– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this (...) principle, I then argue that for any agent, S, faced with any decision under risk, S should rank his or her decision options (in terms of how choiceworthy they are) according to their comparative expected comparative utility (CECU) and should choose whichever option carries the greatest CECU. For any option, a, a's CECU is the difference between its ECU and that of whichever alternative to a carries the greatest ECU, where a's ECU is a probability-weighted sum of a's CUs across the various possible states of the world. I lastly demonstrate that in some ordinary decisions under risk, ECU theory delivers different verdicts from those of standard decision theory. (shrink)

This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for (...) the possibility of radical interpretation, associated most closely with David Lewis and Donald Davidson, gives a central role to decision theoretic representation theorems, which demonstrate that if an agent’s preferences satisfy certain constraints, it is possible to deduce probability and utility functions that represent her beliefs and desires. We argue that an interpretationist who wants to rely on existing representation theorems in defence of the possibility of radical interpretation faces a trilemma, each horn of which is incompatible with the possibility of radical interpretation. (shrink)

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)

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)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...) calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

In their recently published book Nudge (2008) Richard H. Thaler and Cass R. Sunstein (T&S) defend a position labelled as ‘libertarian paternalism’. Their thinking appeals to both the right and the left of the political spectrum, as evidenced by the bedfellows they keep on either side of the Atlantic. In the US, they have advised Barack Obama, while, in the UK, they were welcomed with open arms by the David Cameron's camp (Chakrabortty 2008). I will consider the following questions. What (...) is Nudge? How is it different from social advertisement? Does Nudge induce genuine preference change? Does Nudge build moral character? Is there a moral difference between the use of Nudge as opposed to subliminal images to reach policy objectives? And what are the moral constraints on Nudge? (shrink)

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)

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. We (...) end the paper by investigating the conditions necessary and sufficient for a desirability function to be an expected utility. It turns out that the additional conditions imply highly implausible epistemic principles. (shrink)

This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences defined on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Jeffrey and others can be stated and compared, but also allows for the postulation of an extended Bayesian model of rational belief and desire from which they can be derived as (...) special cases. The main theorem of the paper establishes the existence of a such a Bayesian representation of preferences over conditional prospects, i.e. the existence of a pair of real-valued functions respectively measuring the agent’s degrees of belief and desire and which satisfy the postulated rationality conditions on partial belief and desire. The representation of partial belief is shown to be unique and that of partial desire, unique up to a linear transformation. (shrink)

The central problem of the dissertation concerns the possibility of a distinction between truth-evaluable and non-truth-evaluable utterances of a natural language. The class of truth-evaluable utterances includes assertions, con. ectures and other kinds of speech act susceptible of truth evaluation. The class of non-truth-evaluable utterances includes commands, exhortations, wishes i.e. utterances not evaluated as being true or false. The problem is placed in the context of radical interpretation theory and it shown that it is a substantial problem of Davidson‘s early (...) theory of radical interpret at ion. I consider the possibility of distinguishing between locutionary and illocutionary act in uttering a sentence and its significance in the present project. I discuss the suggestion that the mood of the verb of the sentence signifies the required distinction between truth-evaluable utterances and non-truth-evaluable ones. I argue that no criterion for the distinction based on the mood of the verb is adequate. The solution that I propose to the problem of classifylng truth-evaluable utterances appeals to mental states. The view that grounds this line of inquiry is that the truth-evaluability of an utterance is a characteristic of it exclusively relevant to the doxastic dimension of the speaker’s mind. I discuss the constraints that the nature of radical interpretation puts upon the way we construe the notion of belief. I propose that a possible classification of mental states into doxastic and non-doxastic that would result in a classification of utterances into truth-evaluable and non-truthevaluable ones can be given by an elaborated version of a decision theoretic scheme. I suggest that a decision theoretic scheme based on a decision theory that, like Savage’s theory, grants independence axioms is a better candidate to offer a solution to the central problem of the dissertation than a scheme based on a non- standard decision theory such as Richard Jeffrey’s. I conclude by showing that the proposal I make satisfies the constraints I have considered and that it can be accommodated by a radical interpretation theory. (shrink)

Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...) changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating. (shrink)

This article examines Becker's thesis that the hypothesis that choices maximize expected utility relative to fixed and universal tastes provides a general framework for the explanation of behaviour. Three different models of preference revision are presented and their scope evaluated. The first, the classical conditioning model, explains all changes in preferences in terms of changes in the information held by the agent, holding fundamental beliefs and desires fixed. The second, the Jeffrey conditioning model, explains them in terms of changes in (...) both the information held by the agent and changes in her prior beliefs, holding her fundamental desires fixed. The final model, that of generalized conditioning, allows for explanations in terms of changes in the values of all three variables. Key Words: preference change • decision theory • probability • desirability • attitude change. (shrink)

In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this (...) principle, I then argue that for any agent, S, faced with any decision under risk, S should rank his or her decision options (in terms of how choiceworthy they are) according to their comparative expected comparative utility (CECU) and should choose whichever option carries the greatest CECU. For any option, a, a’s CECU is the difference between its ECU and that of whichever alternative to a carries the greatest ECU, where a’s ECU is a probability‐weighted sum of a’s CUs across the various possible states of the world. I lastly demonstrate that in some ordinary decisions under risk, ECU theory delivers different verdicts from those of standard decision theory. (shrink)

Isaac Levi and I have different views of probability and decision making. Here, without addressing the merits, I will try to answer some questions recently asked by Levi (1985) about what my view is, and how it relates to his.

Changing preferencesis a phenomenonoften invoked but rarely properlyaccounted for. Throughout the history of the social sciences, researchers have come against the possibility that their subjects’ preferenceswere affected by the phenomenato be explainedor by otherfactorsnot taken into accountin the explanation.Sporadically, attempts have been made to systematically investigate these in uences, but none of these seems to have had a lasting impact. Today we are still not much further with respect to preference change than we were at the middle of the last (...) century. This anthology hopes to provide a new impulse for research into this important subject. In particular, we have chosen two routes to amplify this impulse. First, we stress the use of modellingtechniquesfamiliar from economicsand decision theory. Instead of constructing complex, all-encompassing theories of preference change, the authors of this volume start with very simple, formal accounts of some possible and hopefully plausible mechanism of preference change. Eventually, these models may nd their way into larger, empirically adequate theories, but at this stage, we think that the most importantwork lies in building structure.Secondly,we stress the importance of interdisciplinary exchange. Only by drawing together experts from different elds can the complex empirical and theoretical issues in the modelling of preference change be adequately investigated. (shrink)

The paper builds on the basically Humean idea that A is a cause of B iff A and B both occur, A precedes B, and A raises the metaphysical or epistemic status of B given the obtaining circumstances. It argues that in pursuit of a theory of deterministic causation this ‘status raising’ is best explicated not in regularity or counterfactual terms, but in terms of ranking functions. On this basis, it constructs a rigorous theory of deterministic causation that successfully deals (...) with cases of overdetermination and pre-emption. It finally indicates how the account's profound epistemic relativization induced by ranking theory can be undone. Introduction Variables, propositions, time Induction first Causation Redundant causation Objectivization. (shrink)

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations (...) of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. (shrink)

We propose a model of an agent’s probability and utility that is a compromise between Savage (The foundations of statistics, Wiley, 1954) and Jeffrey (The Logic of Decision, McGraw Hill, 1965). In Savage’s model the probability–utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey’s model has no consequences, and both probability and utility are defined on the same set of (...) propositions. The probability–utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (Econometrica 55:1–18, 1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability–utility pair. We characterize the family of all the probability–utility pairs that represent a given desirability relation. (shrink)

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and in which (...) at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)

The notion of a proposition as a set of possible worlds or states occupies central stage in probability theory, semantics and epistemology, where it serves as the fundamental unit both of information and meaning. But this fact should not blind us to the existence of prospects with a different structure. In the paper I examine the use of random variables—in particular, proposition-valued random variables— in these fields and argue that we need a general account of rational attitude formation with respect (...) to them. (shrink)

We present experimental evidence that supports the thesis :602–625, 2015, Br J Philos Sci 70:77–102, 2019; Bradley in Decisions theory with a human face, Cambridge University Press, Cambridge, 2017; Goldschmidt and Nissan-Rozen in Synthese 198:7553–7575, 2021) that people might positively or negatively desire risky prospects conditional on only some of the prospects’ outcomes obtaining. We argue that this evidence has important normative implications for the central debate in normative decision theory between two general approaches on how to rationalize several common (...) patterns of preference, which are ruled out as irrational by orthodox decision theory, namely the re-individuation approach and the non-expected utility approach. (shrink)

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief (...) and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. (shrink)

Orthodox expected utility theory imposes too stringent restrictions on what attitudes to risk one can rationally hold. Focusing on a life-and-death gamble, I identify as the main culprit the theory’s Linearity property, according to which the utility of a particular change in the risk of a bad outcome is independent of the original level of risk. Finally, I argue that a recent non-standard Bayesian decision theory, that does not have this property, handles risky gambles better than the orthodox theory.

Suppose we have a group of Bayesian agents, and suppose that theywould like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that thoseagents want the probabilities and utilities attached to this group agent to be aggregated from theindividual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data areavailable to them, viz., ex ante aggregation and ex post aggregation. The former aggregatesexpected utilities directly, whereas the latter aggregates probabilities and utilities (...) separately.A number of recent formal results show that both approaches have problematic implications. This studydiscusses the philosophical issues arising from those results. In this process, I hope to convincethe reader that these results about Bayesian aggregation are highly significant to decision theorists, butalso of immense interest to theorists working in areas such as ethics and political philosophy. (shrink)

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves one’s (...) conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’. (shrink)

We suscribe to an account of framing-effects in decision theory in terms of an inference to a background informationa by the hearer when a speaker uses a certain frame while other equivalent frames were also available. This account was sketched by Craig McKenzie. We embed it in Bolker-Jeffrey decision model - one main reason of this is that this latter model makes preferences bear on propositions. We can deduce a given anomaly or cognitive bias in a formal decision theory. This (...) leads to some philosophical considerations on the relationship between the rationality of preferences and the sensitivity to descriptions or labels of states of affairs in decision-making. (shrink)

In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way of (...) formalizing Keynes' theory of economic action. (shrink)

Causal decision theory (CDT) is the best theory of rational choice now available.2 I intend to provide some support for that claim in part I of this paper by responding to two criticisms of CDT. The first criticism says that CDT is superfluous, since it does no better in the problems that matter than does evidential decision theory (EDT) at recommending correct choices. A second criticism says that CDT by itself is flawed: according to this view, there are problems in (...) which CDT makes bad recommendations, unless it is supplemented with an additional deliberation mechanism, either involving metatickles or screening for ratifiable choices.3 I will argue in response to the first criticism that CDT is genuinely better than any EDT of the most sophisticated sort: there are problems where CDT gives better recommendations, and they are problems that do matter. (shrink)