Wlodek Rabinowicz

In addressing a complex issue that is decomposable into several sub-questions, a committee can use different voting procedures: Either it can let the committee members vote on each sub-question and then use the outcomes as premises for its conclusion on the main issue (premise based-procedure, pbp), or it can let the members directly vote on the conclusion (conclusion-based procedure, cbp). The procedures can lead to different results, but which of them is a better truth-tracker? On the basis of Condorcet's jury theorem, we show that the pbp is clearly superior if the objective is to reach truth for the right (= correct) reasons. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the cbp turns out to be more reliable, even though, for the most part, the pbp will retain its superiority. In that connection, we also consider the truth-tracking potential of a “sophisticated” variant of the pbp, which is sensitive to the size of the majorities supporting each of the premises.

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 it has been suggested.

Piccione and Rubinstein (1997) present and analyse the sequential decision problem of an “absentminded driver”. The driver's absentmindedness (imperfect recall) leads him to time-inconsistent strategy evaluations. His original evaluation gets replaced by a new one under impact of the information that the circumstances have changed, notwithstanding the fact that this change in circumstances has been expected by him all along. The time inconsistency in strategy evaluation suggests that such an agent might have reason to renege on his adopted strategy. As we shall see, however, this danger is only apparent. There is no serious problem of dynamic inconsistency in this case. My diagnosis of the case under consideration is in many respects similar to the one provided by Aumann, Hart and Perry (1997), but the analysis leading to this diagnosis is not quite the same.

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.

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.

Backward induction has been the standard method of solving finite extensive-form games with perfect information, notwithstanding the fact that this procedure leads to counter-intuitive results in various games (iterated prisoner's dilemma, centipede, chain store, etc.). However, beginning in the late eighties, the method of backward induction became an object of criticism. It is claimed (most notably, by Reny 1988, 1989, Binmore 1987, Bicchieri 1989, and Pettit & Sugden 1989) that the assumptions needed for its defence are quite implausible, if not incoherent. It is therefore natural to ask for the justification of backward induction: Can one show that rational players who know the structure of the game, have trust in each other's practical rationality and reason correctly, will act in accordance in backward induction? Several researchers have tried a justification of this kind, but the argument presented in Robert Aumann's paper from 1995 is perhaps the most well-known and influential attempt to provide such a justification. Clausing (1999) provides a sustained discussion of the justification problem for backward induction. It is an excellent work and the criticism I will present below does not detract from this evaluation: the issues discussed by the author are complex and it is difficult to get everything right. Furthermore, I hope that the criticism to be presented may be instructive; Even though it has not been Clausing's intention, his logical reconstruction of Aumann's defence of backward induction allows us to see very clearly what is wrong with that argument. It also provides us with * This paper was presented at workshops in Lund and in Uppsala, in the Fall of 1999. I am indebted to the participants for their useful comments. The work on the paper was supported by a generous research grant from The Bank of Sweden Tercentenary Foundation.

Standard approaches to possible-world semantics allow us to define necessity and logical truth, but analyticity is considerably more difficult to account for. The source of this difficulty lies in the received model-theoretical conception of a language interpretation. In intuitive terms, analyticity amounts to truth in virtue of meaning alone, i.e. solely in virtue of the interpretation of linguistic expressions. In other words, an analytic sentence should remain true under all variations of ‘extralinguistic reality’ as long as the interpretation is kept constant. However, the received conception of an interpretation as a mapping from language to a model frame hinders keeping the interpretation constant while varying other components of the model. To make room for analyticity, the concept of an interpretation should therefore be revised. The latter should be made richer in content than it has usually been assumed. As a by-product, this revision also gives us a one-dimensional analogue of the influential two-dimensional account of a priori. We are thus able to map out the network of formal connections between the notions of analyticity, apriority, logical truth and necessity.

The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a proposition A does not coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A.

According to Ruth Chang, two items may be evaluatively comparable even when neither is better than, worse than, or equally good as the other. There is a fourth kind of comparability: The two items may be on a par. Recently, Joshua Gert has suggested that this somewhat elusive notion of evaluative parity can be easily accounted for if one interprets value comparisons as normative assessments of preference: The distinction between equality in value and parity becomes unproblematic on this approach. As I show, the approach in question, if appropriately extended, also allows for a straightforward distinction between parity and incomparability. However, while Gert’s basic proposal is attractive, the way he develops it is flawed. He takes it that rationally permissible preferences for each item can vary in strength and then models value comparisons by comparing intervals of permissible preference strengths for different items. As will be seen, however, such an interval modeling has features that make it unfit for the representation of the structure of value relationships. I provide an alternative modeling, in terms of intersections of rationally permissible preference orderings, delineate a general taxonomy of binary value relations, and conclude with some remarks about the connection between value comparisons and various concepts of choiceworthiness.

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.

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.

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.

This paper puts forward the following claims: (i) The size of inequality in welfare should be distinguished from its badness. (ii) The size of a pairwise inequality between two individuals can be measured by the absolute or the relative welfare distance between their welfare levels, but it does not depend on the welfare levels of other individuals. (iii) The size of inequality in a social state may be understood either as the degree of pairwise inequality or as its amount. (iv) The badness of a pairwise inequality may differ from its size in several ways; for example, the badness measure might go by the distance between priority-transformed welfare levels and/or it might assign heavier weight to larger distances. (v) The badness of a pairwise inequality may be either personal or impersonal, with the personal interpretation being internally consistent and, pace Temkin, independently tenable even if we reject the so-called Slogan (i.e., the Person-Affecting Claim). (vi) The aggregation procedure by which we arrive from the badness of pairwise inequalities to the badness of the inequality in a social state takes different forms depending on whether the badness of a pairwise inequality is interpreted in a personal or in an impersonal way. (vii) Since Temkin's complaint-based measures of the badness of inequality follow the format appropriate for the personal interpretation, they seem out of place if one, like him, treats the badness of inequality as an impersonal value.