What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

This paper explores two non-standard supermajority rules in the context of judgment aggregation over multiple logically connected issues. These rules set the supermajority threshold in a local, context sensitive way—partly as a function of the input profile of opinions. To motivate the interest of these rules, I prove two results. First, I characterize each rule in terms of a condition I call ‘Block Preservation’. Block preservation says that if a majority of group members accept a judgment set, then so should (...) the group. Second, I show that one of these rules is, in a precise sense, a judgment aggregation analogue of a rule for connecting qualitative and quantitative belief that has been recently defended by Hannes Leitgeb. The structural analogy is due to the fact that Leitgeb sets thresholds for qualitative beliefs in a local, context sensitive way—partly as a function of the given credence function. (shrink)

Judgment aggregation is naturally applied to the modeling of collective attitudes. In the individual case, we represent agents as having not just beliefs, but also as supporting them with reasons. Can the Judgment Aggregation help model a concept of collective reason? I argue that the resources of the standard judgment aggregation framework are insufficiently general. I develop a generalization of the framework that improves along this dimension. In the new framework, new aggregation rules become available, as well as a natural (...) account of collective reasons. (shrink)

Though the social world is real and objective, the way that social facts arise out of other facts is in an important way shaped by human thought, talk and behaviour. Building on recent work in social ontology, I describe a mechanism whereby this distinctive malleability of social facts, combined with the possibility of basic human error, makes it possible for a consistent physical reality to ground an inconsistent social reality. I explore various ways of resisting the prima facie case for (...) social inconsistency. I conclude, however, that the prima facie case survives scrutiny, and draw out some of the ramifications. (shrink)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

“Divine hiddenness”, as the phrase suggests, refers, most fundamentally, to the hiddenness of God, i.e., the alleged fact that God is hidden, absent, silent. In religious literature, there is a long history of expressions of annoyance, anxiety, and despair over divine hiddenness, so understood. For example, ancient Hebrew texts lament God’s failure to show up in experience or to show proper regard for God’s people or some particular person, and two Christian Gospels portray Jesus, in his cry of dereliction on (...) the cross, as experiencing abandonment by God, whom he regarded as “Abba, Father”, an experience shared by many mystics, saints, and ordinary folk of all theistic traditions, described at its worst as “the dark night of the soul”. Understood in this way, divine hiddenness poses an existential problem for those who have such experiences. -/- However, “divine hiddenness” refers to something else in recent philosophical literature, especially since the publication of J.L. Schellenberg’s landmark book, Divine Hiddenness and Human Reason (1993). In this context, it refers to alleged facts about the absence of belief of God, on the basis of which one might think there is no God. For example, Schellenberg argues that, since there are nonbelievers who are capable of a personal relationship with God and who do not resist it, there is no perfectly loving God, while Stephen Maitzen argues that naturalism better explains the “demographics” of nonbelief than theism and Jason Marsh argues that naturalism better explains “natural nonbelief” than theism. Understood in this way, divine hiddenness constitutes putative evidence for atheism. -/- Although some of the recent philosophical literature addresses the problem understood in the first way (e.g., DeWeese-Boyd 2016; Garcia 2002), this entry focuses on divine hiddenness understood in the second way. The first section discusses the relationships between nonbelief and another source of alleged evidence for atheism: evil. The second section states and defends the argument from nonresistant nonbelief. The third section sketches attempts to explain nonresistant nonbelief from a theistic perspective. The fourth section states other responses to the argument from nonresistant nonbelief. The fifth section discusses the argument from the demographics of nonbelief and the sixth section discusses the argument from natural nonbelief. (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (shrink)

Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to have (...) deliberated more versus less effectively. They are not merely a byproduct of increased substantive agreement. Our results both refine and support the idea that deliberation, by increasing proximity to single-peakedness, provides an escape from the problem of majority cycling. (shrink)