I consider statistical criteria of algorithmic fairness from the perspective of the _ideals_ of fairness to which these criteria are committed. I distinguish and describe three theoretical roles such ideals might play. The usefulness of this program is illustrated by taking Base Rate Tracking and its ratio variant as a case study. I identify and compare the ideals of these two criteria, then consider them in each of the aforementioned three roles for ideals. This ideals program may present a way (...) forward in the normative evaluation of candidate statistical criteria of algorithmic fairness. (shrink)

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)

The precautionary principle is invoked in a number of important personal and policy decision contexts. Peterson shows that certain ways of making the principle precise are inconsistent with other criteria of decision-making. Some object that the results do not apply to cases of deep uncertainty or value incommensurability which are alleged to be in the principle’s wheelhouse. First, I show that Peterson’s impossibility results can be generalized considerably to cover cases of both deep uncertainty and incommensurability. Second, I contrast an (...) alternative way of giving voice to the precautionary impulse. (shrink)

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as providing (...) a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...) Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

Recent impossibility theorems for fair risk assessment extend to the domain of epistemic justice. We translate the relevant model, demonstrating that the problems of fair risk assessment and just credibility assessment are structurally the same. We motivate the fairness criteria involved in the theorems as also being appropriate in the setting of testimonial justice. Any account of testimonial justice that implies the fairness/justice criteria must be abandoned, on pain of triviality.

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...) stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also (...) generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

We introduce a fairness criterion that we call Spanning. Spanning i) is implied by Calibration, ii) retains interesting properties of Calibration that some other ways of relaxing that criterion do not, and iii) unlike Calibration and other prominent ways of weakening it, is consistent with Equalized Odds outside of trivial cases.

Given the role consensus is supposed to play in the social aspects of inquiry and deliberation, it is important that we may always identify a consensus as the basis of joint inquiry and deliberation. However, it turns out that if we think of an agent revising her beliefs to reach a consensus, then, on the received view of belief revision, AGM belief revision theory, certain simple and compelling consensus positions are not always available.

This paper studies a generalization of rational choice theory. I briefly review the motivations that Helzner gives for his conditional choice construction . Then, I focus on the important class of conditional choice functions with vacuous second tiers. This class is interesting for both formal and philosophical reasons. I argue that this class makes explicit one of conditional choice’s normative motivations in terms of an account of neutrality advocated within a certain tradition in decision theory. The observations recorded—several of which (...) are generalizations of central results in the standard theory of rational choice—are intended to provide further insight into how conditional choice generalizes the standard account and are offered as additional evidence of the fruitfulness of the conditional choice framework. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely (...) ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...) short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and (...) Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

We reply to Eva's comment on our "New Possibilities for Fair Algorithms," comparing and contrasting our Spanning criterion with his suggested Spacing criterion.

Analysis (2021), https://doi.org/10.1093/analys/anab012.

This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...) that we make by drawing an analogy with de Finetti's argument against mandating countable additivity. Having presented the best version of the Orgulity Argument, our second aim is to develop a reply to it. We extend Elga's idea of appealing to finitely additive probability to show that the challenge posed by the Orgulity Argument can be met. (shrink)

We provide counterexamples to some purported characterizations of dilation due to Pedersen and Wheeler :1305–1342, 2014, ISIPTA ’15: Proceedings of the 9th international symposium on imprecise probability: theories and applications, 2015).

In lieu of an abstract, here is a brief excerpt of the content:The Transformation:Power in Persistence and PerspectiveTyler BendrickWe've got another meth napper," my resident stated. With an introduction like that, it is hard not to be immediately labeled as a "difficult patient." Being the only Spanish-speaking person on the team, I, a third-year medical student, became the primary point of contact for this severely injured patient. He was an only-Spanish-speaking, 36-year-old male admitted [End Page 7] to our trauma service (...) after he was hit by a truck while riding his bicycle. Unbeknownst to me at the time, the 14 days I spent caring for this man would become one of the most pivotal learning experiences of my medical school career. It changed not only how I understand and approach "difficult patients" but expanded my knowledge of the complexities and challenges of the current healthcare system and how we, as physicians and healthcare providers, can deliver the best care to patients with low health literacy and limited resources.So, what is a "meth napper?" I questioned. "Well, meth is a super stimulant," my resident explained. "When people are frequent meth users, they get used to functioning normally with high levels of stimulants in their body, reducing the normal regulation of wakefulness. When the amphetamine is removed (such as upon admission to the hospital), the body is left to fend for itself, and thus patients oftentimes sleep for 23 hours a day for about 3 to 5 days while their body works to detox and normalize hormones."As predicted, my new friend, "Joe," was napping when I first went to see him. Thinking back, the word "napping" does not accurately describe his level of somnolence. He was virtually unarousable, and I took to a sternal rub to wake him up at 5 a.m. after his traumatic exploratory laparotomy the night before. Once aroused, he was furious. "Estoy bien. Tengo dolor y tengo hambre," he grunted at me. (I am fine, and I am in pain and hungry!). "Ok, Joe," I replied in Spanish, "I am just going to do a quick exam and you can go back to sleep. We will give you medications for your pain. You had a big surgery on your intestines, so you cannot eat or drink right now. If everything goes well in the next couple of days and you start walking around, we can advance your diet." He begrudgingly let me examine him, never opening his eyes, and I left and went about my day.We continued this routine for five days. I would periodically check on him and usually found him sleeping. When awake, he refused to work with physical therapists, get up and walk or go to the bathroom, shower, use his spirometer, or converse with the nursing staff. He seemed completely disinterested in recovery. About day three, we slowly advanced his diet to clear liquids so he could quench his thirst. Sometimes his wife was there, and she would ask for updates, to which I could only reply, "We have to wait until he is more awake or willing to work with us." I was getting frustrated, as it seemed that his noncompliance was becoming his barrier to discharge.But on day six, everything changed. I went to check on Joe, and he was wide awake, vomiting, and irate. He shouted that he was in incredible pain, and his incision was wet. He was also complaining that he had not eaten in five days, and was insisting that we were starving him. Again, I calmly explained (as I had multiple times a day for the past five days) that his major abdominal surgery prevented us from feeding him until his intestines healed. We were giving him fluids and nutrition through his IV lines, so he was not starving to death. I rushed to get my resident to examine his oozing wound, and after a CT scan and an x-ray, we discovered what we feared: His wound had opened down to the fascia, "dehiscence," as it is called. On top of this, he now had a bowel obstruction, causing his vomiting. His lack of mobility for the past five days had slowed his... (shrink)

HellmanGeoffrey ** and ShapiroStewart. **** Mathematical Structuralism. Cambridge Elements in the Philosophy of Mathematics, RushPenelope and ShapiroStewart, eds. Cambridge University Press, 2019. Pp. iv + 94. ISBN 978-1-108-45643-2, 978-1-108-69728-6. doi: 10.1017/9781108582933.

During the early years of the COVID-19 pandemic, preclinical and clinical research were sped up and scaled up in both the public and private sectors and in partnerships between them. This resulted in some extraordinary advances, but it also raised a range of issues regarding the ethics, rigour, and integrity of scientific research, academic publication, and public communication. Many of the failures of scientific rigour and integrity that occurred during the pandemic were exacerbated by the rush to generate, disseminate, (...) and implement research findings, which not only created opportunities for unscrupulous actors but also compromised the methodological, peer review, and advisory processes that would usually identify sub-standard research and prevent compromised clinical or policy-level decisions. While it would be tempting to attribute these failures of science and its translation solely to the “unprecedented” circumstances of the COVID-19 pandemic, the reality is that they preceded the pandemic and will continue to arise once it is over. Existing strategies for promoting scientific rigour and integrity need to be made more rigorous, better integrated into research training and institutional cultures, and made more sophisticated. They might also need to be modified or supplemented with other strategies that are fit for purpose not only in public health emergencies but in any research that is sped-up and scaled up to address urgent unmet medical needs. (shrink)

Biology, during the last decade in particular, is making substantial headway into our social theories of business and behavior. While the social sciences rush to keep up with the advancement of knowledge, we highlight the need for an ethics discussion to also keep pace. Although the implications to theory are important, our focus is on how new knowledge has the capacity to alter the formulation and practice of business policy, which we believe is potentially profound. Furthermore, the ethicality of (...) a set of issues can depend heavily on one’s perspective, and differing views may not always be compatible. With this in mind, we discuss the ways in which one area of emerging biological knowledge—behavioral genetics—invites a rethinking of the nuances of four long-standing topic areas of business ethics surrounding personnel selection; and we do so from two perspectives—that of the employer and of the job seeker. The four ethical topics are the static nature of genetic information that is out of an individual’s control, faking and lying during selection processes, privacy, and stigmatization of minority groups. (shrink)

Draft for the Oxford Handbook of Margaret Cavendish (edited by Julie Crawford with Jacqueline Broad). -/- This chapter looks at Margaret Cavendish's treatment of the supernatural, beginning by asking how she distinguishes the natural from the supernatural, and then by examining her treatment of a series of alleged supernatural beings: fairies, ghosts, witches, the human supernatural soul, angels, and God. Throughout, it argues that Cavendish's approach to the supernatural is often similar to Thomas Hobbes's.

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...) the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. (shrink)

It is argued that david lewis' account of convention in "convention" required too much self-Consciousness of parties participating in a convention. In particular, It need not be known that there are equally good alternatives to the convention. This point affects other features of the definition, And suggests that the account is too much guided by the "rational assembly" picture of human conventions. (edited).

Critique of Norman Malcolm’s ‘Wittgenstein: The Relation of Language to Instinctive Behaviour’. Rhees points out the danger of thinking of instinctive reactions as the foundations of language. The reactions are primitive, Rhees argues, in relation to primitive means of communication, ie, in relation to people who already speak a language. What we need to emphasise is the way in which primitive reactions are taken up in our ways of thinking and forms of life. That cannot be reduced to something ‘instinctive’.

There is a general impression among Kant scholars that he has no robust theory of work. Most of his references to the topic appear in his historical and anthropological writings, where he tells us that work is burdensome, and valuable only for the sake of whatever we produce. In this paper, I argue that Kant has an under-explored theory of work in the third Critique. This theory bears little resemblance to his depiction of work in the historical and anthropological writings. (...) The third Critique will depict work as self-expressive, creative, and free, features Kant will go on to associate with art. Kant’s contention is that when work resembles art, it is both agreeable and something we enjoy for its own sake. However, when work fails to resemble art — when it is, in Kant’s words, natural, scientific, and mercenary — it is both disagreeable and constrained, and begins to sound like his description of work from the historical and anthropological writings. Kant’s theory of work in the third Critique has a number of important implications. The first is that it provides a new foundation for a contemporary philosophy of work that places freedom and creativity at the center of the labor process. My analysis also engages a part of Kant scholarship that has, until recently, been largely neglected. It is only in the last decade that the English-language Kant literature has taken up the question of how to make sense of Kant’s remarks about work. However the focus is rarely on Kant’s aesthetic theory of work, but rather on the place of work in his moral and political philosophy. I discuss the implications of Kant’s third Critique theory of work for these other debates, as well as for our understanding of the third Critique as a whole. (shrink)