The Conjunction Problem and the Logic of Jury Findings

For several decades, evidence theorists have puzzled over the following paradox, known as the “conjunction paradox” or “conjunction problem.” Probability theory appears to tell us that the probability of a conjunctive claim is the product resulting from multiplying the probabilities of its separate conjuncts. In a three element negligence case (breach of duty, causation, damages), a plaintiff who proves each element to a 0.6 probability will have proven her overall claim to a very low probability of 0.216. Either the plaintiff wins the verdict based on this low probability (if the jury focuses on elements), or the plaintiff loses despite having met the condition of proving each element to the stated threshold. To solve this “conjunction problem,” evidence theorists have advanced such proposals as changing the rules of probability, barring probability theory entirely from analysis of adjudicative fact-finding, abandoning the procedural principle that the defendant need not present a narrative of innocence or nonliability, or dispensing with the requirement that the overall claim meet an established burden of proof. This Article argues that the conjunction paradox in fact presents a theoretical problem of little if any consequence. Dropping the condition that proving each element is a sufficient, as opposed to merely a necessary, condition for proof of a claim makes the conjunction problem disappear. Nothing in logic or probability theory requires this “each element/sufficiency” condition, and the legal decision rules reflected in most jury instructions do not mandate it. Once this “each element/sufficiency” condition is removed, all that is left of the conjunction problem is a “probability gap,” an intuitive but ill-founded impression that the mathematical underpinnings of the conjunction problem are unfair to claimants. This probability gap is considerably narrowed by recognizing the probabilistic dependence of most facts internal to a given claim, and by applying the correct multiplication rule for probabilistically dependent events. Finally, this Article argues that solving the conjunction problem is an insufficient ground either to abandon probability theory as a useful analytical tool in the context of adjudicative fact-finding, or to reform decision rules for trial fact-finders

Appendix: Conjunction-Problem v. Non-Conjunction-Problem Jurisdictions

This appendix presents the relevant data from our survey of jury instructions in support of the article in the print edition of the William & Mary Law Review. The Conjunction Problem and the Logic of Jury Findings (59 Wm. & Mary L. Rev. 619, 673-87 (2017)

Investigation, Development, and Evaluation of Performance Proving for Fault-tolerant Computers

A number of methodologies for verifying systems and computer based tools that assist users in verifying their systems were developed. These tools were applied to verify in part the SIFT ultrareliable aircraft computer. Topics covered included: STP theorem prover; design verification of SIFT; high level language code verification; assembly language level verification; numerical algorithm verification; verification of flight control programs; and verification of hardware logic

Assessment of Offshore Wind Energy Potential in the United States (Poster)

The development of an offshore wind resource database is one of the first steps necessary to understand the magnitude of the resource and to plan the distribution and development of future offshore wind power facilities. The U.S. Department of Energy supported the production of offshore wind resource maps and potential estimates for much of the United States. This presentation discusses NREL's 2010 offshore wind resources report; current U.S., regional, and state offshore maps; methodology for the wind mapping and validation; wind potential estimates; the Geographic Information Systems database; and future work and conclusions

The American Association for the Surgery of Trauma renal injury grading scale: Implications of the 2018 revisions for injury reclassification and predicting bleeding interventions.

BackgroundIn 2018, the American Association for the Surgery of Trauma (AAST) published revisions to the renal injury grading system to reflect the increased reliance on computed tomography scans and non-operative management of high-grade renal trauma (HGRT). We aimed to evaluate how these revisions will change the grading of HGRT and if it outperforms the original 1989 grading in predicting bleeding control interventions.MethodsData on HGRT were collected from 14 Level-1 trauma centers from 2014 to 2017. Patients with initial computed tomography scans were included. Two radiologists reviewed the scans to regrade the injuries according to the 1989 and 2018 AAST grading systems. Descriptive statistics were used to assess grade reclassifications. Mixed-effect multivariable logistic regression was used to measure the predictive ability of each grading system. The areas under the curves were compared.ResultsOf the 322 injuries included, 27.0% were upgraded, 3.4% were downgraded, and 69.5% remained unchanged. Of the injuries graded as III or lower using the 1989 AAST, 33.5% were upgraded to grade IV using the 2018 AAST. Of the grade V injuries, 58.8% were downgraded using the 2018 AAST. There was no statistically significant difference in the overall areas under the curves between the 2018 and 1989 AAST grading system for predicting bleeding interventions (0.72 vs. 0.68, p = 0.34).ConclusionAbout one third of the injuries previously classified as grade III will be upgraded to grade IV using the 2018 AAST, which adds to the heterogeneity of grade IV injuries. Although the 2018 AAST grading provides more anatomic details on injury patterns and includes important radiologic findings, it did not outperform the 1989 AAST grading in predicting bleeding interventions.Level of evidencePrognostic and Epidemiological Study, level III

International criteria for electrocardiographic interpretation in athletes: Consensus statement.

Sudden cardiac death (SCD) is the leading cause of mortality in athletes during sport. A variety of mostly hereditary, structural or electrical cardiac disorders are associated with SCD in young athletes, the majority of which can be identified or suggested by abnormalities on a resting 12-lead electrocardiogram (ECG). Whether used for diagnostic or screening purposes, physicians responsible for the cardiovascular care of athletes should be knowledgeable and competent in ECG interpretation in athletes. However, in most countries a shortage of physician expertise limits wider application of the ECG in the care of the athlete. A critical need exists for physician education in modern ECG interpretation that distinguishes normal physiological adaptations in athletes from distinctly abnormal findings suggestive of underlying pathology. Since the original 2010 European Society of Cardiology recommendations for ECG interpretation in athletes, ECG standards have evolved quickly, advanced by a growing body of scientific data and investigations that both examine proposed criteria sets and establish new evidence to guide refinements. On 26-27 February 2015, an international group of experts in sports cardiology, inherited cardiac disease, and sports medicine convened in Seattle, Washington (USA), to update contemporary standards for ECG interpretation in athletes. The objective of the meeting was to define and revise ECG interpretation standards based on new and emerging research and to develop a clear guide to the proper evaluation of ECG abnormalities in athletes. This statement represents an international consensus for ECG interpretation in athletes and provides expert opinion-based recommendations linking specific ECG abnormalities and the secondary evaluation for conditions associated with SCD

Anthropic predictions for vacuum energy and neutrino masses in the light of WMAP-3

Anthropic probability distributions for the cosmological constant and for the sum of neutrino masses are updated using the WMAP-3 data release. The new distribution for Lambda is in a better agreement with observation than the earlier one. The typicality of the observed value, defined as the combined probability of all values less likely than the observed, is no less than 22%. We discuss the dependence of our results on the simplifying assumptions used in deriving the distribution for Lambda and show that the agreement of the anthropic prediction with the data is rather robust. The distribution for the sum of the neutrino masses is peaked at 1 eV, suggesting degenerate masses, but a hierarchical mass pattern is still marginally allowed at a 2 sigma level.Comment: References added; 11 pages, 6 figure

Varespladib and cardiovascular events in patients with an acute coronary syndrome: the VISTA-16 randomized clinical trial

IMPORTANCE: Secretory phospholipase A2(sPLA2) generates bioactive phospholipid products implicated in atherosclerosis. The sPLA2inhibitor varespladib has favorable effects on lipid and inflammatory markers; however, its effect on cardiovascular outcomes is unknown. OBJECTIVE: To determine the effects of sPLA2inhibition with varespladib on cardiovascular outcomes. DESIGN, SETTING, AND PARTICIPANTS: A double-blind, randomized, multicenter trial at 362 academic and community hospitals in Europe, Australia, New Zealand, India, and North America of 5145 patients randomized within 96 hours of presentation of an acute coronary syndrome (ACS) to either varespladib (n = 2572) or placebo (n = 2573) with enrollment between June 1, 2010, and March 7, 2012 (study termination on March 9, 2012). INTERVENTIONS: Participants were randomized to receive varespladib (500 mg) or placebo daily for 16 weeks, in addition to atorvastatin and other established therapies. MAIN OUTCOMES AND MEASURES: The primary efficacy measurewas a composite of cardiovascular mortality, nonfatal myocardial infarction (MI), nonfatal stroke, or unstable angina with evidence of ischemia requiring hospitalization at 16 weeks. Six-month survival status was also evaluated. RESULTS: At a prespecified interim analysis, including 212 primary end point events, the independent data and safety monitoring board recommended termination of the trial for futility and possible harm. The primary end point occurred in 136 patients (6.1%) treated with varespladib compared with 109 patients (5.1%) treated with placebo (hazard ratio [HR], 1.25; 95%CI, 0.97-1.61; log-rank P = .08). Varespladib was associated with a greater risk of MI (78 [3.4%] vs 47 [2.2%]; HR, 1.66; 95%CI, 1.16-2.39; log-rank P = .005). The composite secondary end point of cardiovascular mortality, MI, and stroke was observed in 107 patients (4.6%) in the varespladib group and 79 patients (3.8%) in the placebo group (HR, 1.36; 95% CI, 1.02-1.82; P = .04). CONCLUSIONS AND RELEVANCE: In patients with recent ACS, varespladib did not reduce the risk of recurrent cardiovascular events and significantly increased the risk of MI. The sPLA2inhibition with varespladib may be harmful and is not a useful strategy to reduce adverse cardiovascular outcomes after ACS. TRIAL REGISTRATION: clinicaltrials.gov Identifier: NCT01130246. Copyright 2014 American Medical Association. All rights reserved

Gender differences in developmental links between antisocial behavior, friends' antisocial behavior and peer rejection in childhood: Results in two cultures

This study addressed gender differences in the developmental links among antisocial behavior, friends' anti-social behavior, and peer rejection. High and increasing, moderate, and low antisocial developmental trajectories were identified among 289 Dutch children, ages 7 to 10, and 445 French-Canadian children, ages 9 to 12. Only boys followed the high trajectory. These boys had more deviant friends and were more often rejected than other children. A minority of girls followed the moderate antisocial behavior trajectory. These girls had fewer deviant friends than moderate antisocial boys, but moderate antisocial boys and girls were equally likely to be rejected. The influence of friends and poor peer relations plays a crucial but different role in the development of antisocial behavior among boys and girls. © 2005 by the Society for Research in Child Development, Inc. All rights reserved