A common type of change in science occurs as theorists generalize a model of a phenomenon by removing some idealizations of the model. This type of change occurs in the decision sciences and also in the normative branch of the decision sciences that treats rational choice. After presenting a general ac-count of model generalization, the paper illustrates generalization of models in normative decision theory. The principal illustration generalizes a standard model of rational choice by removing the idealization that deliberation has (...) no cost. (shrink)

Let us take an example that Bernard Williams (1981: 102) made famous. Suppose that you want a gin and tonic, and you believe that the stuff in front of you is gin. In fact, however, the stuff is not gin but petrol. So if you drink the stuff (even mixed with tonic), it will be decidedly unpleasant, to say the least. Should you choose to drink the stuff or not?

Stanley Stevens draws a useful distinction among ordinal scales, interval scales, and ratio scales. Most recent discussions of confirmation measures have proceeded on the ordinal level of analysis. In this article, I give a more quantitative analysis. In particular, I show that the requirement that our desired confirmation measure be at least an interval measure naturally yields necessary conditions that jointly entail the log-likelihood measure. Thus, I conclude that the log-likelihood measure is the only good candidate interval measure.

According to a widespread but implicit thesis in Bayesian confirmation theory, two confirmation measures are considered equivalent if they are ordinally equivalent—call this the “ordinal equivalence thesis”. I argue that adopting OET has significant costs. First, adopting OET renders one incapable of determining whether a piece of evidence substantially favors one hypothesis over another. Second, OET must be rejected if merely ordinal conclusions are to be drawn from the expected value of a confirmation measure. Furthermore, several arguments and applications of (...) confirmation measures given in the literature already rely on a rejection of OET. I also contrast OET with stronger equivalence theses and show that they do not have the same costs as OET. On the other hand, adopting a thesis stronger than OET has costs of its own, since a rejection of OET ostensibly implies that people’s epistemic states have a very fine-grained quantitative structure. However, I suggest that the normative upshot of the paper in fact has a conditional form, and that other Bayesian norms can also fruitfully be construed as having a similar conditional form. (shrink)

Risk-weighted expected utility theory is motivated by small-world problems like the Allais paradox, but it is a grand-world theory by nature. And, at the grand-world level, its ability to handle the Allais paradox is dubious. The REU model described in Risk and Rationality turns out to be risk-seeking rather than risk-averse on one natural way of formulating the Allais gambles in the grand-world context. This result illustrates a general problem with the case for REU theory, we argue. There is a (...) tension between the small-world thinking marshaled against standard expected utility theory, and the grand-world thinking inherent to the risk-weighted alternative. (shrink)

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the SEU (...) preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

What distinguishes indicative conditionals from subjunctive conditionals, according to one popular view, is that the so-called Adams’ thesis holds for the former kind of conditionals but the so-called Skyrms’ thesis for the latter. According to a plausible metaphysical view, both conditionals and chances supervene on non-modal facts. But since chances do not supervene on facts about particular events but facts about event-types, the past as well as the future is chancy. Some philosophers have worried that this metaphysical view is incompatible (...) with the aforementioned view on the probability of conditionals. This paper however shows that there is no need to worry, as these views can all be simultaneously satisfied within the so-called Multidimensional Possible World Semantics for conditionals. (shrink)

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant to that hypothesis. (...) However, that result depends on a very strong equal relevance condition on individual pieces of evidence. In this essay, we prove tracking results for focused correlation analogous to Wheeler and Scheines’s results but for cases involving unequal relevance. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation. (shrink)

The current debate about peer disagreement has so far mainly focused on the question of whether peer disagreements provide genuine counterevidence to which we should respond by revising our credences. By contrast, comparatively little attention has been devoted to the question by which process, if any, such revision should be brought about. The standard assumption is that we update our credences by conditionalizing on the evidence that peer disagreements provide. In this paper, we argue that non-dogmatist views have good reasons (...) to reject conditionalization. Instead, peer disagreements should be understood to call for a revision of our prior conditional probabilities: rather than merely adding to our original evidence, they pose a challenge to the thought that we have properly assessed the probative force of our original evidence. (shrink)

I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f/PK), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.

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.

A transformative decision rule alters the representation of a decision problem, either by changing the set of alternative acts or the set of states of the world taken into consideration, or by modifying the probability or value assignments. A set of transformative decision rules is order-independent in case the order in which the rules are applied is irrelevant. The main result of this paper is an axiomatic characterization of order-independent transformative decision rules, based on a single axiom. It is shown (...) that the proposed axiomatization resolves a problem observed by Teddy Seidenfeld in a previous axiomatization by Peterson. (shrink)

This paper argues that just as full beliefs can constitute knowledge, so can properties of your credence distribution. The resulting notion of probabilistic knowledge helps us give a natural account of knowledge ascriptions embedding language of subjective uncertainty, and a simple diagnosis of probabilistic analogs of Gettier cases. Just like propositional knowledge, probabilistic knowledge is factive, safe, and sensitive. And it helps us build knowledge-based norms of action without accepting implausible semantic assumptions or endorsing the claim that knowledge is interest-relative.

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

outlined. This account is partly inspired by the work of C.S. Peirce. When we want to consider how degree of confirmation varies with changing I show that a large class of quantitative Bayesian measures of con-.

A transformative decision rule transforms a given decision probleminto another by altering the structure of the initial problem,either by changing the framing or by modifying the probability orvalue assignments. Examples of decision rules belonging to thisclass are the principle of insufficient reason, Isaac Levi'scondition of E-admissibility, the de minimis rule, andthe precautionary principle. In this paper some foundationalissues concerning transformative decision rules are investigated,and a couple of formal properties of this class of rules areproved.

In this essay, I will examine Broome’s argument in Weighing Goods (1991; sections 5.4 and 5.5) that aims to show that moderate Humeanism, according to which any coherent sets of preferences should be rationally acceptable, is not a sustainable view of decision theory. I will focus more specifically on the argument Broome uses to support his claim, and show that although it may get some traction, it does not undermine moderate Humeanism as we know it. After reconstructing Broome’s argument, I (...) argue that standard decision theory supposes that the representation of a decision problem fully captures what is relevant to the agent, and therefore has nothing to say about the legitimacy of the representation in question. I argue that although Broome’s criticism does not jeopardize moderate Humeanism, it does pave the way for a new area of research in decision theory. (shrink)

Naive deductive accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H & X, for any X—even if X is utterly irrelevant to H (and E). Bayesian accounts of confirmation also have this property (in the case of deductive evidence). Several Bayesians have attempted to soften the impact of this fact by arguing that—according to Bayesian accounts of confirmation— E will confirm the conjunction H & X less strongly than E confirms (...) H (again, in the case of deductive evidence). I argue that existing Bayesian “resolutions” of this problem are inadequate in several important respects. In the end, I suggest a new‐and‐improved Bayesian account (and understanding) of the problem of irrelevant conjunction. (shrink)

It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the (...) method of update or learning such that linear pooling com- mutes with it. As it turns out, the resulting update scheme – imaging on the evidence – is well-known from areas such as the study of conditionals and cau- sal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors in a different con- text. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma. (shrink)

Clark Glymour, together with his students Peter Spirtes and Richard Scheines, did pioneering work on graphical causal models . One of the central advances provided by these models is the ability to simply represent the effects of interventions. In an elegant paper , Glymour and his student Christopher Meek applied these methods to problems in decision theory. One of the morals they drew was that causal decision theory should be understood in terms of interventions. I revisit their proposal, and extend (...) the analysis by showing how graphical causal models might be used to address decision problems that arise in “exotic” situations, such as those involving crystal balls or time travelers. (shrink)

Some of the information we receive comes to us in an explicitly conditional form. It is an open question how to model the accommodation of such information in a Bayesian framework. This paper presents data suggesting that there may be no strictly Bayesian account of updating on conditionals. Specifically, the data seem to indicate that such updating at least sometimes proceeds on the basis of explanatory considerations, which famously have no home in standard Bayesian epistemology. The paper also proposes a (...) still broadly Bayesian model of updating on conditionals that explicitly factors in explanation. The model is shown to have clear empirical content and thus to be open to empirical testing. (shrink)

This paper is a response to Paul Bartha’s ‘Making Do Without Expectations’. We provide an assessment of the strengths and limitations of two notable extensions of standard decision theory: relative expectation theory and Paul Bartha’s relative utility theory. These extensions are designed to provide intuitive answers to some well-known problems in decision theory involving gaps in expectations. We argue that both RET and RUT go some way towards providing solutions to the problems in question but neither extension solves all the (...) relevant problems. (shrink)

The logic of dominance arguments is analyzed using two different kinds of conditionals: indicative (epistemic) and subjunctive (counter-factual). It is shown that on the indicative interpretation an assumption of independence is needed for a dominance argument to go through. It is also shown that on the subjunctive interpretation no assumption of independence is needed once the standard premises of the dominance argument are true, but that independence plays an important role in arguing for the truth of the premises of the (...) dominance argument. A key feature of the analysis is the interpretation of the doubly conditional comparative "I will get a better outcome if A than if B" which is taken to have the structure "(the outcome if A) is better than (the outcome if B)". (shrink)

Case-based reasoning is a familiar method of evaluating sentences. But when applied to conditionals, it seems to lead to implausible conclusions. In this paper I argue that the problem arises from equating the probability of a conditional sentence on the evidential supposition of some condition with the conditional probability of the former, given the latter.

In this paper I discuss the challenges of several authors to the claims I make in Decision Theory with a Human Face regarding the relation between preference and choice, the nature of conditional desire, the semantics of conditionals, attitudes to chances and their role in individuating prospects, belief change under growing awareness and choice under ambiguity.

This paper discusses the conditions under which an agent is rationally permitted to leave some uncertain propositions relevant to her decision out of her deliberation. By relying on the view that belief involves a defeasible disposition to treat a proposition as true in one’s reasoning, we examine the conditions under which such a disposition can be overridden and under which an agent should take into account her uncertainty as to a proposition she believes in the course of a particular deliberation. (...) We argue that, in some contexts, an agent can be faced with the choice of either accepting or not accepting a proposition she believes in the course of her deliberation. We provide a description of such higher-order deliberations within the framework of expected utility theory and draw conclusions regarding the phenomenon of pragmatic encroachment on knowledge. (shrink)

In deciding whether to read this paper, it might seem reasonable for you to base your decision on your confidence (i) that, if you read this paper, you will become a better person. It might also seem reasonable for you to base your decision on your confidence (ii) that, if you were to read this paper, you would become a better person. Is there a difference between (i) and (ii)? If so, are you rationally required to base your decision on (...) your confidence in one of the two conditionals, rather than the other? Keith DeRose (2010) proposes a provocative pair of answers to these questions. In this paper, I argue that DeRose’s answers are incorrect, and I defend a rival pair of answers. (shrink)

A prominent philosophical debate concerns whether we should accept causal decision theory or evidential decision theory as our best theory of rational choice. However, instead of accepting one of these theories at the expense of the other, an alternative would be to accept that both theories play a partial role in the true account of rational choice. In this paper, I defend a pluralist account of this sort. In particular, I argue that rational permissibility is an indeterminate notion, with EDT (...) and CDT each corresponding to one sharpening of this notion. (shrink)

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we (...) do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

It is intuitively attractive to think that it makes a difference in Newcomb’s problem whether or not the predictor is infallible, in the sense of being certainly actually correct. This paper argues that that view is irrational and manifests a well-documented cognitive illusion.

Probably many people have cyclic preferences: they prefer A to B, B to C and C to A for some objects of choice A, B and C. Recent work has resurrected the objection to cyclic preference that agents possessing them are open to exploitation by means of ‘money pumps’. The paper briefly reviews this work and proposes a general approach to problems of sequential choice that makes cyclic preference immune to exploitation by means of these new mechanisms.

Sophisticated ‘tickle’-style defences of Evidential Decision Theory take your motivational state to screen off your act from any state that is causally independent of it, thus ensuring that EDT and CDT converge. That leads to unacceptable instability in cases in which the correct action is obvious. We need a more liberal conception of what the agent controls. It follows that an ordinary deliberator should sometimes consider the past and not only the future to be subject to her present choice.

The technique of imaging was first introduced by Lewis, in order to provide a novel account of the probability of conditional propositions. In the intervening years, imaging has been the object of significant interest in both AI and philosophy, and has come to be seen as a philosophically important approach to probabilistic updating and belief revision. In this paper, we consider the possibility of generalising imaging to deal with uncertain evidence and partial belief revision. In particular, we introduce a new (...) logical criterion that any update rule should satisfy, and use it to evaluate a range of different approaches to generalising imaging to situations involving uncertain evidence. We show that none of the currently prevalent approaches to imaging allow for such a generalisation, although a lesser known version of imaging, introduced by Joyce, can be generalised in a way that mitigates these problems. (shrink)

This volume concerns Rational Agents - humans, players in a game, software or institutions - which must decide the proper next action in an atmosphere of partial information and uncertainty. The book collects formal accounts of Uncertainty, Rationality and Agency, and also of their interaction. It will benefit researchers in artificial systems which must gather information, reason about it and then make a rational decision on which action to take.

"Chance" crops up all over philosophy, and in many other areas. It is often assumed -- without argument -- that chances are probabilities. I explore the extent to which this assumption is really sanctioned by what we understand by the concept of chance.

This essay addresses the methodology of philosophy of science and illustrates how formal and empirical methods can be fruitfully combined. Special emphasis is given to the application of experimental methods to confirmation theory and to recent work on the conjunction fallacy, a key topic in the rationality debate arising from research in cognitive psychology. Several other issue can be studied in this way. In the concluding section, a brief outline is provided of three further examples.

Concrete Causation centers about theories of causation, their interpretation, and their embedding in metaphysical-ontological questions, as well as the application of such theories in the context of science and decision theory. The dissertation is divided into four chapters, that firstly undertake the historical-systematic localization of central problems (chapter 1) to then give a rendition of the concepts and the formalisms underlying David Lewis' and Judea Pearl's theories (chapter 2). After philosophically motivated conceptual deliberations Pearl's mathematical-technical framework is drawn on for (...) an epistemic interpretation and for emphasizing the knowledge-organizing aspect of causality in an extension of the interventionist Bayes net account of causation (chapter 3). Integrating causal and non-causal knowledge in unified structures ultimately leads to an approach towards solving problems of (causal) decision theory and at the same time facilitates the representation of logical-mathematical, synonymical, as well as reductive relationships in efficiently structured, operational nets of belief propagation (chapter 4). (shrink)