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)

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)

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)

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)

Epistemic democracy aims to show, often by appeal to the Condorcet Jury Theorem, that democracy has a high chance of reaching correct decisions. It has been argued that epistemic democracy is compatible with various metaethical accounts, such as moral realism, conventionalism and majoritarianism. This paper casts doubt on that thesis and reveals the following metaethical dilemma: if we adopt moral realism, it is doubtful that voters are, on average, more than 0.5 likely to track moral facts and identify the correct (...) alternative. By contrast, if we adopt conventionalism or majoritarianism, we cannot expect that voters are both competent and sincere. Either way, the conditions for the application of Condorcet’s theorem are not met. (shrink)

According to the skeptical argument from disagreement, we are mandated to suspend judgement about a question if we discover that others disagree with us. Critics, however, have proposed that this skeptical argument fails if there are not equally many people on either side of the debate: numbers matter. The present paper explicates this as the argument that a group can be more likely to arrive at the correct view by majority rule than the members are on their own. Defenders of (...) the skeptical argument have resisted that numbers matter by observing that if group members depend on each other when forming their beliefs, then the group can be less competent than its members. However, neither side of the debate has accompanied their views with quantitative estimates of how detrimental dependence is for group competence. This paper tries to improve this situation by drawing on jury theorems from social choice theory. The paper cannot settle the debate, but it shows that even the lower limit on group competence will exceed the average individual competence when dependence among voters remains moderate. This should give confidence to those who propose that asymmetry between the disputing parties can counter the skeptical argument from disagreement since being in the majority can thus be higher-order evidence for the disputed proposition. (shrink)

In a homogeneous jury, the votes are exchangeable correlated Bernoulli random variables. We derive the bounds on a homogeneous jury’s competence as the minimum and maximum probability of the jury being correct, which arise due to unknown correlations among the votes. The lower bound delineates the downside risk associated with entrusting decisions to the jury. In large and not-too-competent juries the lower bound may fall below the success probability of a fair coin flip—one half, while the upper bound may not (...) reach a certainty. We also derive the bounds on the voting power of an individual juror as the minimum and maximum probability of her/his casting a decisive vote. The maximum is less than one, while the minimum of zero can be attained for infinitely many combinations of distribution moments. (shrink)

The agents of a jury have to decide between a good and a bad option through simple majority voting. In this paper the jury consists of N independent couples. Each couple consists of two correlated agents of the same competence level. Different couples may have different competence levels. In addition, each agent is assumed to be better than completely random guessing. We prove tight lower and upper bounds for the quality of the majority decision. The lower bound is the same (...) as the competence of majority voting of N independent agents. The upper bound cases for negatively correlated couples can be much better than the value for 2N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2 \, N$$\end{document} independent agents. (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)

A jury and two valid options are given. Each agent of the jury picks exactly one of these options. The option with the most votes will be chosen by the jury. In the N-couple model of Althöfer and Thiele, the jury consisted of 2N agents. These agents form N independent couples, with dependencies within the couples. The authors assumed that the agents who form a couple have the same competence level. In this note, we relax this assumption by allowing different (...) competence levels within the couples. We show that the theoretical results of Althöfer and Thiele remain valid under this relaxation. (shrink)

We briefly review Condorcet's and Young's epistemic interpretations of preference aggregation rules as maximum likelihood estimators. We then develop a general framework for interpreting epistemic social choice rules as maximum likelihood estimators, maximum a posteriori estimators, or expected utility maximizers. We illustrate this framework with several examples. Finally, we critique this program.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage (...) Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)