It is one thing to hold that merely statistical evidence is _sometimes_ insufficient for rational belief, as in typical lottery and profiling cases. It is another thing to hold that merely statistical evidence is _always_ insufficient for rational belief. Indeed, there are cases where statistical evidence plainly does justify belief. This project develops a dispositional account of the normativity of statistical evidence, where the dispositions that ground justifying statistical (...) class='Hi'>evidence are connected to the goals (= proper function) of objects. There are strong intuitive motivations for doing this. For we can turn almost any case of _non-justifying_ merely statistical evidence into a case of _justifying_ merely statistical evidence by adding information about the dispositions and goals of the objects involved. The resulting view not only helps us understand when and why merely statistical evidence is normatively significant, but it also helps us understand how statistical evidence relates to more standard forms of evidence (perceptual, testimonial). The emerging view also has surprising applications, as it imposes limitations on the epistemic value of fine-tuning arguments for theism as well as undermines a standard class of case-based arguments for moral encroachment. (shrink)

The relation of normic support offers a novel solution to the proof paradox: a paradox in evidence law arising from legal cases involving merely statistical evidence (Smith 2018). Central to the normic support solution has been the thesis that merely statistical evidence cannot confer normic support. However, it has been observed that there are exceptions to this: there exist cases where merely statistical evidence can give rise to normic support (Blome-Tillmann (...) 2020). If correct, this fact seems to undermine the normic support solution to the proof paradox. This paper explores a resolution: normic support can resolve the proof paradox even though merely statistical evidence sometimes gives rise to normic support. The key to understanding this resolution lies with a source of evidential support that arises out of bodies of evidence that involve *character evidence* (Colyvan, et al. 2001). It turns out that character evidence can provide normic support when it is grounded in our knowledge of a certain kind of disposition individuals can have: *goal-directed dispositions*. The upshot is the recovery of the normic support solution to the puzzle of whether statistical evidence can meet legal standards of proof. (shrink)

The lottery problem is the problem of explaining why mere reflection on the long odds that one will lose the lottery does not yield knowledge that one will lose. More generally, it is the problem of explaining why true beliefs merely formed on the basis of statistical evidence do not amount to knowledge. Some have thought that the lottery problem can be solved by appeal to a violation of the safety principle for knowledge, i.e., the principle that (...) if S knows that p, not easily would S have believed that p without p being the case. Against the standard safety‐based solution, I argue that understanding safe belief as belief that directly covaries with the truth of what is believed in a suitably defined set of possible worlds forces safety theorists to make a series of theoretical choices that ultimately prevent a satisfactory solution to the problem. In this way, I analyze several safety principles that result from such choices—the paper thus gives valuable insights into the nature of safety—and explain why none solves the lottery problem, including their inability to explain away Gettierized lottery cases. On a more positive note, I show that there is a viable solution in terms of safety if we get rid of the unquestioned assumption that safe beliefs directly track the truth. The alternative is a conception of safe belief according to which what safe beliefs directly track is the appropriateness of the circumstances and, indirectly, the truth. The resulting safety principle, I argue, explains why mere statistical evidence is not a safe source of knowledge. (shrink)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases (...) suggests standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

In this paper, we put forth an analysis of sensitivity which aims to discern individual from merely statistical evidence. We argue that sensitivity is not to be understood as a factive concept, but as a purely epistemic one. Our resulting analysis of epistemic sensitivity gives rise to an account of legal proof on which a defendant is only found liable based on epistemically sensitive evidence.

There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the (...) idea of statistical frequency. The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

The replication crisis has prompted many to call for statistical reform within the psychological sciences. Here we examine issues within Frequentist statistics that may have led to the replication crisis, and we examine the alternative—Bayesian statistics—that many have suggested as a replacement. The Frequentist approach and the Bayesian approach offer radically different perspectives on evidence and inference with the Frequentist approach prioritising error control and the Bayesian approach offering a formal method for quantifying the relative strength of (...) class='Hi'>evidence for hypotheses. We suggest that rather than mere statistical reform, what is needed is a better understanding of the different modes of statistical inference and a better understanding of how statistical inference relates to scientific inference. (shrink)

Statistical fairness criteria are widely used for diagnosing and ameliorating algorithmic bias. However, these fairness criteria are controversial as their use raises several difficult questions. I argue that the major problems for statistical algorithmic fairness criteria stem from an incorrect understanding of their nature. These criteria are primarily used for two purposes: first, evaluating AI systems for bias, and second constraining machine learning optimization problems in order to ameliorate such bias. The first purpose typically involves treating each criterion (...) as a necessary condition for fairness. The second use involves treating criteria as sufficient conditions for fairness. Since the criteria are used for both roles, some researchers have treated them as both necessary and sufficient conditions, i.e., as definitions of algorithmic fairness. However, serious problems have been raised for the use of these fairness criteria. Under ordinary circumstances, it is impossible to satisfy multiple criteria at the same time. Moreover, there are counterexamples to both the sufficiency and necessity for fairness of each criterion. I argue that we should instead understand fairness criteria as merely providing evidence of fairness. In other words, satisfaction (or violation) of these criteria should be understood as potential evidence of fairness (or bias). Whether a criterion counts as evidence in a particular case will depend on stakeholders' background knowledge and the specific features of the system's task. This evidence account of fairness conditions provides guidance for recognizing both the appropriate uses and the limitations of fairness criteria. (shrink)

Cancer research is experiencing ‘paradigm instability’, since there are two rival theories of carcinogenesis which confront themselves, namely the somatic mutation theory and the tissue organization field theory. Despite this theoretical uncertainty, a huge quantity of data is available thanks to the improvement of genome sequencing techniques. Some authors think that the development of new statistical tools will be able to overcome the lack of a shared theoretical perspective on cancer by amalgamating as many data as possible. We think (...) instead that a deeper understanding of cancer can be achieved by means of more theoretical work, rather than by merely accumulating more data. To support our thesis, we introduce the analytic view of theory development, which rests on the concept of plausibility, and make clear in what sense plausibility and probability are distinct concepts. Then, the concept of plausibility is used to point out the ineliminable role played by the epistemic subject in the development of statistical tools and in the process of theory assessment. We then move to address a central issue in cancer research, namely the relevance of computational tools developed by bioinformaticists to detect driver mutations in the debate between the two main rival theories of carcinogenesis. Finally, we briefly extend our considerations on the role that plausibility plays in evidence amalgamation from cancer research to the more general issue of the divergences between frequentists and Bayesians in the philosophy of medicine and statistics. We argue that taking into account plausibility-based considerations can lead to clarify some epistemological shortcomings that afflict both these perspectives. (shrink)

Traditional philosophical discussions of knowledge have focused on the epistemic status of full beliefs. In this book, Moss argues that in addition to full beliefs, credences can constitute knowledge. For instance, your .4 credence that it is raining outside can constitute knowledge, in just the same way that your full beliefs can. In addition, you can know that it might be raining, and that if it is raining then it is probably cloudy, where this knowledge is not knowledge of propositions, (...) but of probabilistic contents. -/- The notion of probabilistic content introduced in this book plays a central role not only in epistemology, but in the philosophy of mind and language as well. Just as tradition holds that you believe and assert propositions, you can believe and assert probabilistic contents. Accepting that we can believe, assert, and know probabilistic contents has significant consequences for many philosophical debates, including debates about the relationship between full belief and credence, the semantics of epistemic modals and conditionals, the contents of perceptual experience, peer disagreement, pragmatic encroachment, perceptual dogmatism, and transformative experience. In addition, accepting probabilistic knowledge can help us discredit negative evaluations of female speech, explain why merely statistical evidence is insufficient for legal proof, and identify epistemic norms violated by acts of racial profiling. Hence the central theses of this book not only help us better understand the nature of our own mental states, but also help us better understand the nature of our responsibilities to each other. (shrink)

In a backlash against the prevalence of statistical methods, recently social scientists have focused more on studying causal mechanisms. They increasingly rely on a technique called process-tracing, which involves contrasting the observable implications of several alternative mechanisms. Problematically, process-tracers do not commit to a fundamental notion of causation, and therefore arguably they cannot discern between mere correlation between the links of their purported mechanisms and genuine causation. In this paper, I argue that committing to Woodward's interventionist notion of causation (...) would solve this problem: process-tracers should take into account evidence for possible interventions on the mechanisms they study. (shrink)

This article argues that legal proof should be tantamount to justified belief of guilt. A defendant should be found guilty just in case it is justified to believe that the defendant is guilty. My notion of justified belief implies a threshold view on which justified belief requires high credence, but mere statistical evidence does not give rise to justified belief.

In this paper, I provide an argument for rejecting Sarah Moss's recent account of legal proof. Moss's account is attractive in a number of ways. It provides a new version of a knowledge-based theory of legal proof that elegantly resolves a number of puzzles about mere statistical evidence in the law. Moreover, the account promises to have attractive implications for social and moral philosophy, in particular about the impermissibility of racial profiling and other harmful kinds of statistical (...) generalisation. In this paper, I show that Moss's account of legal proof crucially depends on a moral norm called the rule of consideration. I argue that we have a number of reasons to be sceptical of this rule. Once we reject the rule, it is not clear that Moss's account of legal proof is either plausible or attractive. (shrink)

This entry introduces the Lockean Thesis and sketches the ways in which the lottery paradox, the preface paradox, and the problem of merely statistical evidence can be used to put pressure on the Lockean Thesis.

Michael Huemer argues, on statistical grounds, that ``existence is evidence for immortality". On reasoning derived from the anthropic principle, however, mere existence cannot be evidence against any non-indexical, ``eternal'' hypothesis that predicts observers. This note attempts to advertise the much-flouted anthropic principle's virtues and workings in a new way, namely by calling attention to the fact that it is the primary intension of one's indexically-described evidence that best characterizes one's epistemic position.

Philosophical debates over statistical evidence have long been framed and dominated by L. Jonathan Cohen's Paradox of the Gatecrasher and a related hypothetical example commonly called Prison Yard. These examples, however, raise an issue not discussed in the large and growing literature on statistical evidence – the question of what statistical evidence is supposed to be evidence of. In actual practice, the legal system does not start with a defendant and then attempt to (...) determine if that defendant has committed some unspecified or under-specified act, as these examples appear to suppose. Rather, both criminal and civil litigation start with a sufficiently specified act and then attempt to determine if the defendant has committed it. And when we start with a more fully specified act, the statistics look very different, and these prominent examples no longer present the paradox they are claimed to support. Examining the issue of specification, however, does more than simply undercut the prominent examples in a long and extensive literature. The examination also raises normative issues challenging the legal system's traditional reluctance to base liability on the conjunction of probabilities. (shrink)

Moral behaviour, based on social norms, is commonly regarded as a hallmark of humans. Hitherto, humans are perceived to be the only species possessing social norms and to engage in moral behaviour. There is anecdotal evidence suggesting their presence in chimpanzees, but systematic studies are lacking. Here, we examine the evolution of human social norms and their underlying psychological mechanisms. For this, we distinguish between conventions, cultural social norms and universal social norms. We aim at exploring whether chimpanzees possess (...) evolutionary precursors of universal social norms seen in humans. Chimpanzees exhibit important preconditions for their presence and enforcement: tolerant societies, well-developed social-cognitive skills and empathetic competence. Here, we develop a theoretical framework for recognizing different functional levels of social norms and distinguish them from mere statistical behavioural regularities. Quasi social norms are found where animals behave functionally moral without having moral emotions. In proto social norms, moral emotions might be present but cannot be collectivized due to the absence of a uniquely human psychological trait, i.e. shared intentionality. Human social norms, whether they are universal or cultural, involve moral emotions and are collectivized. We will discuss behaviours in chimpanzees that represent potential evolutionary precursors of human universal social norms, with special focus on social interactions involving infants. We argue that chimpanzee infants occupy a special status within their communities and propose that tolerance towards them might represent a proto social norm. Finally, we discuss possible ways to test this theoretical framework. (shrink)

The law views with suspicion statistical evidence, even evidence that is probabilistically on a par with direct, individual evidence that the law is in no way suspicious of. But it has proved remarkably hard to either justify this suspicion, or to debunk it. In this paper, we connect the discussion of statistical evidence to broader epistemological discussions of similar phenomena. We highlight Sensitivity – the requirement that a belief be counterfactually sensitive to the truth (...) in a specific way – as a way of epistemically explaining the legal suspicion towards statistical evidence. Still, we do not think of this as a satisfactory vindication of the reluctance to rely on statistical evidence. Knowledge – and Sensitivity, and indeed epistemology in general – are of little, if any, legal value. Instead, we tell an incentive-based story vindicating the suspicion towards statistical evidence. We conclude by showing that the epistemological story and the incentive-based story are closely and interestingly related, and by offering initial thoughts about the role of statistical evidence in morality. (shrink)

Moral behaviour, based on social norms, is commonly regarded as a hallmark of humans. Hitherto, humans are perceived to be the only species possessing social norms and to engage in moral behaviour. There is anecdotal evidence suggesting their presence in chimpanzees, but systematic studies are lacking. Here, we examine the evolution of human social norms and their underlying psychological mechanisms. For this, we distinguish between conventions, cultural social norms and universal social norms. We aim at exploring whether chimpanzees possess (...) evolutionary precursors of universal social norms seen in humans. Chimpanzees exhibit important preconditions for their presence and enforcement: tolerant societies, well-developed social-cognitive skills and empathetic competence. Here, we develop a theoretical framework for recognizing different functional levels of social norms and distinguish them from mere statistical behavioural regularities. Quasi social norms are found where animals behave functionally moral without having moral emotions. In proto social norms, moral emotions might be present but cannot be collectivized due to the absence of a uniquely human psychological trait, i.e. shared intentionality. Human social norms, whether they are universal or cultural, involve moral emotions and are collectivized. We will discuss behaviours in chimpanzees that represent potential evolutionary precursors of human universal social norms, with special focus on social interactions involving infants. We argue that chimpanzee infants occupy a special status within their communities and propose that tolerance towards them might represent a proto social norm. Finally, we discuss possible ways to test this theoretical framework. (shrink)

Statistical evidence is pervasive in medicine. In this chapter we will focus on the reliability of randomized clinical trials (RCTs) conducted to test the safety and efficacy of medical treatments. RCTs are scientific experiments and, as such, we expect them to be replicable: if we repeat the same experiment time and again, we should obtain the same outcome (Norton 2015). The statistical design of the test should guarantee that the observed outcome is not a random event, but (...) rather a real effect of the treatments administered. However, for more than a decade now, we have been discussing a replicability crisis across different experimental disciplines including medicine: the outcomes of trials published in very prestigious journals often disappear when the experiment is repeated (see, e.g., Lehrer 2010, Begley and Ellis 2012, Horton 2015). -/- There are different accounts of the reason for this replicability crisis, ranging from scientific fraud to lack of institutional incentives to double-check someone else’s results. In this chapter we will use the replicability crisis as a thread to introduce some central issues in the design of scientific experiments in medicine. First, in section 1, we will see how replicability and statistical significance are connected: we can only make sense of the p-value of a trial outcome within a series of replications of the test. But in order to conduct these replications properly, we need to agree on the proper design of the experiment we are going to repeat. In particular, we need to prevent the preferences of the experimenters from biasing the outcome of the experiment. If there is such a bias, when the experiment is replicated by a third party, the observed outcome will vanish. In section 2, we will argue that trialists need to agree on the debiasing procedures and the statistical quality controls that feature in the trial protocol, if they want the outcome to be replicable. In section 3, we will make two complementary points. On the one hand, replicability per se is not everything: we need trial outcomes that are not only statistically significant but also clinically relevant. On the other hand, trials are not everything: the experts analyzing the evidence can improve the reliability of statistical evidence, although they sometimes fail; we need to further study how they make their decisions. In section 4, we will use a controversy about the overprescription of statins to show how non-replicable effects are obtained in trials and how experts may fail at detecting such flaws, if the commercial interests are big enough. (shrink)

Can the evidence provided by software systems meet the standard of proof for civil or criminal cases, and is it individualized evidence? Or, to the contrary, do software systems exclusively provide bare statistical evidence? In this paper, we argue that there are cases in which evidence in the form of probabilities computed by software systems is not bare statistical evidence, and is thus able to meet the standard of proof. First, based on the (...) case of State v. Loomis, we investigate recidivism predictions provided by software systems used in the courtroom. Here, we raise problems for software systems that provide predictions that are based on bare statistical evidence. Second, by examining the case of People v. Chubbs, we argue that the statistical evidence provided by software systems in cold hit DNA cases may in some cases suffice for individualized evidence, on a view on which individualized evidence is evidence that normically supports the relevant proposition (Smith, in Mind 127:1193–1218, 2018). (shrink)

Recently, the practice of deciding legal cases on purely statistical evidence has been widely criticised. Many feel uncomfortable with finding someone guilty on the basis of bare probabilities, even though the chance of error might be stupendously small. This is an important issue: with the rise of DNA profiling, courts are increasingly faced with purely statistical evidence. A prominent line of argument—endorsed by Blome-Tillmann 2017; Smith 2018; and Littlejohn 2018—rejects the use of such evidence by (...) appealing to epistemic norms that apply to individual inquirers. My aim in this paper is to rehabilitate purely statistical evidence by arguing that, given the broader aims of legal systems, there are scenarios in which relying on such evidence is appropriate. Along the way I explain why popular arguments appealing to individual epistemic norms to reject legal reliance on bare statistics are unconvincing, by showing that courts and individuals face different epistemic predicaments (in short, individuals can hedge when confronted with statistical evidence, whilst legal tribunals cannot). I also correct some misconceptions about legal practice that have found their way into the recent literature. (shrink)

The use of algorithms to support prediction-based decision-making is becoming commonplace in a range of domains including health, criminal justice, education, social services, lending, and hiring. An assumption governing such decisions is that there is a property Y such that individual a should be allocated resource R by decision-maker D if a is Y. When there is uncertainty about whether a is Y, algorithms may provide valuable decision support by accurately predicting whether a is Y on the basis of known (...) features of a. Based on recent work on statistical evidence in epistemology this article presents an argument against relying exclusively on algorithmic predictions to allocate resources when they provide purely statistical evidence that a is Y. The article then responds to the objection that any evidence that will increase the proportion of correct decisions should be accepted as the basis for allocations regardless of its epistemic deficiency. Finally, some important practical aspects of the conclusion are considered. (shrink)

Martin Smith has recently proposed, in this journal, a novel and intriguing approach to puzzles and paradoxes in evidence law arising from the evidential standard of the Preponderance of the Evidence. According to Smith, the relation of normic support provides us with an elegant solution to those puzzles. In this paper I develop a counterexample to Smith’s approach and argue that normic support can neither account for our reluctance to base affirmative verdicts on bare statistical evidence (...) nor resolve the pertinent paradoxes. Normic support is, as a consequence, not a successful epistemic anti-luck condition. (shrink)

Courts and jurors sometimes refuse to assign liability to defendants on the basis of statistics alone, despite their apparent reliability. I argue that this refusal is best understood as a recognition of defendants’ right to security. Understood as a robust good in Philip Pettit’s sense, security requires that someone risking harm to others’ protected interests adopt a disposition of concern that controls against wrongfully harming them. Since trials risk harm, the state must adopt such a disposition. Statistics leave open the (...) possibility of innocence and so wrongful harm in a way that the state cannot ignore; if it does use such statistics, it makes defendants wrongfully insecure. This explanation of the problem of bare statistical evidence is especially apt because security grounds the right to a fair trial and judicial procedural rights more generally. (shrink)

Many philosophers have pointed out that statistical evidence, or at least some forms of it, lack desirable epistemic or non-epistemic properties, and that this should make us wary of litigations in which the case against the defendant rests in whole or in part on statistical evidence. Others have responded that such broad reservations about statistical evidence are overly restrictive since appellate courts have expressed nuanced views about statistical evidence. In an effort to (...) clarify and reconcile, I put forward an interpretive analysis of why statistical evidence should raise concerns in some cases but not others. I argue that when there is a mismatch between the specificity of the evidence and the expected specificity of the accusation, statistical evidence—as any other kind of evidence—should be considered insufficient to sustain a conviction. I rely on different stylized court cases to illustrate the explanatory power of this analysis. (shrink)

Abstract. Suppose that the word of an eyewitness makes it 80% probable that A committed a crime, and that B is drawn from a population in which the incidence rate of that crime is 80%. Many philosophers and legal theorists have held that if this is our only evidence against those parties then (i) we may be justified in finding against A but not against B; but (ii) that doing so incurs a loss in the accuracy of our findings. (...) This paper argues against (ii). It argues that accuracy considerations can motivate taking different attitudes towards individualized and statistical evidence even across cases where they generate the same probability that the defendant is guilty. (shrink)

The rapidly increasing role of automation throughout the economy, culture and our personal lives has generated a large literature on the risks of algorithmic decision-making, particularly in high-stakes legal settings. Algorithmic tools are charged with bias, shrouded in secrecy, and frequently difficult to interpret. However, these criticisms have tended to focus on particular implementations, specific predictive techniques, and the idiosyncrasies of the American legal-regulatory regime. They do not address the more fundamental unease about the prospect that we might one day (...) replace judges with algorithms, no matter how fair, transparent, and intelligible they become. The aim of this paper is to propose an account of the source of that unease, and to evaluate its plausibility. I trace foundational unease with algorithmic decision-making in the law to the powerful intuition that there is a basic moral and legal difference between showing that something is true of many people just like you and showing that it is true of you. Human judgment attends to the exception; automation insists on blindly applying the rule. I show how this intuitive thought is connected to both epistemological arguments about the value of statistical evidence, as well as to court-centered conceptions of the rule of law. Unease with algorithmic decision-making in the law thus draws on an intuitive principle that underpins a disparate range of views in legal philosophy. This suggests the principle is deeply ingrained. Nonetheless, I argue that the powerful intuition is not as decisive as it may seem, and indeed runs into significant epistemological and normative challenges. At an epistemological level, I show how concerns about statistical evidence's ability to track the truth can be resolved by adopting a probabilistic, rather than modal, conception of truth-tracking. At a normative level, commitment to highly individualized decision-making co-exists with equally ingrained and competing principles, such as consistent application of law. This suggests that the “rule of law” may not identify a discrete set of institutional arrangements, as proponents of a court-centric conception would have it, but rather a more loosely defined set of values that could potentially be operationalized in multiple ways, including through some level of algorithmic adjudication. Although the prospect of replacing judges with algorithms is indeed unsettling, it does not necessarily entail unreasonable verdicts or an attack on the rule of law. (shrink)

Patient preference predictors (PPPs) promise to provide medical professionals with a new solution to the problem of making treatment decisions on behalf of incapacitated patients. I show that the use of PPPs faces a version of a normative problem familiar from legal scholarship: the problem of naked statistical evidence. I sketch two sorts of possible reply, vindicating and debunking, and suggest that our reply to the problem in the one domain ought to mirror our reply in the other. (...) The conclusion is thus conditional: if we think the problem of naked statistical evidence is a serious problem in the legal domain, then we should be concerned about the symmetrical problem for PPPs. (shrink)

Recent attempts to resolve the Paradox of the Gatecrasher rest on a now familiar distinction between individual and bare statistical evidence. This paper investigates two such approaches, the causal approach to individual evidence and a recently influential (and award-winning) modal account that explicates individual evidence in terms of Nozick's notion of sensitivity. This paper offers counterexamples to both approaches, explicates a problem concerning necessary truths for the sensitivity account, and argues that either view is implausibly committed (...) to the impossibility of no-fault wrongful convictions. The paper finally concludes that the distinction between individual and bare statistical evidence cannot be maintained in terms of causation or sensitivity. We have to look elsewhere for a solution of the Paradox of the Gatecrasher. (shrink)

According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to (...) statistical evidence as rational credence. The aim of this paper is twofold. First, we argue that, in addition to playing a decisive role in rationalizing outright belief, non-statistical evidence also plays a preponderant role in rationalizing credence. More precisely, when both types of evidence are present in a context, non-statistical evidence should receive a heavier weight than statistical evidence in determining rational credence. Second, based on this result, we argue that a modified version of the Rational Threshold View can avoid the problem of statistical evidence. We conclude by suggesting a possible explanation of the varying sensitivity to different types of evidence for belief and credence based on the respective aims of these attitudes. (shrink)

Hacking’s Law of Likelihood says – paraphrasing– that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio for H1 over H2 exceeds 1. But Hacking noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I don’t believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, and (...) I sketch the rudiments of a methodology for so doing. (shrink)

In responding to Prof. Allen's paper, I make several general methodological points: about the use of hypothetical cases, about the point of theorizing, and about the role of idealization. Then I make some more specific points about his claims about (and against) previous work on statistical evidence.

Discrimination law is a possible application of the methods of causal modelling. With it, it brings the possibility of direct statistical evidence on counterfactual questions, something that traditional techniques like multiple regression lack. The kinds of evidence that causal modelling can provide, in large part due to its attention to counterfactuals, is very close to the key question that we ask of jurors in discrimination cases. With this new kind of evidence comes new opportunities. We can (...) better proportion punitive damages to the severity of the discrimination that manifests in a hiring process. We can avoid making certain kinds of assumptions regarding the relationship between protected classes and hiring qualifications that other statistical methods demand from statisticians. We can also distribute restitution to individual claimants in a way that is proportionate to how their application was treated in the hiring process. Here we explore where and how causal modelling can be useful in discrimination law and policy. What elements of law provide friction with this mode of gathering statistical evidence, what new possibilities does it reveal, and how does this integrate with prior judgments regarding statistical evidence? (shrink)

Philosophical Issues, Volume 31, Issue 1, Page 128-145, October 2021.

PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1978, Volume Two: Symposia and Invited Papers. (1978), pp. 478-489.

What is it for the verdict of a criminal trial to be just? It is widely agreed that a Guilty verdict is just only if the defendant did the relevant deed, and only if his rights were not violated in the process of apprehending, charging, and convicting him. I argue that more is required: he must be found Guilty because he is guilty, and not solely for other reasons. The conviction must be based on the guilt. I argue that many (...) rules of evidence and procedural rules designed to protect a defendant's rights also encourage fulfillment of this basing condition and that the condition helps to explain how an erroneous conviction involving no misconduct can nevertheless be a moral wrong. I argue that the condition also gives an explanation (among others) of why a naked statistic is insufficient for a just conviction. (shrink)

Epistemologists have posed the following puzzle, known as the proof paradox: Why is it intuitively problematic for juries to convict on the basis of statistical evidence and yet intuitively unproblematic for juries to convict on the basis of far less reliable, non-statistical evidence? To answer this question, theorists have explained the exclusion of statistical evidence by arguing that legal proof requires certain epistemic features. In this paper, I make two contributions to the debate. First, (...) I establish the Criminal Verdict Asymmetry, a previously-unarticulated asymmetry between the epistemic norms of guilty and not guilty verdicts. I argue that the prosecution and defense’s different epistemic burdens influence whether statistical evidence can generate the type of verdict each side pursues. Second, I point out a mistake in how theorists have understood the role of statistical evidence in criminal trials. Though epistemologists have primarily focused on whether statistical evidence can generate specific epistemic features required for convictions, I consider whether statistical evidence can demonstrate a lack of such features. I find that there are epistemic advantages to allowing the defense to introduce statistical evidence which can reveal the prosecution’s failure to prove the defendant’s guilt. (shrink)

A jury needs “proof beyond a reasonable doubt” in order to convict a defendant of a crime. The standard is vexingly difficult to pin down, but some legal epistemologists have given this account: knowledge is the standard of legal proof. On this account, a jury should deliver a guilty verdict just in case they know that the defendant is guilty. In this paper, I’ll argue that legal proof requires more than just knowledge that a defendant is guilty. In cases of (...) “merely predictive evidence,” a jury knows that the defendant is guilty but does not have legal proof. What are they missing? Evidence that is causally downstream from the crime. Legal proof requires a “smoking gun.” The point generalizes outside of the courtroom. A professor needs to read a term paper before assigning a grade, even if she knows the student will produce A + work. You may know that your roommate will forget to water the plants while you are away—she is scatterbrained and always forgets these things—but you can’t blame her until you get back home and see that the plants are wilting. In order to have appropriate reactions or reactive attitudes, we must respond causally to what other people have done. (shrink)

Do privacy rights restrict what is permissible to infer about others based on statistical evidence? This paper replies affirmatively by defending the following symmetry: there is not necessarily a morally relevant difference between directly appropriating people’s private information—say, by using an X-ray device on their private safes—and using predictive technologies to infer the same content, at least in cases where the evidence has a roughly similar probative value. This conclusion is of theoretical interest because a comprehensive justification (...) of the thought that statistical inferences can violate privacy rights is lacking in the current literature. Secondly, the conclusion is of practical interest due to the need for moral assessment of emerging predictive algorithms. (shrink)

Whenever a litigant needs to prove that a certain result was caused in a specific way, what could be more compelling than citing the infinitesimal probability of that result emanating from an alternative natural cause? Contrary to this intuitive position, in the present article, I argue that the contention that a result was due to a certain cause should remain unaffected by statistical evidence of the extremely low probability of an alternative cause. The only scenario in which the (...) low probability of a natural cause would be relevant to the case at hand is if it were contrasted with another piece of statistical evidence: the frequency of the criminal activity among people who are similar to the accused. However, by connecting the use of probabilistic generalisations in legal fact-finding to the issue of free will, I hold that, in Criminal Law, contrasting frequencies in this manner is objectionable—as a matter of principle—regardless of how reliable the statistical analysis is. Consequently, if the low probability of a natural cause is probative only if contrasted with another piece of statistical evidence that is objectionable, then neither piece of evidence should be admitted in criminal trials. (shrink)

Evidence, as viewed through the lens of statistical significance, is not always as it appears! In the investigation of clinical research findings arising from statistical analyses, a fundamental initial step for the emerging fraud detective is to retrieve the source data for cross-examination with the study data. Recognizing that source data are not always forthcoming and that, realistically speaking, the investigator may be uninitiated in fraud detection and investigation, this paper will highlight some key methodological procedures for (...) providing a sounder evidence base for withdrawing from a study on grounds of integrity. The promotion of patient safety is paramount. However, there is a broader rationale for disseminating these ideas. This includes empowering researchers to optimize their personal integrity, make informed choices regarding membership of future research collaborations and successfully voice their concerns to journal editors, particularly where a conflict of interests can render such dialogues particularly difficult. Recommendations will be supported by topical case studies and practical steps involving data exploration, testing of baseline data and application of Benford’s Law. While this paper has a clinical focus, the advice provided is transferrable to a wide range of multidisciplinary research settings outside of Medicine. (shrink)

This article examines Smith’s recent treatment of the problem of statistical evidence and the conception of epistemic justification that he puts forward. Two possible solutions to the problem of statistical evidence that result from his analysis of cases involving a contrast between statistical and individual evidence are considered. The solution resulting from Smith’s conception of epistemic justification is shown to be inferior to the solution calling for an explanationist conception of epistemic justification. As a (...) result, Smith’s analysis of cases illustrating the problem of statistical evidence, given his own standards of theory choice, is shown to support an explanationist conception of epistemic justification as an alternative to the probabilistic conception that he urges us to reject. (shrink)

To whatever extent the use of a behavioral, not an evidential, interpretation of decisions in the Lindley-Savage argument for Bayesian theory undermines its cogency as a criticism of typical standard practice, it also undermines the Neyman-Pearson theory as a support for typical standard practice. This leaves standard practice with far less theoretical support than Bayesian methods. It does nothing to resolve the anomalies and paradoxes of standard methods. (Similar statements apply to the common protestation that the models are not real (...) anyway.) The appropriate interpretation of tests as evidence, if possible at all, is difficult and counterintuitive. Any attempt to support tests as more than rules of thumb is doomed to failure. (shrink)