Wlodek Rabinowicz

The Puzzle of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable.

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty.

The authors of this paper earlier argued that concrete objects, such as things or persons, may have final value (value for their own sake), which is not reducible to the value of states of affairs that concern the object in question.Our arguments have been challenged. This paper is an attempt to respond to some of these challenges, viz. those that concern the reducibility issue. The discussion presupposes a Brentano‐inspired account of value in terms of fitting responses to value bearers. Attention is given to a yet another type of reduction proposal, according to which the ultimate bearers of final value are abstract particulars (so‐called tropes) rather than abstract states or facts. While the proposal is attractive ((fone entertains the existence of tropes), it confronts serious difficulties. To recognise tropes as potential bearers of final value, along with other objects, is one thing; but to reduce the final value of concrete objects to the final value of tropes is another matter.

Suppose one sets up a sequence of less and less valuable objects such that each object in the sequence is only marginally worse than its immediate predecessor. Could one in this way arrive at something that is dramatically inferior to the point of departure? It has been claimed that if there is a radical value difference between the objects at each end of the sequence, then at some point there must be a corresponding radical difference between the adjacent elements. The underlying picture seems to be that a radical gap cannot be scaled by a series of steps, if none of the steps itself is radical. We show that this picture is incorrect on a stronger interpretation of value superiority, but correct on a weaker one. Thus, the conclusion we reach is that, in some sense at least, abrupt breaks in such decreasing sequences cannot be avoided, but that such unavoidable breaks are less drastic than has been suggested. In an appendix written by John Broome and Wlodek Rabinowicz, the distinction between two kinds of value superiority is extended from objects to their attributes.

In Rabinowicz 2008, I considered how value relations can best be analyzed in terms of fitting pro-­‐attitudes. In the formal model presented in that paper fitting pro-­‐attitudes are represented by the class of permissible preference orderings on a domain of items that are being compared. As it turns out, this approach opens up for a multiplicity of different types of value relationships, along with the standard relations of "better", "worse", "equally as good as" and "incomparable in value". Unfortunately, though, the approach is vulnerable to a number of objections. I believe these objections can be avoided if one re-interprets the underlying notion of preference: Instead of treating preference as a 'dyadic' attitude directed towards a pair of items, we can think of it as a difference of degree between 'monadic' attitudes of favouring. Each such monadic attitude has just one item as its object. Given this re-interpretation, permissible preferences can be modelled by the class of permissible assignments of degrees of favouring to items in the domain. From this construction, we can then recover the old modelling in terms of the class of permissible preference orderings, but the previous objections to that model no longer apply. Thus, what we get is the old wine in new and hopefully tighter barrels.

My focus is on pragmatic arguments for various ‘rationality constraints’ on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which he will act to his guaranteed disadvantage. Dramatically put, he can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. The proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, he can be exploited only if he is disunified in his decision-making. Exploitation is possible only if the agent makes decisions on various issues he confronts one by one, rather than on all of them together. Unity in decision making may be quite costly and is often inconvenient, especially when it concerns opportunity packages that are spread over time. On my view, therefore, pragmatic arguments should be seen as delivering conditional conclusions: “If you want to afford being disunified as a decision maker, then you’d better satisfy these constraints.” The arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Levi’s view of the status of pragmatic arguments is opposed to mine. According to him, only synchronic pragmatic arguments are valid. The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in my paper.

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty.

in Undetermined On an influential interpretation, the agent's degrees of belief asr identified with her betting rates. However, being placed in a betting situation can itself change one’s degree of belief in the proposition in question. The problem as such isn’t new. Ramsey, for example, was right on to this idea when he wrote: "… the proposal of a bet may inevitably alter [one’s] state of opinion; just as we could not always measure electric intensity by actually introducing a charge and seeing what force it was subject to, because the introduction of the charge would change the distribution to be measured." This ‘interference problem’ for the betting interpretation can best be put in the following way: The bets we are disposed to accept do not manifest our current unconditional degrees of belief in various propositions. Whether a bet on A would be accepted or not does not depend on the agent’s degree of belief in A but rather on the degree of belief she would have if she were confronted with this bet proposal, or – more generally – the degree of belief she would have if she were in a position to bet on A. Assuming the conditionalization model for belief change, this means that whether the agent would be willing to bet depends on her current conditional beliefs concerning A on the hypothetical supposition that she has an opportunity to make this bet. Furthermore, her disposition to bet also depends on the expected effects the act of betting would have on the truth of the proposition to be betted on. Both these phenomena imply that finding oneself in a betting situation might alter one’s expectations in important ways. Consequently, the identification of degrees of belief with betting rates is a mistake. We show that this problem comes up in several different versions, or – equivalently – that different kinds of arguments against the betting interpretation stem from the same source.

In this short summary, which is aimed to give a rough picture of the main lines of research in practical philosophy in Sweden during the last decade, I have decided to organize the presentation by universities rather than by particular research subjects. It is to be hoped that this will give the reader a better grasp of what is going on at various departments. The summary is to a large extent a collective work: It is based on the reports prepared by professors Erik Carlson, Uppsala University, Sven-Ove Hansson, Royal Institute of Technology, Stockholm, Christian Munthe, University of Gothenburg, Bo Petersson, Linköping University, Hans Ruin, Södertörn University College, Torbjörn Tännsjö, Stockholm University, and on my own report for Lund University.

In “Weighing Lives” (2004) John Broome criticizes a view common to many population axiologists. On that view, population increases with extra people leading decent lives are axiologically neutral: they make the world neither better nor worse, ceteris paribus. Broome argues that this intuition, however, attractive, cannot be sustained, for several independent reasons. I respond to his criticisms and suggest that the neutrality intuition, if correctly interpreted, can after all be defended.On the version I defend,the world with added extra people at wellbeing levels within the neutrality range is incommensurable in value with the world in which these peaople are absent.

My focus is on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on his beliefs or preferences. An argument of this kind purports to show that a violator of a given constraint can be exposed to a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent himself. Examples of pragmatic arguments of this kind are synchronic Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the transitivity requirement on preferences. It is suggested that the proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, she can be exploited only if she is disunified in his decision-making, i.e., only if she makes decisions on various issues she confronts separately rather than jointly. In other words, exploitation is possible only if the decision problem has been framed in a certain way. Unification in decision making is relatively unproblematic in synchronic contexts, but it may be quite costly and inconvenient diachronically, especially when the issues under consideration are widely spread over time. On my view, therefore, pragmatic arguments should be seen as delivering conditional recommendations: If you want to afford disunification, then you’d better satisfy these constraints. The arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Isaac Levis view of the status of pragmatic arguments is diametrically opposed to mine. According to him, only synchronic pragmatic arguments are valid. The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in my paper.

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical language: a dynamic modal logic. Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL). This framework may be seen as an extension of standard Hintikka-style doxastic logic with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about undergoes a change. But then his introspective (higher-order) beliefs have to be adjusted accordingly. In the paper we shall consider various ways of solving this problem.

This paper argues that expected utility theory for actions in chancy environments should be formulated in terms of centered chances. The subjective expected utility of an option A may be seen as a weighted sum of the utilities of A in different possible worlds, with weights being the credences that the agent assigns to these worlds. The utility of A in a given world is then definable as a weighted sum of the values of A’s different possible outcomes, with weights being the conditional chances of these outcomes if A were performed. On the centered-chance view, the chances to be used as weights in the definition of utility are centered. Unlike ordinary chances, centered chances depend not only on what happens prior to the agent’s choice but also on the events that occur after the choice. Thus, to give an example, suppose that the action under consideration results in a bad outcome due to some event whose ordinary chance of occurring was very low at the time of choice. Then the utility of that action in the actual world could be high on the non-centered view, but on the centered view that utility is negative, since the centered chance of the event in question given the action was one, given that it did actually take place. A precise definition of centered chances is not easy to frame, but the concept can be made intuitively clear. The resulting decision theory is, in my opinion, philosophically more satisfactory than the extant proposals, even though it doesn’t differ much in its practical recommendations, with the exception of some rather peculiar cases.

According to the standard objection to backward induction in games, its application depends on highly questionable assumptions about the players' expectations as regards future counterfactual game developments. It seems that, in order to make predictions needed for backward reasoning, the players must expect each player to act rationally at each node that in principle could be reached in the game, and also to expect that this confidence in the future rationality of the players would be kept by each player come what may: even at the game-nodes that could only be reached by irrational play. Both expectations seem to be rather unreasonable: a player's initial disposition to rational behaviour may be weakened by a long stretch of irrational play on his part and, even more importantly, his initial confidence in the other players' future rationality may be undermined by an irrational play on their part. For different formulations of this objection see Binmore, Reny and, Bicchieri, Pettit and Sugden. and Aumann and.)

Seidenfeld (Seidenfeld, T. [1988a], Decision theory without 'Independence' or without 'Ordering', Economics and Philosophy 4: 267-290) gave an argument for Independence based on a supposition that admissibility of a sequential option is preserved under substitution of indifferents at choice nodes (S). To avoid a natural complaint that (S) begs the question against a critic of Independence, he provided an independent proof of (S) in his (Seidenfeld, T. [1988b], Rejoinder [to Hammond and McClennen], Economics and Philosophy 4: 309-315). In reply to my (Rabinowicz, W. [1995], To have one's cake and eat it too: Sequential choice and expected-utility violations, The Journal of Philosophy 92: 586-620), in which I argue that the proof is invalid, Seidenfeld (Seidenfeld, T. [2000], Substitution of indifferent options at choice nodes and admissibility: A reply to Rabinowicz, Theory and Decision 48: 305–310 this issue) submits that I fail to give due consideration to one of the underlying assumptions of his derivation: it is meant to apply only to those cases in which the agent's preferences are stable throughout the sequential decision process. The purpose of this note is to clarify the notion of preference stability so as meet this objection.

The paper argues that the final value of an object-i.e., its value for its own sake-need not be intrinsic. Extrinsic final value, which accrues to things in virtue of their relational rather than internal features, cannot be traced back to the intrinsic value of states that involve these things together with their relations. On the contrary, such states, insofar as they are valuable at all, derive their value from the things involved. The endeavour to reduce thing-values to state-values is largely motivated by a mistaken belief that appropriate responses to value must consist in preferring and/or promoting. A pluralist approach to value analysis obviates the need for reduction: the final value of a thing or person can be given an independent interpretation in terms of the appropriate thing- or person-oriented responses: admiration, love, respect, protection, care, cherishing, etc

An agent who violates independence can avoid dynamic inconsistency in sequential choice if he is sophisticated enough to make use of backward induction in planning. However, Seidenfeld has demonstrated that such a sophisticated agent with dependent preferences is bound to violate the principle of dynamic substitution, according to which admissibility of a plan is preserved under substitution of indifferent options at various choice nodes in the decision tree. Since Seidenfeld considers dynamic substitution to be a coherence condition on dynamic choice, he concludes that sophistication cannot save a violator of independence from incoherence. In response to McClennen’s objection that relying on dynamic substitution when independence is at stake must be question-begging, Seidenfeld undertakes to prove that dynamic substitution follows from the principle of backward induction alone, provided we assume that the agent’s admissible choices from different sets of feasible plans are all based on a fixed underlying preference ordering of plans. This paper shows that Seidenfeld's proof fails: depending on the interpretation, it is either invalid or based on an unacceptable assumption.

This paper argues that expected utility theory for actions in chancy environments should be formulated in terms of centered chances. The subjective expected utility of an option A may be seen as a weighted sum of the utilities of A in different possible worlds, with weights being the credences that the agent assigns to these worlds. The utility of A in a given world is then definable as a weighted sum of the values of A’s different possible outcomes, with weights being the conditional chances of these outcomes if A were performed. On the centered-chance view, the chances to be used as weights in the definition of utility are centered. Unlike ordinary chances, centered chances depend not only on what happens prior to the agent’s choice but also on the events that occur after the choice. Thus, to give an example, suppose that the action under consideration results in a bad outcome due to some event whose ordinary chance of occurring was very low at the time of choice. Then the utility of that action in the actual world could be high on the non-centered view, but on the centered view that utility is negative, since the centered chance of the event in question given the action was one, given that it did actually take place. A precise definition of centered chances is not easy to frame, but the concept can be made intuitively clear. The resulting decision theory is, in my opinion, philosophically more satisfactory than the extant proposals, even though it doesn’t differ much in its practical recommendations, with the exception of some rather peculiar cases.

It is a popular view thatpractical deliberation excludes foreknowledge of one's choice. Wolfgang Spohn and Isaac Levi have argued that not even a purely probabilistic self-predictionis available to thedeliberator, if one takes subjective probabilities to be conceptually linked to betting rates. It makes no sense to have a betting rate for an option, for one's willingness to bet on the option depends on the net gain from the bet, in combination with the option's antecedent utility, rather than on the offered odds. And even apart from this consideration, assigning probabilities to the options among which one is choosing is futile since such probabilities could be of no possible use in choice. The paper subjects these arguments to critical examination and suggests that, appearances notwithstanding, practical deliberation need not crowd outself-prediction.

Presumption of Equality requires that individuals be treated equally in the absence of relevant information that would discriminate between them. Our objective is to make this principle more precise, if viewed as a principle of fairness, and to determine why and under what conditions it should be obeyed. Presumption norms are procedural constraints, but their justification can be sought in the possible or expected outcomes of the procedures they regulate. This is the avenue pursued here. The suggestion is that in the absence of information that would discriminate between the individuals, equal treatment minimizes the expected unfairness of the outcome. A related suggestion is that equal treatment under these circumstances also minimizes the maximal possible unfairness of the outcome. Whether these suggestions are correct or not depends on the properties of the underlying unfairness measure. The required properties are specified

The paper presents and discusses the so-called Wrong Kind of Reasons Problem (WKR problem) that arises for the fitting-attitudes analysis of value. This format of analysis is exemplified for example by Scanlon's buck-passing account, on which an object's value consists in the existence of reasons to favour the object- to respond to it in a positive way. The WKR problem can be put as follows: It appears that in some situations we might well have reasons to have pro-attitudes toward objects that are not valuable. Or vice versa: we might have reasons not to have pro-attitudes toward some valuable objects. The paper goes through several attempts to solve (or dissolve) the WKR problem and argues that none of them is fully satisfactory.