Luc Bovens

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence.

Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses, whereas the witnesses in Olsson's model are not independent in the standard sense. We argue that there is much more than, in Olsson's words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen's characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decision-making under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson's argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson's model is applicable. 1 Claim (C) examined for Olsson's characterization of the relationship between the witnesses 2 Claim (C) examined for two or more independent witnesses 3 Robustness and multiple measures of corroboration 4 Discussion.

If we receive information from multiple independent and partially reliable information sources, then whether we are justified to believe these information items is affected by how reliable the sources are, by how well the information coheres with our background beliefs and by how internally coherent the information is. We consider the following question. Is coherence a separable determinant of our degree of belief, i.e. is it the case that the more coherent the new information is, the more justified we are in believing the new information, ceteris paribus? We show that if we consider sets of information items of any size (Holism), and if we assume that there exists a coherence Ordering over such sets and that coherence is a function of the probability distribution over the propositions in such sets (Probabilism), then Separability fails to hold.

The novelty in Adam Burgess’ paper is that he assesses nudge policies in the context of the shift in the UK government’s approach to risk from the nannying policies of Labour to the nudge policies of the Conservatives. There is a wealth of ideas in this paper. I find it useful to disentangle some of these ideas focusing on the following two questions: 1. In what respects do Labour’s nannying policies and the Conservatives’ nudge policies differ? 2. What is problematic about Labour’s nannying and the Conservatives’ nudge policies? Subsequently I will reflect on how a particular strand of research in the social sciences can be made relevant to designing a more responsible way of dealing with societal risk and show how this approach can evade some of Burgess’ concerns.

There are two curious features about the backward induction argument (BIA) to the effect that repeated non-cooperation is the rational solution to the finite iterated prisoner’s dilemma (FIPD). First, however compelling the argument may seem, one remains hesitant either to recommend this solu- tion to players who are about to engage in cooperation or to explain cooperation as a deviation from rational play in real-life FIPD’s. Second, there seems to be a similarity between the BIA for the FIPD and the surprise exam paradox (SEP) and one cannot help but wonder whether the former is indeed no more than an instance of the latter. I argue that there is an important difference between the BIA for the FIPD and the SEP, but that a comparison to the SEP can help us understand why the conclusion of the BIA for the FIPD strikes us as a counterintuitive solution to real-life FIPD’s.

In decision-theory, the notion of regret enters into the minimax decision-rule and has a determinate usage in this context. However, there are many alternative ways of conceiving of regret. The chapter constructs the einmalist- nicht-keinmal ('once is not never') game, in which a single sampling radically changes the expected value of the game in a way that is quite counterintuitive, as the basis for studying regret after a loss following the choice of an uncertain action. Crucially, the very loss affects the posterior expectation of the game and the posterior credence about the objective chances of a win. Our taxonomy of regret contains regret over the action chosen and regret over the outcome obtained as its main categories, and is mirrored by a taxonomy of joy after a win following the choice of an uncertain action, and is used to critique of Krähmer and Stone's analysis of risk aversion for uncertain actions.

It is important in its own right to determine what conception of mutual disinterest Rawls has in mind at the various junctions in the text. Furthermore, disambiguating this notion counters a common objection that there is no reason to accept principles of justice that are chosen by rational egoists. The persons in Rawls' OP are not rational egoists. Rather, in identifying with the token persons in society they make the actual interests of the token persons into their ends and they know that they are choosing principles of justice for a society in which moderate selfishness reigns. But this is very remote from stipulating a selfish disposition for the persons in the OP. Hence, the objection is contingent on a natural misreading of Rawls' notion of mutual disinterest and can be readily dispelled by disambiguating this notion into a motivational and an epistemic constraint on the OP.

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty.

The coherentist theory of justification provides a response to the sceptical challenge: even though the independent processes by which we gather information about the world may be of dubious quality, the internal coherence of the information provides the justification for our empirical beliefs. This central canon of the coherence theory of justification is tested within the framework of Bayesian networks, which is a theory of probabilistic reasoning in artificial intelligence. We interpret the independence of the information gathering processes (IGPs) in terms of conditional independences, construct a minimal sufficient condition for a coherence ranking of information sets and assess whether the confidence boost that results from receiving information through independent IGPs is indeed a positive function of the coherence of the information set. There are multiple interpretations of what constitute IGPs of dubious quality. Do we know our IGPs to be no better than randomization processes? Or, do we know them to be better than randomization processes but not quite fully reliable, and if so, what is the nature of this lack of full reliability? Or, do we not know whether they are fully reliable or not? Within the latter interpretation, does learning something about the quality of some IGPs teach us anything about the quality of the other IGPs? The Bayesian-network models demonstrate that the success of the coherentist canon is contingent on what interpretation one endorses of the claim that our IGPs are of dubious quality.

Consider the following two seemingly unrelated questions. First, why does Rousseau (1993 [1762]) believe that the formation of factions or partial associations is not conducive to the general will in Du Contrat Social, II, 3? Second, why do federal assemblies typically strive for some form of degressive proportionality, i.e. a balance between equal and proportional representation, for the countries in the federation? We will show that there is a surprising connection between these questions. We turn to our first question. It is often thought that Rousseau’s opposition to factions can be interpreted in reference to the Condorcet Jury Theorem. The Condorcet Jury Theorem states that if voters are more likely to be right on some issue than not and cast their votes independently, then the chance that the majority is correct converges to one as the number of voters goes to infinity. This interpretation is tempting, but it is inconsistent with some crucial textual evidence. We turn to our second question. Consider a federation of countries with a decision-making assembly in which each country casts a block vote. On equal representation, the vote of each country has the same weight. On proportional representation, the weights of the votes are proportional to the countries’ population sizes. In between these extremes, we can let the weights increase as a function of population sizes, but smaller countries receive greater weights and larger countries receive lesser weights than proportionality would warrant. Such weightings are called degressively proportional weightings. How can degressive proportionality be justified? And does this justification provide us any guidance as to how these weights should be set? A correct understanding of Rousseau’s misgivings about the formation of factions will hold the key to these questions.

We consider a special set of risky prospects in which the outcomes are either life or death. There are various alternatives to the utilitarian objective of minimizing the expected loss of lives in such prospects. We start off with the two-person case with independent risks and construct taxonomies of ex ante and ex post evaluations for such prospects. We examine the relationship between the ex ante and the ex post in this restrictive framework: There are more possibilities to respect ex ante and ex post objectives simultaneously than in the general framework, i.e. without the restriction to binary utilities. We extend our results to n persons and to dependent risks. We study optimal strategies for allocating risk reductions given different objectives. We place our results against the backdrop of various pro-poorly off value functions for the evaluation of risky prospects.

There are two seemingly unrelated paradoxes of democracy. The older one is the doctrinal paradox or the discursive dilemma. or a comprehensive bibliography, see List 1995. The younger one is the mixed motivation problem introduced by Jonathan Wolff (1994) in this journal. In the mixed motivation problem, we have voters with mixed Benthamite and Rousseauian motivations who reach a majority on an issue that is neither in the self-interest of a majority of the voters, nor considered to be conducive to the common good by a majority of the voters. What has gone unnoticed so far is that both of these paradoxes share a common structure.