Condorcet Jury Theorem Research Articles

Integrating spatial, morphological, and textural information for improved cell type differentiation using Raman microscopy

AbstractRaman microscopy is a well‐established tool for distinguishing different cell types in cell biological or cytopathological applications, since it can provide maps that show the specific distribution of biochemical components in the cell, with high lateral and spatial resolution. Currently, established data analysis approaches for differentiating cells of different types mostly rely on conventional chemometrics approaches, which tend to not systematically utilise the advantages provided by Raman microscopic data sets. To address this, we propose 2 approaches that explicitly exploit the large number of spectra as well as the morphological and textural information that are available in Raman microscopic data sets. Spatial bagging as our first approach is based on a statistical analysis of majority vote over classification results obtained from individual pixel spectra. Based on the Condorcet's Jury Theorem, this approach raises the accuracy of a relatively weak classifier for individual spectra to nearly perfect accuracy at the level of characterising whole cells. Our second approach extracts morphological and textural (morpho‐textural) features from Raman microscopic images to differentiate cell types. While using few wavenumbers of the Raman spectrum only, our results indicate on a quantitative basis that Raman microscopic images carry more morphological and textural information than haematoxylin and eosin (H&E) stained images as the current gold standard in cytopathology. Our 2 approaches promise improved protocols for the fast acquisition of Raman imaging data, for instance, for the morphological analysis of coherent anti‐Stokes Raman spectroscopy microscopic imaging data or for improving the accuracy of fibre optical probe systems by resampling spectra and utilising spatial bagging.

Judicial Deference Allows European Consensus to Emerge

The Emerging Consensus doctrine applied by the European Court of Human Rights (ECHR) directs the court to follow the policies adopted by the majority of states in Europe. If most states protect a certain human right, states that fail to protect this right will be found in violation of the Convention for the Protection of Human Rights and Fundamental Freedoms (Convention). This doctrine may help the court to make good policy decisions because it draws on the choices of many states in a way that follows the logic of a mathematical model called the Condorcet Jury Theorem — at least so long as the states examined are sufficiently similar to one another and decide independently. The court also applies a doctrine called the Margin of Appreciation, which directs it to defer to state policies under certain conditions. These are competing doctrines and the more the court applies one the less it applies the other. Yet this paper argues that a correct application of the Margin of Appreciation may in fact help limit the Emerging Consensus to states who are sufficiently similar to one another and in addition give states an incentive to decide independently. In this way, granting a Margin of Appreciation can help the court to get the best results out of the Emerging Consensus doctrine.

Epistemic democracy with correlated voters

We develop a general theory of epistemic democracy in large societies, which subsumes the classical Condorcet Jury Theorem, the Wisdom of Crowds, and other similar results. We show that a suitably chosen voting rule will converge to the correct answer in the large-population limit, even if there is significant correlation amongst voters, as long as the average covariance between voters becomes small as the population becomes large. Finally, we show that these hypotheses are consistent with models where voters are correlated via a social network, or through the DeGroot model of deliberation.

A note on the Condorcet jury theorem for couples

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 Althofer and Thiele (Theory and Decision 81:1–15, 2016), 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 Althofer and Thiele remain valid under this relaxation.

Are two better than one? A note

This note examines the possibility of extending the Condorcet Jury Theorem (CJT) by relaxing the assumption of homogeneous individual decision-making skills. Our main result provides two sufficient conditions for advantageous extension of a group. These conditions are referred to as (Weak) “Two Are Better than One” (WTBO) and TBO. The latter requires that the average decision-making competence of the two added members exceeds those of any existing group member. The weaker condition WTBO requires that the sum of the optimal weights of the two added members is larger than the optimal weight of any existing group member. Immediate special cases of our result include CJT settings wherein decision-making skills are assumed to be identical as well as situations wherein such skills are of two types: low and high.

Voting, deliberation and truth

There are various ways to reach a group decision on a factual yes–no question. One way is to vote and decide what the majority votes for. This procedure receives some epistemological support from the Condorcet Jury Theorem. Alternatively, the group members may prefer to deliberate and will eventually reach a decision that everybody endorses—a consensus. While the latter procedure has the advantage that it makes everybody happy (as everybody endorses the consensus), it has the disadvantage that it is difficult to implement, especially for larger groups. Besides, the resulting consensus may be far away from the truth. And so we ask: Is deliberation truth-conducive in the sense that majority voting is? To address this question, we construct a highly idealized model of a particular deliberation process, inspired by the movie Twelve Angry Men, and show that the answer is ‘yes’. Deliberation procedures can be truth-conducive just as the voting procedure is. We then explore, again on the basis of our model and using agent-based simulations, under which conditions it is better epistemically to deliberate than to vote. Our analysis shows that there are contexts in which deliberation is epistemically preferable and we will provide reasons for why this is so.

Endogenous competence and a limit to the Condorcet Jury Theorem

The seminal contribution known as the Condorcet Jury Theorem observes that under a specific set of conditions an increase in the size of a group tasked with making a binary decision (“guilty or “innocent, say) leads to an improvement in the group’s ability to make the correct choice. An assumption that is not properly appreciated in the relevant literature is that the competency of the group members is assumed to be exogenous. In numerous applications, members of the group make investments to improve the accuracy of their decision making (e.g., pre-meeting efforts). We consider the collective action problem that arises. We show that if individual competence is endogenous, then increases in the group size encourages free riding. This trades off with the value of information aggregation. Thus, the value of the larger group size is muted. Extensions illustrate that if committee members are allowed to exit/not participate, the equilibrium committee size is reduced. Additionally, supermajority voting rules encourage investments and, consequently, individual competence.

Condorcet meets Ellsberg

The Condorcet Jury Theorem states that given subjective expected utility maximization and common values, the equilibrium probability that the correct candidate wins goes to one as the size of the electorate goes to infinity. This paper studies strategic voting when voters have pure common values but may be ambiguity averse -- exhibit Ellsberg-type behavior -- as modeled by maxmin expected utility preferences. It provides sufficient conditions so that the equilibrium probability of the correct candidate winning the election is bounded above by one half in at least one state. As a consequence, there is no equilibrium in which information aggregates.

On Solving the Problem of Identifying Unreliable Sensors Without a Knowledge of the Ground Truth: The Case of Stochastic Environments.

The purpose of this paper is to propose a solution to an extremely pertinent problem, namely, that of identifying unreliable sensors (in a domain of reliable and unreliable ones) without any knowledge of the ground truth. This fascinating paradox can be formulated in simple terms as trying to identify stochastic liars without any additional information about the truth. Though apparently impossible, we will show that it is feasible to solve the problem, a claim that is counter-intuitive in and of itself. One aspect of our contribution is to show how redundancy can be introduced, and how it can be effectively utilized in resolving this paradox. Legacy work and the reported literature (for example, in the so-called weighted majority algorithm) have merely addressed assessing the reliability of a sensor by comparing its reading to the ground truth either in an online or an offline manner. Unfortunately, the fundamental assumption of revealing the ground truth cannot be always guaranteed (or even expected) in many real life scenarios. While some extensions of the Condorcet jury theorem [9] can lead to a probabilistic guarantee on the quality of the fused process, they do not provide a solution to the unreliable sensor identification problem. The essence of our approach involves studying the agreement of each sensor with the rest of the sensors, and not comparing the reading of the individual sensors with the ground truth-as advocated in the literature. Under some mild conditions on the reliability of the sensors, we can prove that we can, indeed, filter out the unreliable ones. Our approach leverages the power of the theory of learning automata (LA) so as to gradually learn the identity of the reliable and unreliable sensors. To achieve this, we resort to a team of LA, where a distinct automaton is associated with each sensor. The solution provided here has been subjected to rigorous experimental tests, and the results presented are, in our opinion, both novel and conclusive.

Quantitative Extensions of the Condorcet Jury Theorem with Strategic Agents

The Condorcet Jury Theorem justifies the wisdom of crowds and lays the foundations of the ideology of the democratic regime. However, the Jury Theorem and most of its extensions focus on two alternatives and none of them quantitatively evaluate the effect of agents’ strategic behavior on the mechanism’s truth-revealing power. We initiate a research agenda of quantitatively extend- ing the Jury Theorem with strategic agents by characterizing the price of anarchy (PoA) and the price of stability (PoS) of the common interest Bayesian voting games for three classes of mechanisms: plurality, MAPs, and the mechanisms that satisfy anonymity, neutrality, and strategy-proofness (w.r.t. a set of natural probabil- ity models). We show that while plurality and MAPs have better best-case truth-revealing power (lower PoS), the third class of mechanisms are more robust against agents’ strategic behavior (lower PoA).

Linking as voting: how the Condorcet jury theorem in political science is relevant to webometrics

A webmaster's decision to link to a webpage can be interpreted as a "vote" for that webpage. But how far does the parallel between linking and voting extend? In this paper, we prove several "linking theorems" showing that link-based ranking tracks importance on the web in the limit as the number of webpages grows, given independence and minimal linking competence. The theorems are similar in spirit to the voting, or jury, theorem famously attributed to the 18th century mathematician Nicolas de Condorcet. We argue that the linking theorems provide a fundamental epistemological justification for link-based ranking on the web, analogous to the justification that Condorcet's theorems bestow on majority voting as a basic democratic procedure. The analogy extends to the practical limitations facing both kinds of result, in particular due to limited voting/linking independence. However, we argue, referring to the theoretical developments inspired by the jury theorem, that some of the pessimism expressed in the webometrics literature regarding the possibility of a "theory of linking" may be unjustified. The present study connects the two academic disciplines of webometrics in information science and epistemic democracy in political science by showing how they share a common structure. As such, it opens up new possibilities for theoretical cross-fertilization and interdisciplinary transference of concepts and results. In particular, we show how the relatively young field of webometrics can benefit from the extensive and sophisticated literature on the Condorcet jury theorem.

The wisdom of crowds: What do citizens forecast for the 2015 British General Election?

Who do you think will win in your constituency? Most citizens correctly answer this question, and groups are even better at answering it. Combining individual forecasts results in the ‘wisdom of crowds’ explained by Condorcet's jury theorem. This paper demonstrates the accuracy of citizen forecasts in seven British General Elections between 1964 and 2010, and reports what citizens interviewed in February and March forecasted for the election in May 2015. ‘Citizen forecasting’ predicts vote shares and winners in constituency elections, and seat numbers and governments in national elections. The paper also introduces a new method for predicting vote shares from citizen forecasts. Citizen forecasts are direct, accurate, and comprehensible. Pollsters should collect them and communicate their results more often.

A Condorcet jury theorem for couples

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 \(2 \, N\) independent agents.

EPISTEMIC SOLIDARITY AS A POLITICAL STRATEGY

ABSTRACTSolidarity is supposed to facilitate collective action. We argue that it can also help overcome false consciousness. Groups practice ‘epistemic solidarity’ if they pool information about what is in their true interest and how to vote accordingly. The more numerous ‘Masses’ can in this way overcome the ‘Elites,’ but only if they are minimally confident with whom they share the same interests and only if they are (perhaps only just) better-than-random in voting for the alternative that promotes their interests. Being more cohesive and more competent than the Masses, the Elites can employ the same strategy perhaps all the more effectively. But so long as the Masses practice epistemic solidarity they will almost always win, whether or not the Elites do. By enriching the traditional framework of the Condorcet Jury Theorem with group-specific standards of correctness, we investigate how groups can organize to support the alternatives truly in their interests.

HOW TO CONDORCET A GOLDMAN

ABSTRACTIn 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.

Propaganda, ideology, and democracy: A review of Jason Stanley, How Propaganda Works

Propaganda, ideology, and democracy: A review of Jason Stanley, <i>How Propaganda Works</i>

Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation

Recent research on the Condorcet Jury Theorem has proven that informative voting (that is, voting according to one’s signal) is not necessarily rational. With two alternatives, rational voting typically leads to the election of the correct alternative, in spite of the fact that not all voters vote informatively. We prove that with three alternatives, there are cases in which informative voting is rational and yet leads to the election of a wrong alternative.

Are two interviewers better than one?

How many interviewers per job applicant are necessary for a company to achieve the highest hit rate? Are two better than one? Condorcet's Jury Theorem and the “wisdom of the crowd” suggest that more is better. Under quite general conditions this study shows, surprisingly, that two interviewers are on average not superior to the best interviewer. Adding further interviewers will also not increase the expected collective hit rate when interviewers are homogeneous (i.e., their hits are nested), only doing so when interviewers are heterogeneous (i.e., their hits are not nested). The current study shows how these results depend on the number of interviewers, their expertise, and the chance of free riding, and specify the conditions when “less is more”. This analysis suggests that the best policy is to invest resources into improving the quality of the best interviewer rather than distribute these to improve the quality of many interviewers.

Introducing difference into the Condorcet jury theorem

This paper explores the role that difference plays in collective decision-making using the Condorcet jury theorem. Agents facing a dichotomous decision might prove biased toward one of the options facing them. That is, they may be more likely to decide correctly when one of the options is correct than when the other option is. A juror might be more likely to convict a guilty defendant than to acquit an innocent one. Agents may display opposing biases. This paper identifies the optimal committee composition in the presence of such bias. This composition depends upon both the prior probability that each option is correct and the relative costs of the two types of possible error (e.g., convicting an innocent defendant versus acquitting a guilty one). Optimal committee composition will be expressed in terms of the absolute (not relative) margin that a group with one form of bias should enjoy over the other.

Monetary Policy Deliberations: Committee Size and Voting Rules

SummaryHow large should a monetary policy committee be? Which voting rule should a monetary policy committee adopt? This paper builds on Condorcet's jury theorem to analyse the relationships between committee size and voting rules in a model where policy discussions are subject to a time constraint. It suggests that in large committees majority voting is likely to enhance policy outcomes. Under unanimity (consensus) it is preferable to limit the size of the committee. Finally, supermajority voting rules are social contrivances that contribute to policy performance in a more uncertain environment, when initial policy proposals are less likely to be correct, or when payoffs are asymmetric.