Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of false (...) positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness. (shrink)

We defend Uniqueness, the claim that given a body of total evidence, there is a uniquely rational doxastic state that it is rational for one to be in. Epistemic rationality doesn't give you any leeway in forming your beliefs. To this end, we bring in two metaepistemological pictures about the roles played by rational evaluations. Rational evaluative terms serve to guide our practices of deference to the opinions of others, and also to help us formulate contingency plans about what to (...) believe in various situations. We argue that Uniqueness vindicates these two roles for rational evaluations, while Permissivism clashes with them. (shrink)

Value pluralists believe in multiple dimensions of value. What does betterness along a dimension have to do with being better overall? Any systematic answer begins with the Strong Pareto principle: one thing is overall better than another if it is better along one dimension and at least as good along all others. We defend Strong Pareto from recent counterexamples and use our discussion to develop a novel view of dimensions of value, one which puts Strong Pareto on firmer footing. We (...) conclude by defending Dimensionalism, the hypothesis that overall value relations are determined solely by how things compare along value dimensions. These are first steps towards a more systematic value pluralism. (shrink)

I advocate Time-Slice Rationality, the thesis that the relationship between two time-slices of the same person is not importantly different, for purposes of rational evaluation, from the relationship between time-slices of distinct persons. The locus of rationality, so to speak, is the time-slice rather than the temporally extended agent. This claim is motivated by consideration of puzzle cases for personal identity over time and by a very moderate form of internalism about rationality. Time-Slice Rationality conflicts with two proposed principles of (...) rationality, Conditionalization and Reflection. Conditionalization is a diachronic norm saying how your current degrees of belief should fit with your old ones, while Reflection is a norm enjoining you to defer to the degrees of belief that you expect to have in the future. But they are independently problematic and should be replaced by improved, time-slice-centric principles. Conditionalization should be replaced by a synchronic norm saying what degrees of belief you ought to have given your current evidence and Reflection should be replaced by a norm which instructs you to defer to the degrees of belief of agents you take to be experts. These replacement principles do all the work that the old principles were supposed to do while avoiding their problems. In this way, Time-Slice Rationality puts the theory of rationality on firmer foundations and yields better norms than alternative, non-time-slice-centric approaches. (shrink)

We typically have to act under uncertainty. We can be uncertain about the relevant descriptive facts, but also about the relevant normative facts. However, the search for a theory of decision-making under normative uncertainty is doomed to failure. First, the most natural proposal for what to do given normative uncertainty faces two devastating problems. Second, the motivations for wanting a theory of what to do given descriptive uncertainty do not carry over to normative uncertainty. Descriptive facts may be inaccessible even (...) in principle, and ignorance of them excuses one from blame, but normative facts are in principle accessible, and ignorance of them arguably is no excuse. Normative facts differ from descriptive facts: normative facts affect what we ought to do no matter what, while descriptive facts affect what we ought to do only insofar as we are aware of them. (shrink)

Many consequentialists argue that you ought to do your part in collective action problems like climate change mitigation and ending factory farming because (i) all such problems are triggering cases, in which there is a threshold number of people such that the outcome will be worse if at least that many people act in a given way than if fewer do, and (ii) doing your part in a triggering case maximises expected value. I show that both (i) and (ii) are (...) false: Some triggering cases cannot be solved by appeal to expected value, since they involve infinities, and some collective action problems are not triggering cases, since they involve parity. However, I argue that consequentialism can still generally prohibit failure to do your part in those collective action problems where we believe that so acting would be impermissible. (shrink)

Multidimensional adjectives are ubiquitous in natural language. An adjective F is multidimensional just in case whether F applies to an object or pair of objects depends on how those objects stand with respect to multiple underlying dimensions of F-ness. Developing a semantics for multidimensional adjectives requires us to address the problem of dimensional aggregation: how do the application conditions of an adjective F in its positive and comparative forms depend on its underlying dimensions? Here we develop a semantics for multidimensional (...) adjectives that incorporates aggregation functions. We then explore an analogy between dimensional aggregation and preference aggregation, bringing results from social choice theory to bear on the number and kind of aggregation functions that are admissible in a context. These results suggest that, for any given adjective, there will often be multiple aggregation functions admissible, meaning that multidimensional comparatives are often vague. (shrink)

Humans typically display hindsight bias. They are more confident that the evidence available beforehand made some outcome probable when they know the outcome occurred than when they don't. There is broad consensus that hindsight bias is irrational, but this consensus is wrong. Hindsight bias is generally rationally permissible and sometimes rationally required. The fact that a given outcome occurred provides both evidence about what the total evidence available ex ante was, and also evidence about what that evidence supports. Even if (...) you in fact evaluate the ex ante evidence correctly, you should not be certain of this. Then, learning the outcome provides evidence that if you erred, you are more likely to have erred low rather than high in estimating the degree to which the ex ante evidence supported the hypothesis that that outcome would occur. (shrink)

Multidimensional concepts are everywhere, and they are important. Examples include moral value, welfare, scientific confirmation, democracy, and biodiversity. How, if at all, can we aggregate the underlying dimensions of a multidimensional concept F to yield verdicts about which things are Fer than which overall? Social choice theory can be used to model and investigate this aggregation problem. Here, we focus on a particularly thorny problem made salient by this social choice-theoretic framework: the underlying dimensions of a given concept might be (...) measurable on different types of scales—e.g., some ordinal and some cardinal. An underappreciated impossibility theorem due to Anna Khmelnitskaya shows that seemingly plausible constraints on aggregation across scale types are inconsistent. This impossibility threatens to render the notion of overall Fness incoherent. We attempt to defuse this threat, arguing that the impossibility depends on an overly restrictive conception of measurement and of how measurement constrains aggregation. Adopting a more flexible—and, we think, more perspicuous—conception of measurement opens an array of possibilities for aggregation across disparate scale types. (shrink)

I defend counterfactual decision theory, which says that you should evaluate an action in terms of which outcomes would likely obtain were you to perform it. Counterfactual decision theory has traditionally been subsumed under causal decision theory as a particular formulation of the latter. This is a mistake. Counterfactual decision theory is importantly different from, and superior to, causal decision theory, properly so called. Causation and counterfactuals come apart in three kinds of cases. In cases of overdetermination, an action can (...) cause a good outcome without the latter counterfactually depending on the former. In cases of constitution, an action can constitute a good outcome rather than causing it. And in cases of determinism, either the laws or the past counterfactually depend on your action, even though your action cannot cause the laws or the past to be different. In each of these cases, it is counterfactual decision theory which gives the right verdict, and for the right reasons. (shrink)

Philosophy and Phenomenological Research, EarlyView.

I argue that a attractive theory about the metaphysics of belief—the prag- matic, interpretationist theory endorsed by Stalnaker, Lewis, and Dennett, among others—implies that agents have a novel form of voluntary control over their beliefs. According to the pragmatic picture, what it is to have a given belief is in part for that belief to be part of an optimal rationalization of your actions. Since you have voluntary control over your actions, and what actions you perform in part determines what (...) beliefs you count as having, this theory entails that you have some voluntary control over your beliefs. However, the pragmatic picture doesn’t entail that you can believe something as a result of intention to believe it. Nevertheless, I argue that the limited sort of voluntary control implied by the pragmatic picture may be of use in vindicating the deontological conception of epistemic justification. (shrink)

Higher-order evidence is evidence about what is rational to think in light of your evidence. Many have argued that it is special – falling into its own evidential category, or leading to deviations from standard rational norms. But it is not. Given standard assumptions, almost all evidence is higher-order evidence.