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)
In both Great Britain and the United States there has been a growing debate about the modern acceptability of jury nullification. Properly understood, juries do not have any constitutional right to ignore the law, but they do have the power to do so nevertheless. Juries that nullify may be motivated by a variety of concerns: too harsh sentences, improper government action, racism, etc. In this article, I shall attempt to defend jury nullification on a number of grounds. First, (...) I discuss the use of general verdicts and reject their replacement in criminal trials by special verdicts. Second, I examine verdicts based upon mistakes and racial prejudice, turning my attention to perverse verdicts and the question of whether or not juries are guilty of legislating when nullifying the law. Finally, I look at the problem of the awarding of excessive damages by juries. My goal will be to provide a sound theoretical defence of the practice of jury nullification. (shrink)
Many political theorists and philosophers use Condorcet's Jury Theorem to defend democracy. This paper illustrates an uncomfortable implication of Condorcet's Jury Theorem. Realistically, when the conditions of Condorcet’s Jury Theorem hold, even in very high stakes elections, having more than 100,000 citizens vote does no significant good in securing good political outcomes. On the Condorcet model, unless voters enjoy voting, or unless they produce some other value by voting, then the cost to most voters of voting exceeds (...) the expected epistemic benefits to the common good of their casting a vote. Anyone who is committed to democracy on the basis of the Jury Theorem ought also to hold that widespread voting is wasteful, at least unless she can provide some further justification of mass democratic participation. (shrink)
This article offers a justification for the continued use of jury trials. I shall critically examine the ability of juries to render just verdicts, judicial impartiality, and judicial transparency. My contention is that the judicial system that best satisfies these values is most preferable. Of course, these three values are not the only factors relevant for consideration. Empirical evidence demonstrates that juries foster both democratic participation and public legitimation of legal decisions regarding the most serious cases. Nevertheless, juries are (...) costly and, therefore, economically less efficient than competing modes of trial. I do not argue that all human beings possess an inalienable legal right to be tried by a jury. However, it is my hope that this analysis will make clear what we might gain or lose when we propose jury reforms. (shrink)
Condorcet's Jury Theorem shows that on a dichotomous choice, individuals who all have the same competence above 0.5, can make collective decisions under majority rule with a competence that approaches 1 as either the size of the group or the individual competence goes up. The theorem assumes that the probability of each voter's being correct is independent of the probability of any other voter being correct. Contrary to several authors, the presence of mutual or common influences such as opinion (...) leaders does not easily rule independence either in or out. Indeed, and this ought to be surprising,under certain conditions deference to opinion leaders can improve individual competence without violating independence, and so can raise group competence as well. (shrink)
Anglo-American theories of criminal responsibility require scholars to grapple with, inter alia, the relationship between the formal rule of law and the powers of the lay jury as well as two inherent ideas of freedom: freedom of the will and political liberty. Here, by way of canvassing my past work and prefiguring future work, I sketch some elements of the history of the Anglo-American jury and offer some glimpses of commentary on the interplay between the jury—particularly its (...) application of conventional morality to criminal judgments—and the formal rule of law of the state. My central intent is to pose questions for further study (by myself and others) regarding the historical behavior of the jury, the jury’s role in reinforcing notions of political liberty and free will, and, primarily, how scholarly conceptions of the jury’s role and behavior have informed elite theory regarding the justifications for imposing criminal responsibility. (shrink)
The Condorcet jury theorem (CJT) is based on the assumption of homogeneous voters who imperfectly know the correct policy. We reassess the validity of the CJT when voters are homogeneous and each knows the correct decision with an average probability of more than a half.
This paper proves two theorems for homogeneous juries that arise from different solutions to the problem of aggregation of dichotomous choice. In the first theorem, negative correlation increases the competence of the jury, while positive correlation has the opposite effect. An enlargement of the jury with positive correlation can be detrimental up to a certain size, beyond which it becomes beneficial. The second theorem finds a family of distributions for which correlation has no effect on a jury’s (...) competence. The approach allows us to compute the bounds on a jury’s competence as the maximum and minimum probability of it being correct for a given individual competence and dependence structure. (shrink)
In a homogeneous jury, in which each vote is correct with the same probability, and each pair of votes correlates with the same correlation coefficient, there exists a correlation-robust voting quota, such that the probability of a correct verdict is independent of the correlation coefficient. For positive correlation, an increase in the correlation coefficient decreases the probability of a correct verdict for any voting rule below the correlation-robust quota, and increases that probability for any above the correlation-robust quota. The (...)jury may be less competent under the correlation-robust rule than under simple majority rule and less competent under simple majority rule than a single juror alone. The jury is always less competent than a single juror under unanimity rule. (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: (i) whether a premise is justified depends on the notion of probability considered and (ii) none of the notions renders both premises simultaneously justified. Under the perhaps most interesting notions, the independence assumption should be weakened.
This article presents a generalization of the Condorcet Jury Theorem. All results to date assume a fixed value for the competence of jurors, or alternatively, a fixed probability distribution over the possible competences of jurors. In this article, we develop the idea that we can learn the competence of the jurors by the jury vote. We assume a uniform prior probability assignment over the competence parameter, and we adapt this assignment in the light of the jury vote. (...) We then compute the posterior probability, conditional on the jury vote, of the hypothesis voted over. We thereby retain the central results of Condorcet, but we also show that the posterior probability depends on the size of the jury as well as on the absolute margin of the majority. (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)
Despite the venerable place that "justice" occupies in social scientific theory and research, little effort has been made to see how members of society themselves define and use the concept when confronted with determining "what has happened" in some social arena, theorizing about why it happened, and deciding what should ensue. We take an ethnomethodological approach to justice, attempting to recover it as a feature of practical activity or a "phenomenon of order." Our analysis involves an actual videotaped jury (...) deliberation. In his classic study of decision making by juries, Garfinkel observed that jurors changed their reliance on commonsense reasoning very little, even though they were instructed to adhere to official and legal criteria for guilt. The vacillation between commonsense reasoning and using official criteria creates a tension; in our data this tension is manifested as the choice between adhering to law and procedural rules and providing "justice." By articulating this tension as a puzzle, several of the jurors prepare the way for using "justice," and then use this concept in formal ways which, along with other discursive patterns and strategies, constitute the deliberation as a structured, concerted activity. We show four stages in the use of the term justice as it is embedded in jurors' practical reasoning. (shrink)
This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) http://eprints.lse.ac.uk/705/. Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as any (...) other. The present chapter shows, in the three-option case, that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases. (shrink)
The availability of the defence of belief in consent under section 265(4) is a question of law, subject to review on appeal. The statutory provision is based on the common law rule that applies to all defences. Consideration of the defence when it is unavailable in law and failure to consider it when it is available are both incorrect. A judge is most likely to avoid error when ruling on availability of the defence if the ruling: (1) is grounded on (...) sound analysis of the substantive basis for the defence and its relationship to the principles of criminal responsibility; and (2) uses precise legal criteria to govern practical application of section 265(4) to the evidence in specific cases. The guidelines proposed in Part I are based on analyses of the substantive defence and culpable awareness and were developed to ensure that appropriate criteria are properly used when section 265(4) is applied. When a trial judge rules that the defence is available in law, the trier of fact must determine whether the defence is available on the facts as found, based on the evidence in the case. The model jury instructions proposed in Part II are designed to ensure that deliberations by the trier of fact are also guided and shaped by appropriate legal criteria. At both stages, the objective is to ground the deliberation process on fact, not fiction, and to regulate the exculpatory effect of the defence by using legal norms to exclude excuses based on extra-legal considerations such as sexual/racial fantasy, stereotype and myth, or community attitudes and custom. (shrink)
It is often claimed that opinions are more likely to be correct if they are held independently by many individuals. But what does it mean to hold independent opinions? To clarify this condition, we distinguish four notions of probabilistic opinion independence. Which notion applies depends on environmental factors such as commonly perceived evidence. More formally, it depends on the causal network that determines how people interact and form their opinions. In a general theorem, we identify conditions on this network that (...) guarantee the four notions of opinion independence. Our results have implications for ‘wisdom of crowds’ arguments, as we illustrate with old and new jury theorems. (shrink)
In this paper, I have analyzed the right to trial by jury in civil cases as reflected in decisions of the Michigan Supreme Court over approximately a 20 year period dealing with three areas affecting the right to trial by jury in civil cases: (1) entitlement to a jury trial; (2) summary disposition; and (3) directed verdicts. The study was constructed to cover cases over a substantial period of time, so that it would be possible to analyze (...) whether the changing composition of the Michigan Supreme Court, beginning in the late 1990's, impacted on the Court's decisions in these three areas.The conclusion that emerges from the is that the Court, as currently constituted, has diminished the right to trial by jury in civil cases in Michigan. The Court is more inclined than it was prior to 1999 to hold in more cases that there is no genuine issue of material fact, justifying summary disposition, and has now heard cases in which it has held that the defendant is entitled to a directed verdict. And the fact that the Court is more inclined to uphold the granting of summary disposition and directed verdicts is likely to have a demonstrable impact on these kinds cases when they are presented to the Court of Appeals and the trial courts. These courts, following the precedents of the Supreme Court and the results of the cases coming before that Court, will be more likely to rule in favor of granting motions for summary disposition and motions for directed verdicts.Given the Court's view of the diminished role of the jury in resolving factual disputes in civil cases, litigating lawyers must make the best of a bad situation and do everything that they can in order to protect the right to trial by jury in civil cases. They must try to ensure in the early stages of the litigation that their cases are strong enough to survive a motion for summary disposition and get to the jury, and at the trial they must make a determined effort to present sufficient evidence to survive a directed verdict. Hopefully the Court's view of the diminished role of the jury will not have dealt a fatal blow to the right to trial by jury in civil cases in Michigan. Time will tell how well the lawyers of Michigan have succeeded in preserving this fundamental constitutional right. (shrink)
Even though he is mainly known for his concept of constituent power, Sieyès was one of the first constitutional theorists to ask for a guardian of the constitution which closely resembles contemporary constitutional courts. This article reconstructs the main tenets of his proposal, puts them in the larger context of his constitutional theory and then assesses the constitutional nature and functions of this institution. The judgment is mixed: as an organ, Sieyès’ constitutional jury is a hybrid institution, neither a (...) real third chamber nor a full-fledged constitutional court; however, its functions not only are a clear anticipation of the control of constitutionality, but are also intended to tame constituent power and to protect the rights of man in case of legal gaps. (shrink)
This paper shows that the problem of treating people as equals in a world marked by deep-seated and, often, recalcitrant inequalities has implications for the way we approach the provision of security and justice. On the one hand, it means that racial profiling will generally be unjustified even when it might promote collective interests in security, on the other, it means that we should strive to create racially mixed juries, even in cases where defendant and alleged-victim are of the same (...) race. The paper examines a recent report on race and jury trials in the United Kingdom and concludes that, despite the author's claims that all-white juries are fair, the data shows the complex ways in which racial differences are translated into unjustified and arbitrary inequalities. Hence, it concludes, racially mixed juries are desirable, and sometimes necessary for justice, though probably not sufficient. (shrink)
In The Social Contract, Rousseau asserts his infallibility thesis: that the general will can never err, and that one's position in the minority indicates that what one took the general will to be was not actually so. Several theorists have argued that the Condorcet Jury Theorem, which states that in a sufficiently large group the majority opinion on a yes/no question is highly likely to be correct, provides a way to interpret and justify Rousseau's bold claim. I argue that (...) the Jury Theorem cannot be used to interpret the infallibility thesis, since Rousseau takes the majority opinion to be constitutive, and not merely strong evidence, of the content of the general will. Since there is no standard of correctness that is independent of the majority opinion, the Jury Theorem cannot be invoked to support Rousseau's claim. I suggest a different strategy for situating the infallibility thesis in The Social Contract. (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)
Suppose a committee or a jury confronts a complex question, the answer to which requires attending to several sub-questions. Two different voting procedures can be used. On one, the committee members vote on each sub-question and the voting results are used as premises for the committee’s conclusion on the main issue. This premise-based procedure can be contrasted with the conclusion-based approach, which requires the members to directly vote on the conclusion, with the vote of each member being guided by (...) her views on the relevant sub-questions. The two procedures are not equivalent: There may be a majority of voters supporting each of the premises, but if these majorities do not significantly overlap, there will be a majority against the conclusion. Pettit (2001) connects the choice between the two procedures with the discussion of deliberative democracy. The problem we want to examine instead concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. Which of them is better when it comes to tracking truth? As it turns out, the answer is not univocal. On the basis of Condorcet’s jury theorem, the premise-based procedure can be shown to be superior if the objective is reach truth for the right reasons, without making any mistakes on the way. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be cases in which using the conclusion-based procedure turns out to be more reliable, even though, for the most part, the premise-based procedure will retain its superiority. (shrink)
Truth is a fundamental objective of adjudicative processes; ideally, substantive as distinct from formal legal truth. But problems of evidence, for example, may frustrate finding of substantive truth; other values may lead to exclusions of probative evidence, e.g., for the sake of fairness. Jury nullification and jury equity. Limits of time, and definitiveness of decision, require allocation of burden of proof. Degree of truth-formality is variable within a system and across systems.
Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a (...) state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before. (shrink)
The standard epistemic justification for inclusiveness in political decision making is the Condorcet Jury Theorem, which states that the probability of a correct decision using majority rule increases in group size (given certain assumptions). Informally, majority rule acts as a mechanism to pool the information contained in the judgements of individual agents. I aim to extend the explanation of how groups of political agents track the truth. Before agents can pool the information, they first need to find truth-conducive information. (...) Increasing group size is also important in the initial search for truth-conducive information. (shrink)
that a defendant is guilty (a patient has condition C), and the evidence E that a majority of h out of n independent jurors (diagnostic tests) have voted for H, and a minority of k n – h against H. How likely is the majority verdict to be correct? By Condorcet's formula, the probability that H is true given E depends only on each juror's competence and on the absolute margin between the majority and the minority h – k, but (...) neither on the number n, nor on the proportion h/n. This paper reassesses that result and explores its implications. First, using the classical Condorcet jury model, I derive a more general version of Condorcet's formula, confirming the significance of the absolute margin, but showing that the probability that H is true given E depends also on an additional parameter: the prior probability that H is true. Second, I show that a related result holds when we consider not the degree of belief we attach to H given E, but the degree of support E gives to H. Third, I address the implications for the definition of special majority voting, a procedure used to capture the asymmetry between false positive and false negative decisions. I argue that the standard definition of special majority voting in terms of a required proportion of the jury is epistemically questionable, and that the classical Condorcet jury model leads to an alternative definition in terms of a required absolute margin between the majority and the minority. Finally, I show that the results on the significance of the absolute margin can be resisted if the so-called assumption of symmetrical juror competence is relaxed. Introduction The classical Condorcet jury model and the Condorcet jury theorem The significance of the absolute margin for the degree of belief we attach to the hypothesis given the evidence The significance of the absolute margin for the degree of support the evidence gives to the hypothesis An implication for the definition of special majority voting 5.1 Making positive decisions if and only if the truth of the hypothesis is beyond any reasonable doubt 5.2 Tracking the truth in the limit 5.3 Summary The jury model without the assumption of symmetrical competence Concluding remarks. (shrink)
The paper explains and differentiates the concept of `fact' in the legal setting. Fact and evidence, fact/falsity distinguished; fact and law considered -- a real difference or a pragmatic device? Questions of fact and degree considered, in themselves and in the context of jury trial and of appeals. Primary fact, factual inferences from primary fact, questions of classification of fact are considered. Whether inference is supported by evidence, and whether classification is correct may be questions of law. Issues of (...) fact and opinion, fact and comment, relative to freedom of speech, defamation etc: no clear distinction available. Legal problems concerning absence of workable distinctions. (shrink)
How do laypeople sitting on a jury make determinations of expertise? How, if at all, can laypersons epistemically assess the expertise of an expert or rival experts? Given that the domains of expertise are quite technical, if laypersons are to adjudicate the various proposed and often conflicting claims of experts, they must be able to determine the reliability of the experts as well as the truth of their claims. One way to address these concems is to say that the (...) layperson needs to be in a position to make the determination herself. This view I will call individualism. Individualism maintains the burden of epistemic assessment is on the layperson, not on the expert. One such version of individualism is Jason Borenstein’s proposal as to what is needed for laypersons to make such an assessment. Borenstein’s proposal turns on the laypersons’ ability to understand the domain of expertise as well as the putative expert’s ability to satisfy a proficiency test. What I hope to show is that this proposal fails for two reasons. I argue that the move to proficiency tests does not warrant any layperson’s determination of truth or reliability and that given the limited epistemic abilities of laypersons they are not able to satisfy Borenstein’s proposed conditions for determination. (shrink)
The purpose of this paper is to consider Turing's two tests for machine intelligence: the parallel-paired, three-participants game presented in his 1950 paper, and the “jury-service” one-to-one measure described two years later in a radio broadcast. Both versions were instantiated in practical Turing tests during the 18th Loebner Prize for artificial intelligence hosted at the University of Reading, UK, in October 2008. This involved jury-service tests in the preliminary phase and parallel-paired in the final phase.
The presumption of innocence undergirds the American criminal justice system. It is so fundamental that it is derived from the concepts of due process and the importance of a fair trial. An informed, historical understanding of the interaction between the presumption of innocence and key tenets of due process can help clarify the meaning and application of the presumption of innocence in the modern day. Due process, as developed throughout English and US. Colonial history leading up to the formation of (...) the US. Constitution, has two important implications. First, due process provides a general guarantee of liberty against punishment or imprisonment without a fair trial. Second, due process requires that a jury, as opposed to a judge, determine the factual guilt of a defendant at trial. These two key tenets were historically fundamental to due process and should guide how the presumption of innocence impacts various stages of trial, including pretrial detention decisions and sentencing. Returning to a historical understanding of due process requires that judges not determine facts or punish individuals before a trial has occurred. (shrink)
In this essay, I suggest that the criminal trial is not only about the guilt or innocence of the defendant, but also about the character and growth of the jurors and the communities they represent. In earlier work, I have considered the potential impact of law and politics on the character of citizens, and thus on the capacity of citizens to thrive—to live full and rich human lives. Regarding the jury, I have argued that aspects of criminal trial procedure (...) work to fix in jurors a sense of agency in and responsibility for verdicts of conviction. Here, I draw on those ideas with respect to the presumption of innocence. I suggest that the presumption of innocence works not primarily as legal rule, but rather as a moral framing device—a sort of moral discomfort device—encouraging jurors to feel and bear the weight of what they do. I offer an account of character development in which virtues are conceived of not merely as modes of conduct developed through habituation and practice, but also as capacities and ways of being developed in part through understanding and experience. The criminal trial, framed by the presumption of innocence, can be an experience through which jurors and their communities, by learning what it means and feels like to carry a certain sort of moral weight, may engender a certain set of moral strengths—strengths valuable to them not just as jurors, but also as citizens, and as human beings. (shrink)
A donation paradox occurs when a player gives an apparently valuable prerogative to another player, but âdoes betterâ, according to some criterion. Peremptory challenges, used in choosing a American jury, permit each side to veto a certain number of potential jurors. With even a very simple model of jury selection, it is shown that for one side to give a peremptory challenge to the other side may lead to a more favorable jury, an instance of the donation (...) paradox. Both a theorem and examples are given concerning the existence of the donation paradox in the optimal use of peremptory challenges. (shrink)