Wlodek Rabinowicz

Piccione and Rubinstein present and analyse the sequential decision problem of an “absentminded driver”. The driver's absentmindedness 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, but the analysis leading to this diagnosis is not quite the same.

In 2014, Christian List and I published a paper that delineated our view regarding what it takes for an agent to act freely. We suggested that this requires the action to be endorsed by the agent and caused by this endorsement and yet not be necessitated. Free action requires indeterminism at the agential level—the kind of indeterminism that is compatible with physical determinism. I still think that our proposal was on the right track, but I believe it needs elaboration. As we already noted in the paper, our formal modelling—a standard branching model—was too extensional, and therefore in need of revision. Also, on a substantive side, what we say about the causal component of our proposal does not quite take care of the danger of ‘flukishness’ of an undetermined action. It was this threat to agential control that the requirement of causation by endorsement was meant to disarm in the first place. But the threat still remains and needs to be confronted. Revising the formal model and finding a solution to the problem of flukishness are my two objectives in this paper.

Suppose a committee or a jury confronts a complex question, the answer to which requires attending to several sub-questions. Two different voting procedures can be used. On one, the committee members vote on each sub-question and the voting results are used as premises for the committee’s conclusion on the main issue. This premise-based procedure can be contrasted with the conclusion-based approach, which requires the members to directly vote on the conclusion, with the vote of each member being guided by her views on the relevant sub-questions. The two procedures are not equivalent: There may be a majority of voters supporting each of the premises, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit (2001) connects the choice between the two procedures with the discussion of deliberative democracy. The problem we want to examine instead concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. Which of them is better when it comes to tracking truth? As it turns out, the answer is not univocal. On the basis of Condorcet’s jury theorem, the premise-based procedure can be shown to be superior if the objective is reach truth for the right reasons, without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority.

Suppose a committee or a jury confronts a complex question, the answer to which requires attending to several sub-questions. Two different voting procedures can be used. On one, the committee members vote on each sub-question and the voting results are used as premises for the committee’s conclusion on the main issue. This premise-based procedure can be contrasted with the conclusion-based approach, which requires the members to directly vote on the conclusion, with the vote of each member being guided by her views on the relevant sub-questions. The two procedures are not equivalent: There may be a majority of voters supporting each of the premises, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit (2001) connects the choice between the two procedures with the discussion of deliberative democracy. The problem we want to examine instead concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. Which of them is better when it comes to tracking truth? As it turns out, the answer is not univocal. On the basis of Condorcet’s jury theorem, the premise-based procedure can be shown to be superior if the objective is reach truth for the right reasons, without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority.

Can it be better or worse for a person to be than not to be, that is, can it be better or worse to exist than not to exist at all? This old 'existential question' has been raised anew in contemporary moral philosophy. There are roughly two reasons for this renewed interest. Firstly, traditional so-called “impersonal” ethical theories, such as utilitarianism, have counter-intuitive implications in regard to questions concerning procreation and our moral duties to future, not yet existing people. Secondly, it has seemed evident to many that an outcome can only be better than another if it is better for someone, and that only moral theories that are in this sense “person affecting” can be correct. The implications of this Person Affecting Restriction will differ radically, however, depending on which answer one gives to the existential question. Melinda Roberts (2003) and Matthew Adler (2009) have defended an affirmative answer to the existential question using an assumption that one can asribe a zero level of wellbeing to a person in a world in which that person doesn't exist. Contrariwise, Derek Parfit (1984), John Broome (1999), and others have worried that if we take a person’s life to be better for her than non-existence, then we would have to conclude that it would have been worse for her if she did not exist, which is absurd: Nothing would have been worse or better for a person if she had not existed. The paper suggests that an affirmative answer to the existential question can avoid such absurdities: One can claim that, say, it is better for a person to exist than not to exist, without implying that it would have been worse for a person if she had not existed or that her level of wellbeing would then have been lower.

Can it be better or worse for a person to exist than not to exist at all? This old and challenging existential question has been raised anew in contemporary moral philosophy, mainly for two reasons. First, traditional “impersonal” ethical theories, such as utilitarianism, have counterintuitive implications in population ethics, for example, the repugnant conclusion. Second, it has seemed evident to many that an outcome can be better than another only if it is better for someone, and that only moral theories that are in this sense “person affecting” can be correct. The implications of this Person-Affecting Restriction will differ radically, however, depending on which answer one gives to the existential question. The negative answer, which we argue against, would make the restriction quite untenable. Hence, many of the problems regarding our moral duties to future generations turn around the issue at hand.

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

The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, Y might doubt that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through.

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.

This paper addresses a problem for theories of epistemic democracy. In a decision on a complex issue which can be decomposed into several parts, a collective can use different voting procedures: Either its members vote on each sub-question and the answers that gain majority support are used as premises for the conclusion on the main issue (premise based-procedure, pbp), or the vote is conducted on the main issue itself (conclusion-based procedure, cbp). The two procedures can lead to different results. We investigate which of these procedures is better as a truth-tracker, assuming that there exists a true answer to be reached. On the basis of the Condorcet jury theorem, we show that the pbp is universally superior if the objective is to reach truth for the right reasons. If one instead is after truth for whatever reasons, right or wrong, there will be cases in which the cbp is more reliable, even though, for the most part, the pbp still is to be preferred.

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys “continuity for easy cases,” i.e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also – rather counter-intuitively – allow chances of small improvements to compensate risks of huge losses. In this paper, we show that Temkin's argument is flawed but that a better proof is possible. However, it is more difficult to determine what conclusions should be drawn from this result. Contrary to what Temkin suggests, substitutivity of equivalents is a notoriously controversial principle. But even in the absence of substitutivity, the counter-intuitive conclusion is derivable from a strengthened version of continuity for easy cases. The best move, therefore, might be to question the latter principle, even in its original simple version: as we argue, continuity for easy cases gives rise to a sorites.

The spectrum argument purports to show that the better-than relation is not transitive, and consequently that orthodox value theory is built on dubious foundations. The argument works by constructing a sequence of increasingly less painful but more drawn-out experiences, such that each experience in the spectrum is worse than the previous one, yet the final experience is better than the experience with which the spectrum began. Hence the betterness relation admits cycles, threatening either transitivity or asymmetry of the relation. This paper examines recent attempts to block the spectrum argument, using the idea that it is a mistake to affirm that every experience in the spectrum is worse than its predecessor: an alternative hypothesis is that adjacent experiences may be incommensurable in value, or that due to vagueness in the underlying concepts, it is indeterminate which is better. While these attempts formally succeed as responses to the spectrum argument, they have additional, as yet unacknowledged costs that are significant. In order to effectively block the argument in its most typical form, in which the first element is radically inferior to the last, it is necessary to suppose that the incommensurability is particularly acute: what might be called radical incommensurability. We explain these costs, and draw some general lessons about the plausibility of the available options for those who wish to save orthodox axiology from the spectrum argument.

Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we interpret as degrees of commensurability.One payoff is the solution our approach provides to a paradox in population ethics, generated by Parfit's “Continuum Argument”. Parfit imagines a sequence of populations, starting with one consisting of excellent lives and, by a sequence of apparent improvements, reaching a much larger population of lives barely worth living. What he dubs “the Repugnant Conclusion” is that the final population is better than the first. Developing Parfit's response, we argue that some of the populations in the sequence are merely almost better than their immediate predecessors. Almost better is not transitive (unlike better). We offer analogies to other ‘spectrum arguments’, Condorcet's paradox, and to developments in formal epistemology.

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.

My focus is on aggregation of individual value rankings of alternatives to a collective value ranking. This is compared with aggregation o individual prefrences to a collective preference. While in an individual preference ranking the alternatives are ordered in accordance with one’s preferences, the order in a value ranking expresses one’s comparative evaluation of the alternatives, from the best to the worst. I suggest that, despite their formal similarity as rankings, this difference in the nature of individual inputs in two aggregation scenarios has important implications: The kind of procedure that looks fine for aggregation of judgments is inappropriate for aggregation of preferences. The procedure I have in mind consists in similarity maximization, or – more precisely – in minimization of the average distance from individual inputs. When applied to judgment aggregation, this procedure can also be approached from the epistemic perspective: the questions are posed concerning its advantages as a truth-tracker. From that perspective, what matters is not only the probability of the outcome of the procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth.

This paper addresses a problem for theories of epistemic democracy. In a decision on a complex issue which can be decomposed into several parts, a collective can use different voting procedures: Either its members vote on each sub-question and the answers that gain majority support are used as premises for the conclusion on the main issue, or the vote is conducted on the main issue itself. The two procedures can lead to different results. We investigate which of these procedures is better as a truth-tracker, assuming that there exists a true answer to be reached. On the basis of the Condorcet jury theorem, we show that the pbp is universally superior if the objective is to reach truth for the right reasons. If one instead is after truth for whatever reasons, right or wrong, there will be cases in which the cbp is more reliable, even though, for the most part, the pbp still is to be preferred.

One might think that money pumps directed at agents with cyclic preferences can be avoided by foresight. This view was challenged two decades ago by the discovery of a money pump with foresight, which works against agents who use backward induction. But backward induction implausibly assumes that the agent would act rationally and retain her trust in her future rationality even at choice nodes that could only be reached if she were to act irrationally. This worry does not apply to BI-terminating decision problems, where at each choice node backward induction prescribes a move that terminates further action. For BI-terminating decision problems, it is enough to assume that rationality and trust in rationality are retained at choice nodes reachable by rational moves. The old money pump with foresight was not BI-terminating. In this paper, we present a new money pump with foresight, one that is both BI-terminating and considerably simpler.