[Philip Percival] I aim to illuminate foundational epistemological issues by reflecting on 'epistemic consequentialism'-the epistemic analogue of ethical consequentialism. Epistemic consequentialism employs a concept of cognitive value playing a role in epistemic norms governing belief-like states that is analogous to the role goodness plays in act-governing moral norms. A distinction between 'direct' and 'indirect' versions of epistemic consequentialism is held to be as important as the familiar ethical distinction on which it is based. These versions are illustrated, respectively, by cognitive (...) decision-theory and reliabilism. Cognitive decision-theory is defended, and various conceptual issues concerning it explored. A simple dilemma suggests that epistemic consequentialism has radical consequences. /// [Robert Stalnaker] After reviewing the general ideas of the consequentialist framework, I take a critical look at two of the epistemic consequentialist projects that Philip Percival considers in his paper: the first assumes that there is a notion of acceptance that contrasts with belief and that can be evaluated by its expected epistemic utility. The second uses epis utility to evaluate beliefs and partial beliefs themselves, as well as actions, such as gathering information in the course of an inquiry. I express scepticism about the notion of acceptance required for the first project, and argue that the second kind of project can be fruitful only with a richer notion of epistemic utility than has yet been developed. (shrink)

This paper develops a distinction between "substantive agreement" and "meta-agreement" and explores the significance of this distinction for democracy and social choice.

Consider the hypothesis H that a defendant is guilty, and the evidence E that a majority of h out of n independent jurors have voted for H and a minority of k:=n-h against H. How likely is the majority verdict to be correct? By a formula of Condorcet, the probability that H is true given E depends only on each juror's competence and on the absolute margin between the majority and the minority h-k, but neither on the number n, nor (...) on the proportion h/n. This paper reassesses that result and explores its implications. First, using the classical Condorcet jury model, I derive a more general version of Condorcet's formula, confirming the significance of the absolute margin, but showing that the probability that H is true given E depends also on an additional parameter: the prior probability that H is true. Second, I show that a related result holds when we consider not the degree of belief we attach to H given E, but the degree of support E gives to H. Third, I address the implications for the definition of special majority voting, a procedure used to capture the asymmetry between false positive and false negative decisions. I argue that the standard definition of special majority voting in terms of a required proportion of the jury is epistemically questionable, and that the classical Condorcet jury model leads to an alternative definition in terms of a required absolute margin between the majority and the minority. Finally, I show that the results on the significance of the absolute margin can be resisted if the so-called assumption of symmetrical juror competence is relaxed. (shrink)

In this paper, I introduce the emerging theory of judgment aggregation as a framework for studying institutional design in social epistemology. When a group or collective organization is given an epistemic task, its performance may depend on its ‘aggregation procedure’, i.e. its mechanism for aggregating the group members’ individual beliefs or judgments into corresponding collective beliefs or judgments endorsed by the group as a whole. I argue that a group’s aggregation procedure plays an important role in determining whether the group (...) can meet two challenges: the ‘rationality challenge’ and the ‘knowledge challenge’. The rationality challenge arises when a group is required to endorse consistent beliefs or judgments; the knowledge challenge arises when the group’s beliefs or judgments are required to track certain truths. My discussion seeks to identify those properties of an aggregation procedure that affect a group’s success at meeting each of the two challenges. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem that that (...) difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by environmental (...) factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a (...) shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

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. (shrink)