of subjects in a repeated-choice experiment by comparing the explanation power of CBDT to reinforcement learning and to classical decision criteria under (...) uncertainty namely maximin, maximax, and pessimism-optimism. Our findings substantiate a predominant significantly higher validity of CBDT compared to the classical criteria and to reinforcement learning. For this reason, the experimental results confirm the suggested reality adequacy of CBDT in repetitive decision situations of structural ignorance. (shrink)

We describe a logic of preference in which modal connectives reflect reasons to desire that a sentence be true. Various conditions on models are introduced and analyzed.

The problem of how to make optimal choices in the face of risk arises in both economics/decision theory and also evolutionary biology; in the former, ‘optimal’ means utility maximizing, while in the latter it means fitness maximizing. This article explores the links, thematic and formal, between the economic and evolutionary theories of optimal choice in risky situations, with particular reference to the relationship between utility and fitness. It is argued that the link is strongest between evolution and ‘nonexpected’ utility theory, (...) rather than traditional expected utility theory. (shrink)

I discuss the trilemma that consists of the following three principles being inconsistent: 1. The Common Principle: if one distribution, A, necessarily brings a higher total sum of personal value that is distributed in a more egalitarian way than another distribution, B, A is more valuable than B. 2. (Weak) ex-ante Pareto: if one uncertain distribution, A, is more valuable than another uncertain distribution, B, for each patient, A is more valuable than B. 3. Pluralism about attitudes to risk (Pluralism): (...) the personal value of a prospect is a weighted sum of the values of the prospect’s outcomes, but the weight each outcome gets might be different from the probability the prospect assigns to the outcome. (shrink)

: In some cases in which rational and moral agents experience moral uncertainty, they are unable to assign exact degrees of moral value—in a non-arbitrary way—to some of the different acts available to them, and so are unable to choose with certainty the best act. This article presents a new justification for the use of lotteries in this kind of situation. It is argued that sometimes the only rational thing for a morally motivated agent to do here is to use (...) a lottery. (shrink)

A triviality result for what Lewis called “the Desire by Necessity Thesis” and Broome : 265–267, 1991) called “the Desire as Expectation Thesis” is presented. The result shows that this thesis and three other reasonable conditions can be jointly satisfied only in trivial cases. Some meta-ethical implications of the result are discussed. The discussion also highlights several issues regarding Lewis ’ original triviality result for “the Desire as Belief Thesis” that have not been properly understood in the literature.

In 1958, to refute the argument known as the theoretician's dilemma, Hempel suggested that theoretical terms might be logically indispensable for inductive systematization of observational statements. This thesis, in some form or another, has later been supported by Scheffler, Lehrer, and Tuomela, and opposed by Bohnert, Hooker, Stegmüller, and Cornman. In this paper, a critical survey of this discussion is given. Several different putative definitions of the crucial notion inductive systematization achieved by a theory are discussed by reference to the (...) properties of inductive inference. The consequences of the following differences between deductive and inductive inference are emphasized: the lack of simple transitivity properties (even in a modified sense) of inductive inference, and the failure of the inductive analogue of the converse of The Deduction Theorem. The main conclusions are: (i) Hempel's original thesis may very well be right but his argument for it is unsatisfactory, (ii) theoretical terms can be logically indispensable for a non-Hempelian kind of inductive systematization, relative to both Craigian and Ramseyan elimination, (iii) Lehrer's attempt to prove the indispensability of theoretical terms for inductive-probabilistic systematization is, as a modification of Hempelian kind of inductive-deterministic systematization, unsatisfactory, and (iv) there does not seem to be much hope of escaping the conclusion (ii), if it is true, by extending the Craigian replacement programme along the lines suggested by Cornman. (shrink)

I show that de Finetti’s coherence theorem is equivalent to the Hahn-Banach theorem and discuss some consequences of this result. First, the result unites two aspects of de Finetti’s thought in a nice way: a corollary of the result is that the coherence theorem implies the existence of a fair countable lottery, which de Finetti appealed to in his arguments against countable additivity. Another corollary of the result is the existence of sets that are not Lebesgue measurable. I offer a (...) subjectivist interpretation of this corollary that is concordant with de Finetti’s views. I conclude by pointing out that my result shows that there is a sense in which de Finetti’s theory of subjective probability is necessarily nonconstructive. This raises questions about whether the coherence theorem can underwrite a legitimate theory of rational belief. (shrink)

Must probabilities be countably additive? On the one hand, arguably, requiring countable additivity is too restrictive. As de Finetti pointed out, there are situations in which it is reasonable to use merely finitely additive probabilities. On the other hand, countable additivity is fruitful. It can be used to prove deep mathematical theorems that do not follow from finite additivity alone. One of the most philosophically important examples of such a result is the Bayesian convergence to the truth theorem, which says (...) that conditional probabilities converge to 1 for true hypotheses and to 0 for false hypotheses. In view of the long-standing debate about countable additivity, it is natural to ask in what circumstances finitely additive theories deliver the same results as the countably additive theory. This paper addresses that question and initiates a systematic study of convergence to the truth in a finitely additive setting. There is also some discussion of how the formal results can be applied to ongoing debates in epistemology and the philosophy of science. (shrink)

Bayesians since Savage (1972) have appealed to asymptotic results to counter charges of excessive subjectivity. Their claim is that objectionable differences in prior probability judgments will vanish as agents learn from evidence, and individual agents will converge to the truth. Glymour (1980), Earman (1992) and others have voiced the complaint that the theorems used to support these claims tell us, not how probabilities updated on evidence will actually}behave in the limit, but merely how Bayesian agents believe they will behave, suggesting (...) that the theorems are too weak to underwrite notions of scientific objectivity and intersubjective agreement. I investigate, in a very general framework, the conditions under which updated probabilities actually converge to a settled opinion and the conditions under which the updated probabilities of two agents actually converge to the same settled opinion. I call this mode of convergence deterministic, and derive results that extend those found in Huttegger (2015b). The results here lead to a simple characterization of deterministic convergence for Bayesian learners and give rise to an interesting argument for what I call strong regularity, the view that probabilities of non-empty events should be bounded away from zero. (shrink)

Much work in the philosophy of action in the last few decades has focused on the elucidation and justification of a series of purported norms of practical rationality that concern the presence or absence of intention in light of belief, and that demand a kind of structural coherence in the psychology of an agent. Examples of such norms include: Intention Detachment, which proscribes intending to do something in case some condition obtains, believing that such condition obtains, and not intending to (...) do that thing; Intention-Belief Consistency, which proscribes intending to do what you believe you will not do; Intention Consistency, which proscribes intending each of two ends you believe to be inconsistent; and Means-End Coherence, which proscribes intending an end and not intending the means you believe to be implied by your end. In this paper, I present a series of examples that show that these requirements are not genuine requirements of rationality. The reason for this is simple: these requirements concern the presence or absence of intention in light of all-out belief. Rational agents like us, however, do not, and in fact should not, always form or revise their intentions in light of what they all-out believe. When such agents do not form or revise their intentions in light of what they all-out believe, they need not be irrational if they do not conform to these requirements. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

This article assesses two major conceptual arguments against theories of choice.The first argument concerns the circularity of belief-desire psychology, on which decision theory is based. The second argument concerns the normativity arising from the concept of rationality. Each argument is evaluated against experimental practice in economics and psychology, and it is concluded that both arguments fail to establish their skeptical conclusion that there can be no science of intentional human actions.

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of (...) traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap. (shrink)

Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.

In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy (...) that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of utility functions as (...) representing preference differences, while being non- etheless empirically related to choices. We highlight the originality, promises and limits of this choice-based cardinalism. (shrink)

This paper aims to open a dialogue between philosophers working in decision theory and operations researchers and engineers working on decision-making under deep uncertainty. Specifically, we assess the recommendation to follow a norm of robust satisficing when making decisions under deep uncertainty in the context of decision analyses that rely on the tools of Robust Decision-Making developed by Robert Lempert and colleagues at RAND. We discuss two challenges for robust satisficing: whether the norm might derive its plausibility from an implicit (...) appeal to probabilistic representations of uncertainty of the kind that deep uncertainty is supposed to preclude; and whether there is adequate justification for adopting a satisficing norm, as opposed to an optimizing norm that is sensitive to considerations of robustness. We discuss decision-theoretic and voting-theoretic motivations for robust satisficing, and use these motivations to select among candidate formulations of the robust satisficing norm. (shrink)