Jury Size Research Articles

Informing reform: The views of legal professionals on the unique aspects of Scottish Law.

The unique Scottish legal system stands apart from the better-known Anglo-American legal system, with variations relating to jury size (15 vs. 12), the number of verdicts available (3 vs. 2) and majority size (simple majority vs. unanimous). At present, only a handful of investigations have explored the effects of the Scottish ‘not proven’ verdict on jurors, and only a single study has explored the combined impact of the unique elements of the Scottish legal system on juror and jury decision making. The current study is the first to investigate the views of Scottish legal professionals on the three-verdict system, 15-person jury and simple majority verdict system. The aim of the study is to inform public and political debate, involve legal stakeholders in policy changes and decision making and compare legal professionals’ views with findings from previously conducted juror studies. Seventy-eight legal professionals took part in an online survey which asked for ratings and open responses on their attitudes to the Scottish (a) three-verdict system, (b) 15-person jury and (c) simple majority system. The results highlighted strong positive attitudes towards the ‘not proven’ verdict (particularly in a binary-verdict system of proven and not proven), 15-person juries and both the simple and qualified majority verdict systems. There was minimal support for reform towards an Anglo-American system. Instead, the reforms preferred by the legal professionals would be to require a qualified majority of 12/15 jurors, and to use a binary-verdict system of proven and not proven.

Optimizing Voting Order on Sequential Juries: A Sealed Card Model

The celebrated Jury Theorem of Condorcet (1785) considered an odd size jury in which jurors vote simultaneously after receiving independent signals, correct with the same probability p > 1/2, concerning which of two binary possibilities (maybe innocent or guilty) is true. The reliability of the majority verdict, the probability it is correct goes to 1 as the jury size tends to infinity. Recently, Alpern and Chen (2017a) considered a variation of the Condorcet model in which jurors vote sequentially (rather than simultaneously), with knowledge of prior voting. In addition, jurors are heterogeneous in a quality called ability, which affects the usefulness of their signals for predicting the true possibility. Their notion of ability was abstract, modeling for example eyesight quality for jurors making line calls in tennis. For a jury of size three of given distinct abilities, they found that reliability was order dependent and maximized when jurors vote as follows: first the juror of median ability, then of high ability, then of low ability. This paper makes the notion of ability concrete, with a different signal distribution than Alpern-Chen. A (sealed) card is removed from a deck of m red and m black cards. Each juror draws a number of cards equal to his integer-valued ability and votes for the color of the sealed card, based on his draw and prior voting. We find that the Alpern-Chen (median-high-low) ordering has the highest reliability in most cases, and it generally is also better than simultaneous voting. In the cases where the latter is better, the abilities of the jurors tend to be similar. An analog of this ordering has high reliability for larger juries.

Feddersen and Pesendorfer meet Ellsberg

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis (Theor Econo 11(3): 865–895, 2016) shows that when voters have ambiguous prior beliefs—a (closed, convex) set of priors—and follow maxmin expected utility (MEU), such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error (such as conviction in jury trials). In a classical model, Feddersen and Pesendorfer (Am Politi Sci Rev 92(1):23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis (Theor Econo 11(3): 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals.

The Cayman Islands: Paradoxes of Insularity in the Caribbean and Other British Overseas Territories

The Cayman Islands has a population of 63,415 (Cayman Islands Government) and an area of 264 square kilometres, making it the world’s twentieth smallest nation or territory by geographical area and 35th smallest by population (United Nations Statistics Division). As a British Overseas Territory in the Caribbean, there exist many connections to other parts of the world that are geographical, legal and socio-political; yet the Cayman Islands and other such territories exhibit traits that may be described as insular or openly international. The British Overseas Territories amount to 14 distinct and effectively self-governing territories that are spread across the globe. Indeed, of the 50 remote islands gazetted by Schalansky (Atlas of remote Islands: Fifty Islands I have never set foot on and never will, Penguin Books, London, 2010), 20 of these islands share a heritage with the former British Empire and, for those with a population and operant legal system, they share the basic underpinning of the English common law [Eight are, or have been, part of a British Overseas Territory; 12 are part of a Commonwealth Nation with the UK monarch as the head of state (aside from Banaba Island in Kiribati which is a presidential republic but still a member of the Commonwealth of Nations)]. Whilst geographically remote, the British Overseas Territories share a direct connection with elements of supervisory governance (as did the now independent Commonwealth Nations) still exercisable by the UK’s Government in London, UK. This article will explore the provision of legal education, the diversity of the judiciary and the issues associated with jury size, juror selection and fair, impartial decision making in the Cayman Islands in order to explore the concepts of insularity, internal connectivity and remoteness in law for this particular British Overseas Territory (further references in the text, abbreviated as BOT).

Accuracy of Verdicts under Different Jury Sizes and Voting Rules

Juries are a fundamental element of the criminal justice system. In this article, we model jury decision making as a function of two institutional variables: jury size and voting requirement. We ex...

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A functional equation of tail-balance for continuous signals in the Condorcet Jury Theorem

Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Imprim. Royale, Paris, 1785). Recently, Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) developed a model where jurors sequentially receive independent signals from an interval according to a distribution which depends on the state of Nature and on the juror’s “ability”, and vote sequentially. This paper shows that, to mimic Condorcet’s binary signal, such a distribution must satisfy a functional equation related to tail-balance, that is, to the ratio alpha (t) of the probability that a mean-zero random variable satisfies X>t given that |X|>t. In particular, we show that under natural symmetry assumptions the tail-balances alpha (t) uniquely determine the signal distribution and so the distributions assumed in Alpern and Chen (Eur J Oper Res 258:1072–1081, 2017, Theory Decis 83:259–282, 2017) are uniquely determined for alpha (t) linear.

A numerical study on efficient jury size

For judicial democracy, many societies adopt jury trials, where verdicts are made by a unanimous vote of, conventionally, 12 lay citizens. Here, using the majority-vote model, we show that such jury sizes achieve the best balance between the accuracy of verdicts and the time spent for unanimous decision-making. First, we identify two determinants of the efficient jury size: the opinion homogeneity in a community decreases the optimal jury size by affecting the accuracy of verdicts; the anti-conformity tendency in the community also reduces the efficient jury size by prolonging the time to reach unanimous verdicts. Moreover, we find an inverse correlation between these two determinants, which prevents over-shrinking and excessive expansion of the efficient jury size. Finally, by applying these findings into real-life settings, we narrow down the efficient jury size to 11.8 ± 3.0. Given that such a simple toy model can explain the jury sizes in the actual societies, the number of jurors may have been implicitly optimised for efficient unanimous decision-making throughout human history.

Should Jurors Deliberate?

AbstractDoes the accuracy of verdicts improve or worsen if individual jurors on a panel are barred from deliberating prior to casting their votes? I study this question in a model where jurors can choose to exert costly effort to improve the accuracy of their individual decisions. I find that, provided the cost of effort is not too large, it is better to allow jurors to deliberate if jury size exceeds a threshold. For panels smaller than this threshold, it is more effective to instruct jurors to vote on the basis of their private information, without deliberations, and to use a simple majority rule to determine the collective decision (regardless of the voting rule used with deliberations). The smaller the cost of paying attention, the larger the threshold above which the switch to allowing deliberations becomes optimal. However, if the unanimity rule had to be maintained under the no-deliberations system, it would be better to allow deliberation. The results apply to binary decision making in any committee where the committee members incur some effort in reviewing the evidence. Examples are arbitration panels and tenure and promotion committees and some board of director meetings on issues such as whether to dismiss a CEO. As an extension I consider the case where jurors differ in their costs of effort.

Jury Size and Voting Requirements for Criminal Convictions: Assessing the Tradeoffs

Juries are a fundamental element of the criminal justice system. In this article, we model jury decision making as a function of two institutional variables: jury size and voting requirement. We expose the critical interdependence of these two elements in minimizing the probabilities of wrongful convictions, of wrongful acquittals, and of hung juries. We find that the use of either large nonunanimous juries or small unanimous juries offers alternative ways to maximize the accuracy of verdicts while preserving the functionality of juries. Our framework, which lends support to the elimination of the unanimity requirement in the presence of large juries, helps appraise US Supreme Court decisions and state legal reforms that have transformed the structure of American juries.

Secret ballots and costly information gathering: The jury size problem revisited

Suppose paying attention during jury trials is costly, but that jurors do not pool information (as in contemporary Brazil, or ancient Athens). If inattentive jurors are as likely to be wrong as right, I find that small jury panels work better as long as identical jurors behave symmetrically. If not paying attention makes error more likely than not, jurors may coordinate on two different symmetric outcomes: a “high attention” one or a “low attention” one. If social norms stigmatize shirking, jurors coordinate on the high attention equilibrium, and a smaller jury yields better outcomes. However, increasing the jury up to a finite bound works better if norms are tolerant of shirking, in which case coordination on the low attention outcome results. If jurors always act as if they are pivotal, a larger jury may work better. Allowing deliberations is efficient if the jury panel is relatively large, and if the police and prosecution are effective. However, barring deliberations is better at smaller jury sizes, specially if the police and prosecution are not too efficient.

Strategic Jury Selection Games A Theoretical Analysis

I consider a class of selection games where members of a group such as a jury, panel or committee, are to be selected from among a larger pool of individuals by two or more parties with non-aligned interests. Each party may exercise a limited number of vetoes, or challenges, against members who are found to be unfavorable. However, at the time of such a challenge, little may be known about potential replacements. I derive game theory based challenge strategies for single-seat juries and for multi-seat juries where jury utilities are separable functions of individual juror utility. I provide numerically derived optimal challenge thresholds and we show how these thresholds vary with jury size and with the number of challenges available to each party. Finally, using computer- simulated jury selections, I show that game theory based strategies perform significantly better than other challenge strategies commonly used in trials by jury.

Optimal Jury Design: Rethinking Standards of Proof, Jury Size and Voting Rules

Juries are a fundamental element of the criminal justice system. In this paper, we model jury decision-making as a function of three institutional variables: jury size, voting requirement, and the applicable standard of proof. Changes in jury size, voting requirements, and standards of proof affect the accuracy and cost of criminal adjudication. Our framework helps appraise some U.S. Supreme Court decisions and legal reforms on jury design. We find that the use of smaller or non-unanimous juries, if combined with a high standard of proof, may be superior to alternative jury structures. The results apply not only to juries, but also to other collective decision-making bodies such as court panels, corporate boards, and management teams.

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Deliberative Democracy and the American Civil Jury

Civil jury service should be a potent form of deliberative democracy, creating greater civic engagement. However, a 2010 seven‐state study of jury service and voting records found no overall boost in civic engagement following service on civil juries, whereas jurors who served on criminal cases did show increased civic engagement following their jury service. This article reports a project that augments the civil jury data set with information about jury decision rule, jury size, defendant identity, and case type and examines whether specific types of civil jury service influence postservice voting. Taking into account preservice voting records, jurors who serve on a civil jury that is required to reach unanimity or a civil jury of 12 are significantly more likely to vote after their service. Jurors who decide cases with organizational, as opposed to individual, defendants likewise show a boost in voting behavior, as do jurors deciding contract or nonautomotive torts cases compared to automotive torts. Limitations and implications of these findings for deliberative democracy theory and jury practice are discussed.

THE PROBABILITY OF A GUILTY VERDICT IN CRIMINAL TRIALS

ABSTRACT The general role of a judge is that of having the responsibility for interpreting the appropriate law in question and on occasions in higher level cases of importance there will be a panel of judges, usually 3, 5, 7 or even 9. Sometimes the accused can even select for their case to be heard by a single judge or a jury. The first part of this paper deals with the change in a probability of the outcome based on the size of the judicial panel and whether it is in the best interests of an accused or plaintiff to go for a single judge, a small panel or the largest possible jury size. The second part considers some jurisdictions worldwide in which varying types of majority verdicts can secure a conviction, rather than unanimous verdicts, and the effect on the probability of the defendant being found guilty. Keywords statistics, jury, judge, law, probability

Jury Size and the Hung-Jury Paradox

AbstractIn Williams v. Florida (399 U.S. 78 [1970]), the U.S. Supreme Court decided a case addressing the constitutionality of juries composed of fewer than 12 jurors, ruling that smaller juries are not inconsistent with the Sixth Amendment. In an effort to speed deliberation and reduce the rate of mistrials, 11 states have subsequently adopted juries of fewer than 12 in state felony trials, and 40 states have diminished their jury sizes for state misdemeanor trials. Curiously, however, contrary to the predictions of probability theory and common sense, these reductions in jury sizes have failed to deliver the expected reduction in mistrial rates. In this paper, we offer two interrelated explanations for this fact: informational cascades and the heterogeneity of jurors.

The Twelve-Person Federal Civil Jury in Exile

In the mid-1990s, the Advisory Committee on Civil Rules, with Fifth Circuit Judge Patrick Higginbotham as Chair and our honoree, Professor Ed Cooper, in the early years of his long service as Reporter, unanimously (coincidentally, by a 12-0 vote) proposed an amendment to Federal Rule of Civil Procedure 48 that would have required the seating of twelve-member juries in federal civil trials. The requirement of a unanimous verdict, unless waived by the parties, and the abolition of alternate jurors would have been unaffected; attrition could reduce a jury's size below twelve members, with a floor of six unless the parties consented to a verdict rendered by a smaller jury. The Standing Committee approved the final proposal by a wide margin, but the Judicial Conference rejected the change. As a member of the Advisory Committee at the time I was strongly persuaded that the amendment had merit and continue to feel that way, but must admit that the chances of a renewed proposal being adopted seem virtually nil no matter its merit. This brief account is, then, a lament rather than a call to action.

Communication compatible voting rules

We reassess the possibility of full information pooling in a Condorcet jury environment featuring heterogeneous and privately known preference types. We find that in general, with uncorrelated preference types, only very limited heterogeneity is compatible with full pooling. We provide a sufficient condition, based on a simple measure of preference misalignment, under which the set of voting rules compatible with full pooling is at most a singleton. As a caveat to any simplistic conclusions, we identify a case in which an increase in heterogeneity (i.e. polarization) systematically generates the possibility of full pooling. Increased jury size, in contrast, is shown to always render full pooling more difficult.

Jury Size and the Hung-Jury Paradox

In the United States, the 1970 Supreme Court decision Williams v. Florida 399 U.S. 78 (1970) reduced from twelve to six the minimum number of jurors required under the Sixth and Fourteenth Amendments. In the hope of improving the legal process with faster deliberation and fewer mistrials, eleven states have used juries of less than twelve in felony cases. This has given origin to an unprecedented natural experiment on jury decision-making. Contrary to the predictions of probability theory, the reduction in jury size has not brought the expected reduction in the number of mistrials. In this paper we provide a possible explanation for this fact. We formulate some propositions considering the case of jury deliberation in the presence of informational cascades. These results have implications not only for juries, but also for democratic theory.