Judgment Aggregation

Much of our information comes to us indirectly, in the form of conclusions others have drawn from evidence they gathered. When we hear these conclusions, how can we modify our own opinions so as to gain the benefit of their evidence? In this paper we study the method known as geometric pooling. We consider two arguments in its favour, raising several objections to one, and proposing an amendment to the other.

How should your opinion change in response to the opinion of an epistemic peer? We show that the pooling rule known as "upco" is the unique answer satisfying some natural desiderata. If your revised opinion will influence your opinions on other matters by Jeffrey conditionalization, then upco is the only standard pooling rule that ensures the order in which peers are consulted makes no difference. Popular proposals like linear pooling, geometric pooling, and harmonic pooling cannot boast the same. In fact, (...) no alternative to upco can if it possesses four minimal properties which these proposals share. (shrink)

Do the ethical features of an artwork bear on its aesthetic value? This movie endorses misogyny, that song is a civil rights anthem, the clay constituting this statue was extracted with underpaid labor—are facts like these the proper bases for aesthetic evaluation? I argue that this debate has suffered from a false presupposition: that if the answer is “yes” (for at least some such ethical features), such considerations feature as pro tanto contributions to an artwork’s overall aesthetic value, i.e., as (...) merits or flaws which make something have more or less overall aesthetic value. As the case of ethically laden aesthetic evaluation makes clear, however, good aesthetic judgement is irreducibly multi-dimensional, e.g., “the movie has an engaging soundtrack, tasteful camera work, and takes a misogynistically purient perspective on its female lead.” Such a “non-summative” judgement refuses to reduce those various dimensions of aesthetic value to a single aggregate aesthetic evaluation, like “it’s a 6/10” or “it’s a pretty good movie!” I defend both the modest claim that such non-summative evaluations are not mistaken and the extremist claim that summative (i.e., unidimensional) aesthetic evaluation is defective by considering other domains of normative assessment in which summing seems inappropriate, notably including evaluations of people’s character. (shrink)

Suppose a committee, expert panel, or other group is making judgments on some issues, where these may be not just yes/no-questions, such as whether a defendant is guilty, but also variables with many possible values, such as macroeconomic or meteorological variables or travel directions. Furthermore, there may be interconnections between different issues, as in the case of economic or climate variables. How can the group arrive at “intelligent” collective judgments, based on the group members’ individual judgments? We investigate three challenges (...) raised by this judgment-aggregation problem. First, reasonable methods of aggregation (such as defining the collective judgment for each issue as the average or median judgment) can produce inconsistent collective judgments. Secondly, many methods of aggregation are manipulable by strategic voting. Finally, not all methods of aggregation are conducive to tracking the truth on the issues in question. We prove new impossibility or possibility theorems on all three challenges, identifying what it takes to produce collective judgments in a consistent, non-manipulable, and truth-tracking manner and thereby to achieve collective intelligence through aggregation. Overall, the median method, though imperfect, performs reasonably well. We also note the relevance of our analysis for non-human group decisions. (The manuscript has been accepted for publication in Philosophical Transactions of the Royal Society B and is to appear in 2026.). (shrink)

What action-guiding judgments should we rely on in cases of moral uncertainty, when we divide our credence among competing moral views and assign credences between 0 and 1 to propositions such as “action x is better than action y”? We show that the problem of “moral uncertainty resolution” can be viewed as a “belief binarization” problem: how to arrive at all-out (“accept/reject”) judgments on some propositions based on our credences in them. Looking at moral uncertainty through this lens yields a (...) diagnostically useful impossibility result, which identifies a tradeoff between four initially plausible conditions on a moral uncertainty resolution rule. (shrink)

The field of computational social choice brings together principles, techniques, and tools from computer science and social choice theory to create a thriving multidisciplinary field. One of the most well-studied problems in computational social choice focuses on voting rules for selecting the winning candidate in an election. Recent research goes beyond classical voting rules by looking at rules that select multiple winners or drawing on the parallels between machine learning and voting. It is common to encounter voting paradoxes when implementing (...) voting rules in electoral systems. Unfortunately, these paradoxes usually provide little information on the conditions that make them more or less likely to occur. Computer simulations and generative probabilistic models are practical approaches to address this problem. This introductory paper addresses the problem of evaluating voting rules in competitive computer simulations. Multiagent simulations can provide valuable insights into the performances of competing voting rules defined over parametrically generated problems and populations. The outcomes of this work could improve the designs of electoral systems in the absence of theoretical results to support the optimality of a voting method. This line of research could also bridge the gap between axiomatic and experimental analysis of voting systems, leading the way to enhanced explanations and predictions. (shrink)

We give a probabilistic justification of the shape of one of the probability weighting functions used in Prospect Theory. To do so, we use an idea recently introduced by Herzog and Hertwig. Along the way we also suggest a new method for the aggregation of probabilities using statistical distances.

In _Seeing Like a State_, James C. Scott argues that governments act badly when they see the society they govern in distorted and incomplete ways. I argue that this is also a common pitfall of university management. In particular, I scrutinise a particular way of thinking and speaking and deliberating that arises when the part of the organisation over which the manager has control is too large to allow them to think and speak always of the goals, viewpoints, and values (...) of individual members. In response, managers often begin to think and speak and deliberate in terms of groups—for instance, the philosophy department, the HR division, the student body—and ascribes beliefs, goals, and values to them as group agents. But such attitude ascriptions to group agents are badly ambiguous in ways that aren’t resolved by context. This, I argue, leads to bad decision-making. (shrink)

The way we're thinking about generative AI right now is fundamentally individual. We see this not just in how users interact with models but also in how models are built, how they're benchmarked, and how commercial and research strategies using AI are defined. We argue that we should abandon this approach if we're hoping for AI to support groundbreaking innovation and scientific discovery. Drawing on research and formal results in complex systems, organizational behavior, and philosophy of science, we show why (...) we should expect deep intellectual breakthroughs to come from epistemically diverse groups of AI agents working together rather than singular superintelligent agents. Having a diverse team broadens the search for solutions, delays premature consensus, and allows for the pursuit of unconventional approaches. Developing diverse AI teams also addresses AI critics' concerns that current models are constrained by past data and lack the creative insight required for innovation. The upshot, we argue, is that the future of transformative transformer-based AI is fundamentally many, not one. (shrink)

This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers (...) new to the field of judgment aggregation a sense of this rapidly growing research area. (shrink)

In the first half of this paper, I argue that group belief ascriptions are highly ambiguous. What's more, in many cases, neither the available contextual factors nor known pragmatic considerations are sufficient to allow the audience to identify which of the many possible meanings is intended. In the second half, I argue that this ambiguity often has bad consequences when a group belief ascription is heard and taken as testimony. And indeed it has these consequences even when the ascription is (...) true on the speaker's intended interpretation, when the speaker does not intend to mislead and indeed intends to cooperatively inform, and when the audience incorporates the evidence from the testimony as they should. I conclude by arguing that these consequences should lead us to stop using such ascriptions. (shrink)

We often learn the opinions of others without hearing the evidence on which they're based. The orthodox Bayesian response is to treat the reported opinion as evidence itself and update on it by conditionalizing. But sometimes this isn't feasible. In these situations, a simpler way of combining one's existing opinion with opinions reported by others would be useful, especially if it yields the same results as conditionalization. We will show that one method---upco, also known as multiplicative pooling---is specially suited to (...) this role when the opinions you wish to pool concern hypotheses about chances. The result has interesting consequences: it addresses the problem of disagreement between experts; and it sheds light on the social argument for the uniqueness thesis. (shrink)

Many social media platforms enable (nearly) anyone to post (nearly) anything. One clear downside of this permissiveness is that many people appear bad at determining who to trust online. Hacks, quacks, climate change deniers, vaccine skeptics, and election deniers have all gained massive followings in these free markets of ideas, and many of their followers seem to genuinely trust them. At the same time, there are many cases in which people seem to reliably determine who to trust online. Consider, for (...) example, Do It Yourself (DIY) content about how to play guitar, bake, fix one’s plumbing, or repair one’s car. For these topics, those who have the largest accounts and the most popular content typically possess significant expertise. That is, social media users seem to reliably pick out DIY experts. We thus have a puzzle: why are social media users seemingly competent at identifying DIY experts, but not climate science or vaccine experts? In what follows, we solve this puzzle. We begin by identifying a novel wisdom of the crowds phenomenon: specifically we argue that the crowd (in combination with social media search and recommendation algorithms) reliably picks out DIY experts and serves as a credentialing institution for DIY content. Next, we argue that (a) there are five epistemic factors that determine whether the crowd can succeed at recognizing experts on social media platforms, and (b) while many of those factors are satisfied to a sufficiently high degree by DIY content, they are mostly lacking for content about climate change or vaccines. (shrink)

Implicit biases have been studied by social psychologists for almost three decades, mainly as an individual phenomenon. Recent proposals, however, reframe implicit biases as a collective or structural phenomenon. The “Bias of Crowds” framework is one influential such proposal. Its label carries a clear reference to the idea of the “Wisdom of Crowds”. The connection between these two frameworks has, however, hitherto only been stated at the level of superficial analogy, rather than in-depth analysis. Thus, the details of any proposed (...) similarity, and the specific implications for the very idea of a Bias of Crowds, remain as of yet unclear. This paper provides a detailed assessment of the idea of a Bias of Crowds through the Wisdom of Crowds framework. It shows that there are several interpretations of the former expression, which go well beyond what is suggested by the vague analogy. The results are not just conceptual, however, but moreover have explanatory power: the analysis uncovers how collective decision-making can amplify bias. This provides a novel explanation of the observed correlations between average collective bias scores and large-scale structural inequalities, which inspired the Bias of Crowds framework in the first place. An important byproduct of the analysis is the insight that, on an overall picture, amplified collective bias may fly under the radar of amplified collective competence, and thus be nay invisible. Clarifying the idea of a Bias of Crowds in this way answers the crucial question how extremely small-scale biases can have extremely large-scale social effects. (shrink)

A probability aggregation rule assigns to each profile of probability functions across a group of individuals (representing their individual probability assignments to some propositions) a collective probability function (representing the group's probability assignment). The rule is “non-manipulable” if no group member can manipulate the collective probability for any proposition in the direction of his or her own probability by misrepresenting his or her probability function (“strategic voting”). We show that, except in trivial cases, no probability aggregation rule satisfying two mild (...) conditions (non-dictatorship and consensus preservation) is non-manipulable. (shrink)

Does pre-voting group deliberation improve majority outcomes? To address this question, we develop a probabilistic model of opinion formation and deliberation. Two new jury theorems, one pre-deliberation and one post-deliberation, suggest that deliberation is beneficial. Successful deliberation mitigates three voting failures: (1) overcounting widespread evidence, (2) neglecting evidential inequality, and (3) neglecting evidential complementarity. Formal results and simulations confirm this. But we identify four systematic exceptions where deliberation reduces majority competence, always by increasing Failure 1. Our analysis recommends deliberation that (...) is 'participatory', 'neutral', but not necessarily 'equal', i.e., that involves substantive sharing, privileges no evidences, but might privilege some persons. (shrink)

Scientific understanding typically involves multiple specialists performing interdependent tasks. According to several social–epistemological accounts, this suggests that scientific communities are collective epistemic subjects. We argue instead that the data does not warrant the postulation of a collective subject. Our position, rather, is fictionalist: we argue that the use of sentences attributing understanding to scientific communities amounts to loose talk which is best construed as indicating how social environments associated with a scientific community promote individual scientists' understanding.

In this paper, I argue that widespread expert disagreement about sufficiently many issues central to a democratic decision-making procedure can nullify the duty to vote. I begin by drawing a distinction between different ways that we might conceive of the duty to vote, i.e. whether it is a duty to vote, no matter how one votes, or a duty to vote well. I then review some prominent arguments in favor of the existence of the duty to vote and suggest that (...) they go through only when the potential voter in question would vote well. So the most promising existing arguments for the duty to vote, if successful, really show not merely that citizens have a duty to vote, but more strongly that they have a duty to vote well. I then discuss the epistemology of expert disagreement to show how circumstances of expert disagreement can nullify such a duty by making it impossible to vote well. To my knowledge, no one has yet brought considerations of the epistemology of expert disagreement to bear on this topic. That is my aim in the main argument of this paper. The remainder of the paper addresses alternative characterizations of ‘voting well’, and argues that on other plausible characterizations, expert disagreement will still often nullify the duty to vote. (shrink)

This paper focuses on radical pooling, or the question of how to aggregate credences when there is a fundamental disagreement about which is the relevant logical space for inquiry. The solution advanced is based on the notion of consensus as common ground, where agents can find it by suspending judgment on logical possibilities. This is exemplified with cases of scientific revolution. On a formal level, the proposal uses algebraic joins and imprecise probabilities; which is shown to be compatible with the (...) principles of marginalization, rigidity, reverse bayesianism, and minimum divergence commonly endorsed in these contexts. Furthermore, I extend results from previous work by to show that pooling sets of imprecise probabilities can satisfy important pooling axioms. (shrink)

Is the pool of fair predictive algorithms fair? It depends, naturally, on both the criteria of fairness and on how we pool. We catalog the relevant facts for some of the most prominent statistical criteria of algorithmic fairness and the dominant approaches to pooling forecasts: linear, geometric, and multiplicative. Only linear pooling, a format at the heart of ensemble methods, preserves any of the central criteria we consider. Drawing on work in the social sciences and social epistemology on the theoretical (...) foundations of the wisdom of crowds, we explain how our observations present an exception to the general trend of finding tradeoffs between the accuracy and fairness of forecasts. (shrink)

How should rational agents revise their opinions given the opinions of multiple experts? One attractive answer is linear averaging: upon learning multiple experts’ opinions about a proposition A, one’s own probability of A should equal a linear average of the experts’ opinions about A. However, this answer has a well-known problem: it is compatible with Bayesian conditionalization only when the agent is certain that the experts assign the exact same probability to A (Dawid et al. in TEST, 4(2):263–313, 1995, Ranjan (...) and Gneiting in J Royal Stat Soc Ser B Stat Methodol 72(1):71–91, 2010, Bradley in Theory Decis 85(1):5-20, 2018, Gallow in Philos Stud 175(10):2389–2398, 2018). This paper shows that, for priors of finite domains, a similar result holds for the much weaker norm of strict convexity. To this extent, the triviality phenomenon is more widespread than it has been previously appreciated. (shrink)

Three recent results about probabilistic deference, due to Zhang, Geanakoplos, and Dorst et al,. each hold for all finite probability frames but fail when frames are allowed to be infinite. Zhang's result, that a novice cannot defer to two experts while planning to always have a credence strictly between them when they disagree, requires a finite range of possible expert credences; a counterexample using normal distributions shows it fails otherwise. Geanakoplos's result, that more informative experiments are more valuable when experiments (...) are reflexive, transitive, and nested, does not extend to uncountable frames with discontinuous payoffs, nor does it extend when both the state space and the option set are infinite. The equivalence Dorst et al. establish between Total Trust and Value breaks down in both directions on infinite frames: Total Trust can hold without Value (when utilities are unbounded), and Value can hold without Total Trust (when the option set is finite but the state space is countably infinite). These failures raise questions about the philosophical significance of results that hold only in the finite case, though the paper largely sets those questions aside in favour of establishing the formal results. (shrink)

Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...) review will lead on average to more reviewers per paper than journal-solicited peer review. Second, due to the wisdom of the crowds, more reviewers will tend to make better judgments than fewer. We make the second claim precise by looking at the Condorcet Jury Theorem as well as two related jury theorems developed specifically to apply to peer review. (shrink)

This paper suggests a new normative approach for combining beliefs. We call it the evidence-first method. Instead of aggregating credences alone, as the prevailing approaches, we focus instead on eliciting a group’s full probability distribution on the basis of the evidence available to its members. This is an altogether different way of combining beliefs. The method has four main benefits: (1) it captures the weight, or resilience, of a group’s belief; (2) it is sensitive to correlation among its individuals; (3) (...) it is commutative under updating; and (4) it can be seen as a generalization of weighted averaging and likelihood ratio approaches. More broadly, it encourages an overall rethinking of the belief combination problem away from aggregating bare credences and toward appropriately combining evidence. (shrink)

The Condorcet jury theorem (CJT) is the probabilistic foundation that underlies jury decision-making and collective information aggregation at large. It has nonetheless been recognized that Condorcet’s adoption of a statistically implausible premise – identical competence among all individuals – puts his seminal results in question, since jurors typically differ in their abilities. While many have attempted to generalize the CJT to juries consisting of heterogeneously competent individuals, we study the CJT in a more practical and policy-serviceable manner, exploring its degree (...) of generalizability. Rather than stipulating probabilistic conditions for its validity to heterogeneous juries, as generalizations normally do, we run Monte Carlo simulations to find how often would unequally competent jurors satisfy Condorcet’s results, taking into account various jury sizes, and different values of mean competence and standard deviation. Our findings indicate that heterogeneous jurors are typically consistent with, or perform very close to, Condorcet jurors. C15, D71, D72. (shrink)

Disagreement is a common feature of a social world. For various reasons, however, we sometimes need to resolve a disagreement into a single set of opinions. This can be achieved by pooling the opinions of individuals that make up the group. This Element provides an opinionated survey on some ways of pooling opinions: linear pooling, multiplicative pooling (including geometric), and pooling through imprecise probabilities. While this Element gives significant attention to the axiomatic approach in evaluating pooling strategies, it also evaluates (...) them in terms of the epistemic and practical goals they might meet. In doing so, this Element connects opinion pooling to some philosophical problems in social epistemology and the philosophy of action, illuminating different perspectives one might take when figuring out how to pool opinions for a given purpose. This title is also available as Open Access on Cambridge Core. (shrink)

Is speaker knowledge necessary or sufficient for enabling hearers to know from testimony? Here, we offer a novel argument for the answer no, based on the systematic effects of partial belief and the hearer’s view prior to hearing testimony. Modelling partial belief by credence, we show that a requirement entailed by the principles of necessity and sufficiency apparent in the literature is inconsistent with Bayesian updating. Consequently, even when the other grounds of knowledge are in place, the audience correctly updating (...) their partial belief can block the transmission of speaker knowledge, so it need not be sufficient. Nor need speaker knowledge be necessary, because the hearer correctly updating their partial belief can put them in the position to know even though no one in the speaker’s chain knows. We articulate the correct principles of testimonial knowledge transmission. The first supports a shared-credit view of transmission. The second gives a novel and systematic argument for testimony sometimes being a generative (not transmissive) source of knowledge, an argument that makes Lackey’s statement account of testimony otiose. Finally, on at least one account of causation, the two amended principles together show how speaker knowledge can be a cause whose effect is hearer’s knowledge. (shrink)

This chapter reviews research from psychological science on the conditions under which groups make optimal judgements, a subject area often called “wisdom of crowds”. It concludes that good judgements are more likely when the members of a group are selected for expertise, there is cognitive diversity among the members, they make independent judgements which are then aggregated and there is opportunity for sharing information and discussion. When the methods that scientists use to establish deliberative consensus are evaluated against these conditions, (...) none meet them all, but some (Delphi studies and nominal group technique) are better than others. (shrink)

I propose a ranking-based aggregation model utilizing quantiles, such as the median or first quartile. This approach is broader than most in existing literature, as it does not require competent individuals. It recovers the asymptotic convergence property of finite estimations in the Condorcet Jury Theorem as a special case. This procedure is radical in occasionally granting greater respect to minority opinions. An optimistic conclusion is that individual errors can be mitigated and the wisdom of crowds manifested through intelligent aggregation.

This article reports three empirical studies regarding partially aggregative moral theories in distributive ethics (total N = 417). We begin by documenting the widespread occurrence of the intuitions that motivate partial aggregation views. Thereafter, we advance the literature along two dimensions: First, we extend experimental work by ascertaining which amongst existing versions of partial aggregation (localised vs. global) chimes more fully with moral common sense. Specifically, we document how judgments about ‘irrelevant goods’ (Kamm 1993) in tie-breaking cases are just as (...) robust as the original aggregative/non-aggregative pair of judgments that constitute partial aggregation. Second, we conduct an experiment that pairs laypeople’s moral judgments in standard cases with their intuitions about the limits of permissible self-prioritisation. We investigate whether one prominent explanation of why irrelevant claims may not be aggregated (Voorhoeve’s ‘personal prerogative’ argument) can be said to underpin people’s intuitions about the (ir)relevance relation of claims in conflict cases. We close with a discussion of our findings’ import and highlight avenues for future research. (shrink)

How do opinion diversity and belief polarisation affect epistemic group decision-making, particularly if decisions must be made without delay and on the basis of permissive evidence? In an agent-based model, we track the consistency of group opinions aggregated through sentence-wise majority voting. Simulations on the model reveal that high opinion diversity, but not polarisation, incurs a significant inconsistency risk. These results indicate that epistemic group decisions based on permissive evidence can be particularly difficult for diverse groups. The results also improve (...) our understanding of what can reasonably be expected of expert groups, and where expert advice might have limits. (shrink)

Should you defer to individual experts? That is, when a single expert—rather than a group of experts or a expert consensus—testifies that p, should you believe that p? In this paper, I argue that the answer to this question is, generally speaking, “no.” My argument is based on the notion of a complexity‐based defeater. Some questions are complex in a sense that makes inquirers less reliable at answering them. Expert testimony tends to be about such questions. Expert testimony thus tends (...) to be subject to a complexity‐based defeater. The pressing question, then, is whether the speaker's expertise in turn defeats that complexity‐based defeater. I first draw on the extant literature to show why we cannot reliably make case‐by‐case determinations of whether a particular speaker's expertise counteracts the complexity of the particular question they are answering. Next, I argue that a speaker's status as an expert does not, in general, defeat the complexity‐based defeaters that tend to come with expert testimony. We thus should not, generally speaking, defer to individual experts. I then address some issues with the peer review system that are relevant to the core argument. Finally, I briefly discuss a path to rational deference that remains open: a path through expert judgment aggregation. (shrink)

The nature of expertise is usually discussed only within the confines of individualistic epistemology, despite the fact that many tasks typically performed by individual experts are now performed by groups. As a result, some definitions and conditions of expertise may fail to account for group expertise. I will argue that current versions of veritism do not allow for group experts beyond the mere conceptual possibility of them. For non-summativists, this is a problem they should address. I also propose a condition (...) for veritistic expertise that retains the veritistic intuition but makes group expertise more feasible in realistic contexts. (shrink)

The Book of kOA lays out a manifesto and a systems design for a global, open, and merit-based civic platform—Konnaxion—that turns knowledge into a public utility and translates agreement into action. Grounded in principles such as radical lucidity, transparency in governance / privacy of person, inclusive social mobility, ecological responsibility, and cooperation before competition, the book specifies a modular architecture with four interoperable modules: KonnectED (open education), keenKonnect (collaborative development), Ethikos (merit-weighted deliberation and voting), and Kreative (cultural commons). A cross-cutting (...) backbone, EkoH, provides multidimensional merit, certification, and legitimacy across modules. Use-cases include education reform, justice and prison rehabilitation kiosks, open-knowledge “Kristal Farms,” and governance pilots that combine public participation with expertise via weighted votes. The work argues that when information is open and merit is visible, collaboration outperforms zero-sum competition, enabling ethical, resilient progress at scale. This is both political philosophy (institutional design, legitimacy, equity) and philosophy of technology (AI governance, platform ethics), offering a design-level response to contemporary fragmentation and institutional drag. (shrink)

Recent work in judgement and decision-making has stressed that institutions, like individuals, often rely on decision-making heuristics. But most of the institutional decision-making heuristics studied to date are highly firm- and industry-specific. This contrasts to the individual case, where many heuristics are general-purpose rules suitable for a wide range of decision problems. Are there also general-purpose heuristics for institutional decision-making? In this article, I argue that a number of methods recently developed for decision-making under deep uncertainty have a good claim (...) to be understood as general-purpose decision-making heuristics suitable for a broad range of institutional decision problems. (shrink)

Hybrid belief aggregation addresses aggregation of individual probabilistic beliefs into collective binary beliefs. In line with the development of judgment aggregation theory, our research delves into the identification of precise agenda conditions associated with some key impossibility theorems in the context of hybrid belief aggregation. We determine the necessary and sufficient level of logical interconnection between the propositions in an agenda for some key impossibilities to arise. Specifically, we prove three characterization theorems about hybrid belief aggregation: (i) Precisely the path-connected (...) and pair-negatable agendas lead to the ‘oligarchy result’—only oligarchic rules satisfy universal domain, proposition-wise independence, respect for unanimity, and deductive closure of collective beliefs. (ii) Precisely the negation-connected agendas lead to the ‘triviality result’—only unanimity rules satisfy those conditions as well as anonymity. (iii) Precisely the blocked agendas lead to the ‘non-existence result’—no rules satisfy those conditions as well as completeness and consistency of collective beliefs. Furthermore, we compare these novel findings with existing agenda-theoretic characterization theorems in the domains of judgment aggregation and belief binarization. (shrink)

We study the phenomenon of merging of opinions for computationally limited Bayesian agents from the perspective of algorithmic randomness. When they agree on which data streams are algorithmically random, two Bayesian agents beginning the learning process with different priors may be seen as having compatible beliefs about the global uniformity of nature. This is because the algorithmically random data streams are of necessity globally regular: they are precisely the sequences that satisfy certain important statistical laws. By virtue of agreeing on (...) what data streams are algorithmically random, two Bayesian agents can thus be taken to concur on what global regularities they expect to see in the data. We show that this type of compatibility between priors suffices to ensure that two computable Bayesian agents will reach inter-subjective agreement with increasing information. In other words, it guarantees that their respective probability assignments will almost surely become arbitrarily close to each other as the number of observations increases. Thus, when shared by computable Bayesian learners with different subjective priors, the beliefs about uniformity captured by algorithmic randomness provably lead to merging of opinions. (shrink)

The Dispersion of Power is an urgent call to rethink centuries of conventional wisdom about what democracy is, why it matters, and how to make it better. Drawing from history, social science, psychology, and critical theory, it explains why elections do not and cannot realize the classic ideal of popular rule, and why prevailing strategies of democratic reform often make things worse. Instead, Bagg argues, we should see democracy as a way of protecting public power from capture—an alternative vision that (...) is at once more realistic and more inspiring. Despite their many shortcomings, real-world elections do prevent the most extreme forms of tyranny, and are therefore indispensable. In dealing with the vast inequalities that remain, however, we cannot rely on standard solutions such as electoral reform, direct democracy, deliberation, and participatory governance. Instead, Bagg shows, protecting and enriching democracy requires addressing underlying inequalities of power directly. In part, this entails substantive policies attacking the advantages of wealthy elites. Even more crucially, deepening democracy requires the organization of oppositional, countervailing power among ordinary people. Neither task is easy, but historical precedents exist in both cases—and if democracy is to survive contemporary crises, leaders and citizens alike must find ways to revive and reinvent these essential democratic practices for the twenty-first century. (shrink)

Initially, you judge that p. You then learn that most experts disagree. All things considered, you believe that the experts are probably right. Still, p continues to seem right to you, in some sense. You don’t yet see what, if anything, is wrong with your original reasoning. In such a case, we’ll say that you are ‘inclined’ toward p. This paper explores various roles that this state of inclination can play, both within epistemology and more broadly. Specifically, it will be (...) argued that: (i) inclinations can promote the accuracy of inquiring groups; (ii) they can support rational participation within philosophy despite pervasive disagreement; (iii) they allow us to make sense of an important way in which two people can continue to disagree even after they ‘conciliate’; (iv) inclinations carry information about individuals’ independent judgments and for this reason must be accounted for when updating on the opinions of others; (v) inclinations are connected to understanding in a way that belief is not; (vi) and awareness of the inclination-belief distinction enables us to respond to a provocative challenge purporting to show that critical thinking, or ‘thinking for oneself’, typically reduces expected accuracy and hence should be discouraged. (shrink)

In Chapters 4 – 6, we were concerned with making collective decisions by voting, i.e., with methods for how to aggregate the voters’ individual preferences so as to determine the winning alternative(s) as a collective consensus. In the present chapter, we turn to the closely related topic of judgment aggregation, i.e., to methods for how to aggregate the individual judgments of a number of judges so as to determine the joint judgment(s) as a collective consensus.

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light (...) of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)

Scientific findings nowadays often rely on statistical analyses, are expressed in terms of probabilities, and are frequently developed based on model calculations. These circumstances contribute to a disconnect between scientific predictions and people's everyday risk assessments. Situations such as the COVID-19 pandemic, climate issues, or the downsides of global trade are particularly affected by this phenomenon. In these areas especially, the growth of knowledge implies new and far-reaching ethical (preventive) obligations for humanity. This chapter argues that a successful relationship between (...) scientific knowledge and people's everyday decision-making behavior in these domains can only emerge if several demanding prerequisites are met: understanding statistical findings and probabilities must be generally improved; the ethical implications resulting from this understanding must be recognized as moral progress; and the challenging delineations of new ethical obligations and political necessities that arise in risk contexts require careful and patient consideration, rather than being used as an excuse to maintain the status quo. ----- Wissenschaftliche Erkenntnisse basieren heutzutage oft auf statistischen Auswertungen, werden in Wahrscheinlichkeit angegeben und sind nicht selten auf Grundlage von Modellrechnungen entwickelt. Diese Umstände tragen zu einer Abkoppelung der wissenschaftlichen Prognosen von den lebensweltlichen Risikoeinschätzungen der Menschen bei. Situationen wie die COVID-19-Pandemie, die Klimaproblematik oder auch die Nachteile des globalen Handels sind von diesem Phänomen in besonderem Maße betroffen. Gerade auf diesen Gebieten impliziert der Wissenszuwachs neue und weitreichende ethische (Verhinderungs-)Pflichten für die Menschen. In diesem Kapitel wird argumentiert, dass ein gelingendes Verhältnis zwischen wissenschaftlicher Erkenntnis und dem alltäglichen Entscheidungsverhalten der Menschen in diesen Bereichen nur dann entstehen kann, wenn mehrere anspruchsvolle Voraussetzungen erfüllt sind: Das Verständnis von statistischen Erkenntnissen und Wahrscheinlichkeiten muss generell verbessert werden; das Verständnis der hierdurch resultierenden ethischen Implikationen muss als moralischer Fortschritt verstanden werden; und die schwierigen Grenzziehungen für die neuen ethischen Pflichten sowie politischen Notwendigkeiten, die im Rahmen von Risikokontexten notwendig werden, bedürfen einer differenzierten und geduldigen Bearbeitung, anstatt als Ausflucht in ein Weiter-so genutzt zu werden. (shrink)

Multidimensional concepts are everywhere, and they are important. Examples include moral value, welfare, scientific confirmation, democracy, and biodiversity. How, if at all, can we aggregate the underlying dimensions of a multidimensional concept F to yield verdicts about which things are Fer than which overall? Social choice theory can be used to model and investigate this aggregation problem. Here, we focus on a particularly thorny problem made salient by this social choice-theoretic framework: the underlying dimensions of a given concept might be (...) measurable on different types of scales—e.g., some ordinal and some cardinal. An underappreciated impossibility theorem due to Anna Khmelnitskaya shows that seemingly plausible constraints on aggregation across scale types are inconsistent. This impossibility threatens to render the notion of overall Fness incoherent. We attempt to defuse this threat, arguing that the impossibility depends on an overly restrictive conception of measurement and of how measurement constrains aggregation. Adopting a more flexible—and, we think, more perspicuous—conception of measurement opens an array of possibilities for aggregation across disparate scale types. (shrink)

Models of collective deliberation often assume that the chief aim of a deliberative exchange is the sharing of information. In this paper, we argue that an equally important role of deliberation is to draw participants’ attention to pertinent questions, which can aid the assembly and processing of distributed information by drawing deliberators’ attention to new issues. The assumption of logical omniscience renders classical models of agents’ informational states unsuitable for modelling this role of deliberation. Building on recent insights from psychology, (...) linguistics and philosophy about the role of questions in speech and thought, we propose a different model in which beliefs are treated as answers directed at specific questions. Here, questions are formally represented as partitions of the space of possibilities and individuals’ information states as sets of questions and corresponding partial answers to them. The state of conversation is then characterised by individuals’ information together with the questions under discussion, which can be steered by various deliberative inputs. Using this model, deliberation is then shown to shape collective decisions in ways that classical models cannot capture, allowing for novel explanations of how group consensus is achieved. (shrink)

Public reason liberalism demands that political decisions be publicly justified to the citizens who are subjected to them. Much recent literature emphasises the differences between the two main interpretations of this requirement, justificatory and political liberalism. In this paper, I show that both views share structural democratic deficits. They fail to guarantee political autonomy, the expressive quality of law, and the justification to citizens, because they allow collective decisions made by incompletely theorised agreements. I argue that the result can only (...) be avoided by changing public reason’s role in collective decision-making. Instead of incompletely theorised agreements, we should demand agreement both on the public reasons themselves and on the other premises that justify political decisions. In this way, it is always possible to point to a procedure-independent reason that justifies democratic decisions, and the reasoning of the state is public and contestable. Finally, I explain how this, in turn, implies that only political liberalism can be rescued—by accepting what I will call strong political liberalism. Modifying justificatory liberalism in the necessary way will inevitably open the door to an objectionable form of perfectionism. (shrink)

Public reason liberals expect individuals to have justificatory reasons for their views of certain political issues. This paper considers how groups can, and whether they should, give collective public reasons for their political decisions. A problem is that aggregating individuals’ consistent judgments on reasons and a decision can produce inconsistent collective judgments. The group will then fail to give a reason for its decision. The paper considers various solutions to this problem and defends a deliberative procedure by showing how it (...) incentivizes information sharing and leads to outcomes most acceptable to the group members. (shrink)

The purpose of this paper is to illustrate, formally, an ambiguity in the exercise of political influence. To wit: A voter might exert influence with an eye toward maximizing the probability that the political system (1) obtains the correct (e.g. just) outcome, or (2) obtains the outcome that he judges to be correct (just). And these are two very different things. A variant of Condorcet's Jury Theorem which incorporates the effect of influence on group competence and interdependence is developed. Analytic (...) and numerical results are obtained, the most important of which is that it is never optimal--from the point-of-view of collective accuracy--for a voter to exert influence without limit. He ought to either refrain from influencing other voters or else exert a finite amount of influence, depending on circumstance. Philosophical lessons are drawn from the model, to include a solution to Wollheim's "Paradox in the Theory of Democracy". (shrink)

This paper presents two possibility results and one impossibility result about a situation with three voters under a pairwise majoritarian aggregation function voting on a countably infi nite number of candidates. First, from individual orders with no maximal or minimal element, it is possible to generate an aggregate order with a maximal or minimal element. Second, from dense individual orders, it is possible to generate a discrete aggregate order. Finally, I show that, from discrete orders with a particular property, namely (...) the finite-distance property, it is not possible to generate a dense aggregate order. (shrink)