Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans (...) across various disciplines such as economics, political science, philosophy, and computer science. This entry reviews and critically assesses a variety of jury theorems. It first discusses Condorcet's initial jury theorem, and then progressively introduces jury theorems with more appropriate premises and conclusions. It explains the philosophical foundations, and relates jury theorems to diversity, deliberation, shared evidence, shared perspectives, and other phenomena. It finally connects jury theorems to their historical background and to democratic theory, social epistemology, and social choice theory. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most (...) jury theorems; (ii) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (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)

Suppose that a majority of jurors decide that a defendant is guilty (or not), and we want to know the likelihood that they reached the correct verdict. The French philosopher Marquis de Condorcet (1743-1794) showed that we can get a mathematically precise answer, a result known as the “Condorcet Jury Theorem.” Condorcet’s theorem isn’t just about juries, though; it’s about collective decision-making in general. As a result, some philosophers have used his theorem to argue for democratic (...) forms of government. This essay explains Condorcet’s theorem and how philosophers have used it as an argument for democracy. (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 generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (...) (as in Condorcet's paradox) are in large electorates. (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)

My aim in this paper is to explain what Condorcet’s jury theorem is, and to examine its central assumptions, its significance to the epistemic theory of democracy and its connection with Rousseau’s theory of general will. In the first part of the paper I will analyze an epistemic theory of democracy and explain how its connection with Condorcet’s jury theorem is twofold: the theorem is at the same time a contributing historical source, and the model (...) used by the authors to this day. In the second part I will specify the purposes of the theorem itself, and examine its underlying assumptions. Third part will be about an interpretation of Rousseau’s theory, which is given by Grofman and Feld relying on Condorcet’s jury theorem, and about criticisms of such interpretation. In the fourth, and last, part I will focus on one particular assumption of Condorcet’s theorem, which proves to be especially problematic if we would like to apply the theorem under real-life conditions; namely, the assumption that voters choose between two options only. (shrink)

One might think that if the majority of virtue signallers judge that a proposition is true, then there is significant evidence for the truth of that proposition. Given the Condorcet Jury Theorem, individual virtue signallers need not be very reliable for the majority judgment to be very likely to be correct. Thus, even people who are skeptical of the judgments of individual virtue signallers should think that if a majority of them judge that a proposition is true, then (...) that provides significant evidence that the proposition is true. We argue that this is mistaken. Various empirical studies converge on the following point: humans are very conformist in the contexts in which virtue signalling occurs. And stereotypical virtue signallers are even more conformist in such contexts. So we should be skeptical of the claim that virtue signallers are sufficiently independent for the Condorcet Jury Theorem to apply. We do not seek to decisively rule out the relevant application of the Condorcet Jury Theorem. But we do show that careful consideration of the available evidence should make us very skeptical of that application. Consequently, a defense of virtue signalling would need to engage with these findings and show that despite our strong tendencies for conformism, our judgements are sufficiently independent for the Condorcet Jury Theorem to apply. This suggests new directions for the debate about the epistemology of virtue signalling. (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)

Nakba is ignored in Western philosophy encyclopedias, and the notion of genocide is rarely explained. In turn, there is much talk about the Holocaust.

Procedural justifications of democracy emphasize inclusiveness and respect and by doing so come into conflict with instrumental justifications that depend on voters’ competence. This conflict raises questions about jury theorems and makes their standing in democratic theory contested. We show that a type of no-regret learning called meta-induction can help to satisfy the competence assumption without excluding voters or diverse opinion leaders on an a priori basis. Meta-induction assigns weights to opinion leaders based on their past predictive performance to (...) determine the level of their inclusion in recommendations for voters. The weighting minimizes the difference between the performance of meta-induction and the best opinion leader in hindsight. The difference represents the regret of meta-induction whose minimization ensures that the recommendations are optimal in supporting voters’ competence. Meta-induction has optimal truth-tracking properties that support voters’ competence even if it is targeted by mis/disinformation and should be considered a tool for supporting democracy in hyper-plurality. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This (...) theorem rehabilitates the importance of deliberation and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

The scientificity of the research should be evaluated according to the methodology used in the study. However, these are usually the research areas or the institutions that are classified as scientific or non-scientific. Because of various reasons, it may turn out that the scientific institutions are not producing science, while the “non-scientists” are doing real science. In the extreme case, the official science system is entirely corrupt, consisting of fraudsters, while the real scientists have been expelled from academic institutions. Since (...) 2016-2017, there has been much talk about the “post-truth era” and the politicians who are “denying science”. However, simultaneously, many complaints about the corruption of science appeared. The outsider cannot tell who is telling the truth as it may be the case that the science fraudsters are defending themselves and these politicians are aware of the corruption. It is also untrue that the censoring or suppression of science started from 2016-2017. Suppression of science because of political and ideological reasons was present already long ago, and during the last few years, it has been increasing. The picture is highly complicated as there are many pretenders, false accusations, etc. For example, because of political reasons, someone may be set up as a pseudoscientist, the real scientist may be expelled using political accusations, justified criticism may be labelled as political pressure, etc. There is something like an inner information war ongoing in and around science. The classical philosophy of science seems unable to handle it because every formal rule can be misapplied. Science, as a whole, may be unable to persist. (shrink)

Does pre-voting group deliberation increase majority competence? 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)

In his 2010 paper “Philosophical Naturalism and Intuitional Methodology”, Alvin I. Goldman invokes the Condorcet Jury Theorem in order to defend the reliability of intuitions. The present note argues that the original conditions of the theorem are all unrealistic when analysed in connection to the case of intuitions. Alternative conditions are discussed.

This article applies the tools of experimental philosophy to the ongoing debate about both the theoretical viability and the practical import of partially aggregative moral theories in distributive ethics. We conduct a series of three experiments (N=383): First, we document the widespread occurrence of the intuitions that motivate this position. Our study then moves beyond establishing the existence of partially aggregative intuitions in two dimensions: First, we extend experimental work in such a way as to ascertain which amongst existing versions (...) of partial aggregation (localised vs. global) chimes more fully with moral common sense. Specifically, we document how, in tie-breaking cases, ‘irrelevant goods’ judgments (Kamm) are just as robust as the original aggregative/non-aggregative pair of judgments that constitute partial aggregation. Second, by pairing 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’ practical and theoretical import and highlight avenues for future research. (shrink)

Understanding Gravity correctly has a pivotal importance if we would like to understand Anti-gravity. Famously, with the existing theories for Gravity we cannot achieve that. While exploring questions related to Gravity, I realized that it demands reconsidering the nature of Vacuum. For this reason, in this article you will find not only alternative description of the nature of Vacuum, but I also will provide the idea to test it with results that will prove beyond any doubt what it is made (...) of after all. Turns out that mechanisms causing what I call the "Effect of Gravity" might be very simple. Also, this effect might be directly linked to the Magnetism or the magnetic field of Earth, even though objects are not attracted by it. Instead, they are attracted because of it. (shrink)

It has been argued that an epistemically rational agent’s evidence is subjectively mediated through some rational epistemic standards, and that there are incompatible but equally rational epistemic standards available to agents. This supports Permissiveness, the view according to which one or multiple fully rational agents are permitted to take distinct incompatible doxastic attitudes towards P (relative to a body of evidence). In this paper, I argue that the above claims entail the existence of a unique and more reliable epistemic standard. (...) My strategy relies on Condorcet’s Jury Theorem. This gives rise to an important problem for those who argue that epistemic standards are permissive, since the reliability criterion is incompatible with such a type of Permissiveness. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

Can experimental philosophy help us answer central questions about the nature of moral responsibility, such as the question of whether moral responsibility is compatible with determinism? Specifically, can folk judgments in line with a particular answer to that question provide support for that answer. Based on reasoning familiar from Condorcet’s Jury Theorem, such support could be had if individual judges track the truth of the matter independently and with some modest reliability: such reliability quickly aggregates as the number (...) of judges goes up. In this chapter, however, I argue, partly based on empirical evidence, that although non-specialist judgments might on average be more likely than not to get things right, their individual likelihoods fail to aggregate because they do not track truth with sufficient independence. (shrink)

Epistemically immodest agents take their own epistemic standards to be among the most truth-conducive ones available to them. Many philosophers have argued that immodesty is epistemically required of agents, notably because being modest entails a problematic kind of incoherence or self-distrust. In this paper, I argue that modesty is epistemically permitted in some social contexts. I focus on social contexts where agents with limited cognitive capacities cooperate with each other (like juries).

Recent political developments cast doubt on the wisdom of democratic decision-making. Brexit, the Colombian people's (initial) rejection of peace with the FARC, and the election of Donald Trump suggest that the time is right to explore alternatives to democracy. In this essay, I describe and defend the epistocratic system of government which is, given current theoretical and empirical knowledge, most likely to produce optimal political outcomes—or at least better outcomes than democracy produces. To wit, we should expand the suffrage as (...) wide as possible and weight citizens’ votes in accordance with their competence. As it turns out, the optimal system is closely related to J. S. Mill's plural voting proposal. I also explain how voters’ competences can be precisely determined, without reference to an objective standard of correctness and without generating invidious comparisons between voters. (shrink)

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or ‘votes’ and ‘talk.’ The Condorcet Jury Theorem is appealed to as a justification in terms votes, and the Hong-Page “Diversity Trumps Ability” result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how (...) these results hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of that result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)

Under the assumptions of the standard Condorcet Jury Theorem, majority verdicts are virtually certain to be correct if the competence of voters is greater than one-half, and virtually certain to be incorrect if voter competence is less than one-half. But which is the case? Here we turn the Jury Theorem on its head, to provide one way of addressing that question. The same logic implies that, if the outcome saw 60 percent of voters supporting one proposition (...) and 40 percent the other, then average voter competence must either be 0.60 or 0.40. We still have to decide which, but limiting the choice to those two values is a considerable aid in that. Key Words: Condorcet Jury Theorem • epistemic democracy • voter competence. (shrink)

Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting (...) the Arrow–Sen framework for social choice to study grading in groups. (shrink)

Many epistemologists have argued that there is some degree of independence between individual and collective reliability (e.g., Kitcher 1990; Mayo-Wilson, Zollman, and Danks 2011; Dunn 2018). The question, then, is: To what extent are the two independent of each other? And in which contexts do they come apart? In this paper, I present a new case confirming the independence between individual and collective reliability optimization. I argue that, in voting groups, optimizing individual reliability can conflict with optimizing collective reliability. This (...) can happen even if various conditions are held constant, such as: the evidence jurors have access to, the voting system, the number of jurors, some independence conditions between voters, and so forth. This observation matters in many active debates on, e.g., epistemic dilemmas, the wisdom of crowds, independence theses, epistemic democracy, and the division of epistemic labour. (shrink)

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or 'votes' and 'talk.' The Condorcet Jury Theorem is appealed to as a justification in terms of votes, and the Hong-Page "Diversity Trumps Ability" result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore (...) how these results hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of the result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)

In their simplest form, consensus gentium arguments for theism argue that theism is true on the basis that everyone believes that theism is true. While such arguments may have been popular in history, they have all but fallen from grace in the philosophy of religion. In this short paper, we reconsider the neglected topic of consensus gentium arguments, paying particular attention to the value of such arguments when deployed in the defence of theistic belief. We argue that while consensus gentium (...) arguments are unlikely to offer anything close to overwhelming support for theism, their probative value is nevertheless underappreciated, and that they have been unfairly maligned as a consequence. (shrink)

How can democratic governments be relied upon to achieve adequate political knowledge when they turn over their authority to those of no epistemic distinction whatsoever? This deep and longstanding concern is one that any proponent of epistemic conceptions of democracy must take seriously. While Condorcetian responses have recently attracted substantial interest, they are largely undermined by a fundamental neglect of agenda-setting. I argue that the apparent intractability of the problem of epistemic adequacy in democracy stems in large part from a (...) failure to appreciate the social character of political knowledge. A social point of view brings into focus a number of vital factors that bear on our understanding of democratic epistemology and our assessment of its prospects: the essential role of inclusive deliberation, the public's agenda-setting function, institutional provisions for policy feedback, the independence of expert communities, and the knowledge-pooling powers of markets. (shrink)

Una de las bifurcaciones en el debate contemporáneo sobre la legitimidad de la democracia explora si ésta ofrece ventajas distintivamente epistémicas frente a otras alternativas políticas. Quienes defienden la tesis de la democracia epistémica afirman que la democracia es instrumentalmente superior o equiparable a otras formas de organización política en lo que concierne a la obtención de varios bienes epistémicos. En este ensayo presento dos (grupos de) argumentos a favor de la democracia epistémica, que se inspiran en resultados formales: el (...) teorema del jurado de Condorcet [TJC] y el teorema ‘diversidad supera habilidad’ [DSH]. Pese a su gran atractivo, sostengo que estos argumentos son incapaces de respaldar dicha tesis: no brindan razones para considerar que la democracia es epistémicamente superior (o equiparable) a algunas alternativas políticas no democráticas. En su lugar, sugiero que, sin requerir un cambio radical en nuestras formas de organización política, la epistemología democrática –el estudio de las ‘circunstancias epistémicas de la democracia’– puede ofrecer valiosas lecciones de sobre cómo optimizar, en nuestra situación, instituciones y procedimientos de toma de decisiones. Para ello, primero distingo entre varias maneras de evaluar procedimientos de toma de decisión colectiva. Argumento que, al considerarlos como formas de organización política, un factor importante en la evaluación de tales procedimientos involucra asuntos fácticos sobre los cuales puede aspirarse a obtener o promover algunos bienes epistémicos. En este contexto, presento algunos de los argumentos más importantes a favor de la democracia epistémica. A continuación, reúno algunas de las objeciones sobre la aplicabilidad de dichos argumentos y ofrezco razones independientes para dudar de que ofrezcan apoyo a la tesis de la democracia epistémica. Finalmente, defiendo que la epistemología democrática puede desempeñar un papel significativo en la legitimación de formas de organización colectiva que podrían denominarse ‘democráticas’. (shrink)

In this paper, we argue that computer simulations can provide valuable insights into the performance of voting methods on different collective decision problems. This could improve institutional design, even when there is no general theoretical result to support the optimality of a voting method. To support our claim, we first describe a decision problem that has not received much theoretical attention in the literature. We outline different voting methods to address that collective decision problem. Under certain criteria of assessment akin (...) to extensions of the Condorcet Jury Theorem, we run simulations for the methods using MATLAB, in order to compare their performance under various conditions. We consider and respond to concerns about the use of simulations in the assessment of voting procedures for policymaking. (shrink)

In this study I analyse the performance of a democratic decision-making rule: the weighted majority rule. It assigns to each voter a number of votes that is proportional to her stakes in the decision. It has been shown that, for collective decisions with two options, the weighted majority rule in combination with self-interested voters maximises the common good when the latter is understood in terms of either the sum-total or prioritarian sum of the voters’ well-being. The main result of my (...) study is that this argument for the weighted majority rule — that it maximises the common good — can be improved along the following three main lines. (1) The argument can be adapted to other criteria of the common good, such as sufficientarian, maximin, leximin or non-welfarist criteria. I propose a generic argument for the collective optimality of the weighted majority rule that works for all of these criteria. (2) The assumption of self-interested voters can be relaxed. First, common-interest voters can be accommodated. Second, even if voters are less than fully competent in judging their self-interest or the common interest, the weighted majority rule is weakly collectively optimal, that is, it almost certainly maximises the common good given large numbers of voters. Third, even for smaller groups of voters, the weighted majority rule still has some attractive features. (3) The scope of the argument can be extended to decisions with more than two options. I state the conditions under which the weighted majority rule maximises the common good even in multi-option contexts. I also analyse the possibility and the detrimental effects of strategic voting. Furthermore, I argue that self-interested voters have reason to accept the weighted majority rule. (shrink)

From different angles of science, there has been a growing interest in the abilities of groups to track the truth. The Condorcet Jury Theorem (1785) states that without communication, infinitely big groups will reach a correct majority opinion with certainty. Coughlan (2000), meanwhile formulated a model in which all agents communicate with each other, showing that majorities are only just as good as fully-communicating individuals. In reality, communication is usually between these two extremes: some agents communicate with some (...) of the others, but not with all others. We refer to this as partial communication. This thesis provides a Bayesian framework to study the influence of partial communication on individual as well as group accuracy, thereby generalising Condorcet’s as well as Coughlan’s setting. We obtain results for individual and group accuracy in three type of networks. Firstly, we study the extreme case where there is either no communication or everyone communicates with everyone. Secondly, we determine accuracy for regular networks, in which all agents communicate with equally many other agents. Thirdly, we derive a formula to express the expected accuracy in random networks, in which agents can communicate with various numbers of other agents. The formula enables us to determine the effect of various parameters on the individual and group accuracy in a random network with partial communication. Finally, we show that in random networks, despite correlation between agents, we can still obtain accurate majorities under some constraints. (shrink)

There is a substantial class of collective decision problems whose successful solution requires interdependence among decision makers at the agenda-setting stage and independence at the stage of choice. We define this class of problems and describe and apply a search-and-decision mechanism theoretically modeled in the context of honeybees and identified in earlier empirical work in biology. The honeybees’ mechanism has useful implications for mechanism design in human institutions, including courts, legislatures, executive appointments, research and development in firms, and basic research (...) in the sciences. Our paper offers a fresh perspective on the idea of “biomimicry” in institutional design and raises the possibility of comparative institutional analysis across species. (shrink)

Frente a problemas de decisión colectiva de cierta complejidad, distintos métodos de votación pueden considerarse igualmente democráticos. Ante esta situación, argumento que es posible investigar cuáles de esos métodos producen mejores resultados epistémicos sobre asuntos fácticos. Comienzo ilustrando la relación entre democracia y métodos de votación con un sencillo ejemplo. Muestro cómo el uso de modelos idealizados permite descubrir algunas propiedades de los métodos de votación; varios de estos descubrimientos muestran que, frente a problemas de cierta complejidad, no hay una (...) respuesta clara acerca de cuál es el resultado de una elección democrática. Frente a esto, sugiero que deberíamos tomar en cuenta un rasgo epistémico instrumental de varios métodos de votación: su capacidad para generar respuestas correctas ante varias situaciones. Esta intuición ofrece lecciones importantes para el diseño de instituciones electorales. (shrink)

Suppose the members of a group (e.g., committee, jury, expert panel) each form a judgment on which worlds in a given set are possible, subject to the constraint that at least one world is possible but not all are. The group seeks to aggregate these individual judgments into a collective judgment, subject to the same constraint. I show that no judgment aggregation rule can solve this problem in accordance with three conditions: “unanimity,” “independence” and “non-dictatorship,” Although the result is (...) a variant of an existing theorem on “group identification” (Kasher and Rubinstein, Logique et Analyse 160:385–395, 1997), the aggregation of judgments on which worlds are possible (or permissible, desirable, etc.) appears not to have been studied yet. The result challenges us to take a stance on which of its conditions to relax. (shrink)

Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, (...) machine learning results in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Jury science is fraught with difficulty. Since legal and institutional hurdles render it all but impossible to study live criminal jury deliberation, researchers make use of various indirect methods to evaluate jury performance. But each of these methods are open to methodological criticism and, strikingly, some of the highest-profile jury research programmes in recent years have reached opposing conclusions. Uncertainty about jury performance is an obstacle for legal reform—ongoing debates about the ‘justice gap’ for complainants (...) of sexual offences has rendered these problems stark. This paper proposes a way to advance the debate. (shrink)

Researchers face perennial difficulties in studying live jury deliberation. As a result, the academic community struggles to reach a consensus on key matters of legal reform concerning jury trials. The hurdles faced by empirical jury researchers are often legal or institutional. This note argues that the legal and institutional barriers preventing live deliberation research should be removed and discusses two forms that live deliberation research could take.

Der hier vorliegende Text befasst sich mit der Rezeption von Aristoteles’ Metaphysik Λ bei Albertus Magnus und Thomas von Aquin. Er stellt das Material bereit für die Auswertung, die als Band 61 der Bochumer Studien zur Philosophie unter dem Titel Zur mittelalterlichen Herkunft einiger Theoreme in der modernen Aristoteles-Interpretation Eine Fallstudie anhand der Kommentare von Albertus Magnus und Thomas von Aquin zu Aristoteles’ Metaphysik Λ, bei John Benjamins Publishing Company, Amsterdam / Philadelphia 2024, erscheinen wird. **************************** This text deals with (...) the reception of Aristotle's Metaphysics Λ by Albertus Magnus and Thomas Aquinas. It provides the material for the analysis, which will be published as volume 61 of the BochumerStudien zur Philosophie under the title "Zur mittelalterlichenHerkunft einiger Theoreme in der modernenAristoteles-Interpretation. Eine Fallstudie anhand derKommentare von Albertus Magnus und Thomas vonAquin zu Aristoteles' Metaphysik Λ," by John Benjamins Publishing Company, Amsterdam / Philadelphia, 2024. (shrink)

Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...) - and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

What is the Quid Juris in Kant's Deduction? Chapter 3 from my book on the Deduction (Kant's Deduction From Apperception) provides an answer to that question, and also contains an extensive discussion of the relevant literature on this topic (Henrich, Proops, Seeberg & Longuenesse).