Wlodek Rabinowicz

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.

Apart from a short introduction, this contribution consists of a translation of Tadeusz Kotarbinski’s “Utilitarianism and The Ethics of Pity”. In that very concise and relatively unknown early note, written before he embarked on his long and influential career as a nominalist logician and philosopher of science, Kotarbinski had formulated four astonishingly ‘modern’ objections to utilitarianism. Unlike Christian ‘ethics of pity’, utilitarian ethics disregards the normative importance of the distinction between preventing suffering and promoting happiness, leaves no room for supererogation, leaves no room for agent-relativity in morality insofar as it disallows ‘inefficient’ self-sacrifice, and rejects the possibility of genuine ethical dilemmas. To what extent was Kotarbinski a pioneer in his critique? This question is posed but not answered

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

In Rabinowicz (2008), I considered how value relations can best be analysed in terms of fitting pro-attitudes. In the formal model of 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, 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.

The point of departure in my story is the contrast between two models of democratic voting process: popular democracy and what might be called committee democracy. On one interpretation, voting in popular democracy is a procedure whose function is to aggregate the individuals’ preferences to something like a collective preference, while in committee democracy what is being aggregated are committee members’ judgments. The relevant judgments on the agenda often address an evaluative question. It is such value judgments that this paper focuses on. The question is how their aggregation differs from aggregation of preferences. I focus on the case in which the two aggregation scenarios exhibit a far-reaching structural similarity: more precisely, the case in which, in the judgment aggregation scenario, the individual inputs are value rankings. This means that, formally, the individual judgments in this case have the same structure as preference rankings over a given set of alternatives, but while in a preference ranking the alternatives are ordered in accordance with one’s preferences, a value ranking expresses one’s comparative evaluation of the alternatives: say, this alternative is best, those two alternatives are second-best, that alternative is third-best, etc. I suggest that this difference in the nature of individual inputs in two aggregation scenarios has important implications for the task of aggregation. In particular, distance-based methods that look fine for the aggregation of judgments turn out to be inappropriate for the aggregation of preferences: Minimization of distance from individual inputs violates the Pareto condition. When applied to judgment aggregation, distance-based methods can also be approached from the epistemic standpoint: the questions canl be posed concerning their advantages as a truth-tracker. In this context, what matters is not only the probability of the outcome of the aggregation procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth.

An agent whose preferences violate the Independence Axiom or for some other reason are not representable by an expected utility function, can avoid 'dynamic inconsistency' either by foresight ('sophisticated choice') or by subsequent adjustment of preferences to the chosen plan of action ('resolute choice'). Contrary to McClennen and Machina, among others, it is argued these two seemingly conflicting approaches to 'dynamic rationality' need not be incompatible. 'Wise choice' reconciles foresight with a possibility of preference adjustment by rejecting the two assumptions that create the conflict: Separability of Preferences in the case of sophisticated choice and Reduction to Normal form in the case of resolute choice..

The well-known argument of Frederick Fitch, purporting to show that verificationism (= Truth implies knowability) entails the absurd conclusion that all the truths are known, has been disarmed by Dorothy Edgington''s suggestion that the proper formulation of verificationism presupposes that we make use of anactuality operator along with the standardly invoked epistemic and modal operators. According to her interpretation of verificationism, the actual truth of a proposition implies that it could be known in some possible situation that the proposition holds in theactual situation. Thus, suppose that our object language contains the operatorA — it is actually the case that ... — with the following truth condition: vA iff w0, wherew 0 stands for the designated world of the model — the actual world. Then we can formalize the verificationist claim as follows.

According to the so-called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e., strategies that reward cooperation with subsequent cooperation and punish defectionwith subsequent defection. If future interactions are sufficiently important, i.e., if the discount rate is relatively small, each agent may be motivated to cooperate by fear of retaliation in the future. For finite games, however, where the number of plays is known beforehand, there is a backward induction argument showing that rational agents will not be able to achieve cooperation. On behalf of the Hobbesian “Foole”, who cannot see any advantage in cooperation, Gregory Kavka (1983, 1986) has presented an argument that significantly extends the range of the backward induction argument. He shows that, for the backward induction argument to be effective, it is not necessary that the precise number of future interactions be known. It is sufficient that there is a known definite upper bound on the number of interactions. A similar argument is developed by John W. Carroll (1987). We will here question the assumption of a known upper bound. When the assumption is made precise in the way needed for the argument to go through, its apparent plausibility evaporates. We then offer a reformulation of the argument, based on weaker, and more plausible, assumptions.

The paper's 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. Therefore, pragmatic arguments should be seen as delivering conditional conclusions: “To afford being disunified as a decision maker, you’d better satisfy these constraints.” Arguments of this kind fail to establish the inherent rationality of the constraints under consideration. Levi’s view of the status of pragmatic arguments (cf. Levi 2002) is diametrally opposed. According to him, only synchronic pragmatic arguments are valid (indeed, categorically valid). The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in the paper.

This is a short version of Lindström & Rabinowicz 1991.In earlier papers, we proposed a generalization of the AGM approach to belief revision. The proposal was to view belief revision as a relation rather than as a function on theories (or belief sets). Going relational means that one allows for several equally reasonable revisions of a theory with a given proposition. In the present paper, we show that the relational approach is the natural result of generalizing in a certain way an approach to belief revision due to Adam Grove. In his (1988) paper, Grove presented two closely related modelings of functional belief revision, one in terms of a family of "spheres" around the agent's theory G and the other in terms of an epistemic entrenchment ordering of propositions. The "sphere"-terminology is natural when one looks upon theories and propositions as sets of possible worlds. Grove's spheres may be thought of as possible "fallback" theories relative to the agent's original theory: theories that he may reach by deleting propositions that are not "sufficiently" entrenched (according to standards of sufficient entrenchment of varying stringency). The entrenchment ordering can be recovered from the family of fallbacks by the definition: A is at least as entrenched as B iff A belongs to every fallback to which B belongs. To revise a theory T with a proposition A, we go to the smallest sphere that contain A-worlds and intersect it with A. The relational notion of belief revision that we are interested in, results if one allows that some propositions may be incomparable with respect to epistemic entrenchment. As a result, the family of fallbacks around a given theory will no longer have to be nested. This change opens up the possibility for several different ways of revising a theory with a given proposition.

W artykule przedstawiam ogólne ujęcie relacji wartości. Jako punkt wyjścia przyjmuję szczególny typ relacji wartości, równorzędność, stanowiącą zdaniem Ruth Chang pewną postać porównywalności wartości, która rożni się od trzech standardowych postaci porównywalności: lepszości, gorszości i równowartości. Joshua Gert zasugerował niedawno, iż pojęcie równorzędności można wyjaśnić, jeśli porównania wartości zinterpretuje się jako normatywne oceny preferencji. Chociaż podstawowa idea przyświecająca Gertowi jest atrakcyjna, sposób w jaki ją rozwija jest błędny. Jego model wartości sformułowany w kategoriach dopuszczalnych sił preferencji jest nieadekwatny. Zamiast tego proponuję model alternatywny, sformułowany w kategoriach przecięć racjonalnie dopuszczalnych uporządkowań preferencji. Dostarcza on ogólnej taksonomii wszystkich binarnych relacji wartości. Artykuł kończę kilkoma uwagami dotyczącymi następstw tego ujęcia dla teorii racjonalnego wyboru.

In the standard money pump, an agent with cyclical preferences can avoid exploitation if he shows foresight and solves his sequential decision problem using backward induction (BI). This way out is foreclosed in a modified money pump, which has been presented in Rabinowicz (2000). There, BI will lead the agent to behave in a self-defeating way. The present paper describes another sequential decision problem of this kind, the Centipede for an Intransitive Preferrer, which in some respects is even more striking than the modified pump. In the new problem, the BI reasoning that implies self-defeating behavior does not rest on the controversial robustness assumption concerning beliefs in one's future rationality. This strengthens the claim that foresight cannot save the intransitive preferrer from a self-defeating course of action.

In earlier papers (Lindström & Rabinowicz, 1989. 1990), we proposed a generalization of the AGM approach to belief revision. Our proposal was to view belief revision as a relation rather thanas a function on theories (or belief sets). The idea was to allow for there being several equally reasonable revisions of a theory with a given proposition. In the present paper, we show that the relational approach is the natural result of generalizing in a certain way an approach to belief revision due to Adam Grove. In his (1988) paper, Grove presents two closely related modelings of functional belief revision, one in terms of a family of "spheres" around the agent's theory G and the other in terms of an epistemic entrenchment ordering of propositions. The "sphere"-terminology is natural when one looks upon theories and propositions as being represented by sets of possible worlds. Grove's spheres may be thought of as possible "fallback" theories relative to the agent's original theory: theories that he may reach by deleting propositions that are not "sufficiently" entrenched (according to standards of sufficient entrenchment of varying stringency). To put it differently, fallbacks are theories that are closed upwards under entrenchment The entrenchment ordering can be recovered from the family of fallbacks by the definition: A is at least as entrenched as B iff A belongs to every fallback to which B belongs. To revise a theory T with a proposition A, we go to the smallest sphere that contain A-worlds and intersect it with A. The relational notion of belief revision that we are interested in, results from weakening epistemic entrenchment by not assuming it to be connected. I.e., we want to allow that some propositions may be incomparable with respect to epistemic entrenchment. As a result, the family of fallbacks around a given theory will no longer have to be nested. This change opens up the possibility for several different ways of revising a theory with a given proposition.

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.

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.

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.

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.

We discuss various possibilities for developing a dynamic doxastic logic (DDL) for introspective agents: agents who have the ability to form higher-order beliefs. Such agents can reflect upon and change their minds about their own beliefs. The project of constructing such a logic, full DDL or DDL unlimited, is ridden with difficulties due to the fact that the agent's own doxastic state now becomes a part of the reality he is trying to explore. When an introspective agent learns more about the world (and himself), the reality he holds beliefs about undergoes a change in its doxastic part, which means that his introspective beliefs have to be adjusted accordingly.

The ‘buck-passing’ account equates the value of an object with the existence of reasons to favour it. As we argued in an earlier paper, this analysis faces the ‘wrong kind of reasons’ problem: there may be reasons for pro-attitudes towards worthless objects, in particular if it is the pro-attitudes, rather than their objects, that are valuable. Jonas Olson has recently suggested how to resolve this difficulty: a reason to favour an object is of the right kind only if its formulation does not involve any reference to the attitudes for which it provides a reason. We argue that despite its merits, Olson's solution is unsatisfactory. We go on to suggest that the buck-passing account might be acceptable even if the problem in question turns out to be insoluble