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Title: Who Reviews The Reviewers? A Multi-Level Jury Problem
We investigate the problem of determining a binary ground truth using advice from a group of independent reviewers (experts) who express their guess about a ground truth correctly with some independent probability (competence) p_i. In this setting, when all reviewers are competent with p >= 0.5, the Condorcet Jury Theorem tells us that adding more reviewers increases the overall accuracy, and if all p_i's are known, then there exists an optimal weighting of the reviewers. However, in practical settings, reviewers may be noisy or incompetent, i.e., p_i < 0.5, and the number of experts may be small, so the asymptotic Condorcet Jury Theorem is not practically relevant. In such cases we explore appointing one or more chairs (judges) who determine the weight of each reviewer for aggregation, creating multiple levels. However, these chairs may be unable to correctly identify the competence of the reviewers they oversee, and therefore unable to compute the optimal weighting. We give conditions when a set of chairs is able to weight the reviewers optimally, and depending on the competence distribution of the agents, give results about when it is better to have more chairs or more reviewers. Through numerical simulations we show that in some cases it is better to have more chairs, but in many cases it is better to have more reviewers.  more » « less
Award ID(s):
2134857
NSF-PAR ID:
10480654
Author(s) / Creator(s):
; ;
Publisher / Repository:
arXiv Preprint Archive
Date Published:
Journal Name:
arXiv Preprint Archive
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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Method Participants completed six questionnaires (counterbalanced): Need for Cognition Scale (NCS; 18 items), Cognitive Reflection Test (CRT; 7 items), Abbreviated Numeracy Scale (ABS; 6 items), Scientific Reasoning Scale (SRS; 11 items), Trust in Science (TIS; 29 items), and Attitudes towards Science (ATS; 7 items). Participants then viewed a video depicting a civil trial in which the defendant sought damages from the plaintiff for injuries caused by a fall. The defendant (bar patron) alleged that the plaintiff (bartender) pushed him, causing him to fall and hit his head on the hard floor. Participants were informed at the outset that the defendant was liable; therefore, their task was to determine if the plaintiff should be compensated. Participants were randomly assigned to 1 of 6 experimental conditions: 2 (quality of scientific evidence: high vs. low) x 3 (safeguard to improve calibration: gist information, no-gist information [control], jury instructions). An expert witness (neuroscientist) hired by the court testified regarding the scientific strength of fMRI data (high [90 to 10 signal-to-noise ratio] vs. low [50 to 50 signal-to-noise ratio]) and gist or no-gist information both verbally (i.e., fairly high/about average) and visually (i.e., a graph). After viewing the video, participants were asked if they would like to award damages. If they indicated yes, they were asked to enter a dollar amount. Participants then completed the Positive and Negative Affect Schedule-Modified Short Form (PANAS-MSF; 16 items), expert Witness Credibility Scale (WCS; 20 items), Witness Credibility and Influence on damages for each witness, manipulation check questions, Understanding Scientific Testimony (UST; 10 items), and 3 additional measures were collected, but are beyond the scope of the current investigation. Finally, participants completed demographic questions, including questions about their scientific background and experience. 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There were no significant main effects or interactions for witness credibility, indicating that the expert that provided scientific testimony was seen as equally credible regardless of scientific quality or gist safeguard. Finally, for damages, consistent with hypotheses, there was a marginally significant interaction between Gist Safeguard and Scientific Quality, F(2, 273)=2.916, p=.056. However, post hoc t-tests revealed significantly higher damages were awarded for low (M=11.50) versus high (M=10.51) scientific quality evidence F(1, 273)=3.955, p=.048 in the no gist with judge instructions safeguard condition, which was contrary to hypotheses. The data suggest that the judge instructions alone are reversing the pattern, though nonsignificant, those who received the no gist without judge instructions safeguard awarded higher damages in the high (M=11.34) versus low (M=10.84) scientific quality evidence conditions F(1, 273)=1.059, p=.30. Together, these provide promising initial results indicating that participants were able to effectively differentiate between high and low scientific quality of evidence, though inappropriately utilized the scientific evidence through their inability to discern expert credibility and apply damages, resulting in poor calibration. These results will provide the basis for more sophisticated analyses including higher order interactions with individual differences (e.g., need for cognition) as well as tests of mediation using path analyses. [References omitted but available by request] Learning Objective: Participants will be able to determine whether providing jurors with gist information would assist in their ability to award damages in a civil trial. 
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  4. Abstract Expert testimony varies in scientific quality and jurors have a difficult time evaluating evidence quality (McAuliff et al., 2009). In the current study, we apply Fuzzy Trace Theory principles, examining whether visual and gist aids help jurors calibrate to the strength of scientific evidence. Additionally we were interested in the role of jurors’ individual differences in scientific reasoning skills in their understanding of case evidence. Contrary to our preregistered hypotheses, there was no effect of evidence condition or gist aid on evidence understanding. However, individual differences between jurors’ numeracy skills predicted evidence understanding. Summary Poor-quality expert evidence is sometimes admitted into court (Smithburn, 2004). Jurors’ calibration to evidence strength varies widely and is not robustly understood. For instance, previous research has established jurors lack understanding of the role of control groups, confounds, and sample sizes in scientific research (McAuliff, Kovera, & Nunez, 2009; Mill, Gray, & Mandel, 1994). Still others have found that jurors can distinguish weak from strong evidence when the evidence is presented alone, yet not when simultaneously presented with case details (Smith, Bull, & Holliday, 2011). This research highlights the need to present evidence to jurors in a way they can understand. Fuzzy Trace Theory purports that people encode information in exact, verbatim representations and through “gist” representations, which represent summary of meaning (Reyna & Brainerd, 1995). It is possible that the presenting complex scientific evidence to people with verbatim content or appealing to the gist, or bottom-line meaning of the information may influence juror understanding of that evidence. Application of Fuzzy Trace Theory in the medical field has shown that gist representations are beneficial for helping laypeople better understand risk and benefits of medical treatment (Brust-Renck, Reyna, Wilhelms, & Lazar, 2016). Yet, little research has applied Fuzzy Trace Theory to information comprehension and application within the context of a jury (c.f. Reyna et. al., 2015). Additionally, it is likely that jurors’ individual characteristics, such as scientific reasoning abilities and cognitive tendencies, influence their ability to understand and apply complex scientific information (Coutinho, 2006). Methods The purpose of this study was to examine how jurors calibrate to the strength of scientific information, and whether individual difference variables and gist aids inspired by Fuzzy Trace Theory help jurors better understand complicated science of differing quality. We used a 2 (quality of scientific evidence: high vs. low) x 2 (decision aid to improve calibration - gist information vs. no gist information), between-subjects design. All hypotheses were preregistered on the Open Science Framework. Jury-eligible community participants (430 jurors across 90 juries; Mage = 37.58, SD = 16.17, 58% female, 56.93% White). Each jury was randomly assigned to one of the four possible conditions. Participants were asked to individually fill out measures related to their scientific reasoning skills prior to watching a mock jury trial. The trial was about an armed bank robbery and consisted of various pieces of testimony and evidence (e.g. an eyewitness testimony, police lineup identification, and a sweatshirt found with the stolen bank money). The key piece of evidence was mitochondrial DNA (mtDNA) evidence collected from hair on a sweatshirt (materials from Hans et al., 2011). Two experts presented opposing opinions about the scientific evidence related to the mtDNA match estimate for the defendant’s identification. The quality and content of this mtDNA evidence differed based on the two conditions. The high quality evidence condition used a larger database than the low quality evidence to compare to the mtDNA sample and could exclude a larger percentage of people. In the decision aid condition, experts in the gist information group presented gist aid inspired visuals and examples to help explain the proportion of people that could not be excluded as a match. Those in the no gist information group were not given any aid to help them understand the mtDNA evidence presented. After viewing the trial, participants filled out a questionnaire on how well they understood the mtDNA evidence and their overall judgments of the case (e.g. verdict, witness credibility, scientific evidence strength). They filled this questionnaire out again after a 45-minute deliberation. Measures We measured Attitudes Toward Science (ATS) with indices of scientific promise and scientific reservations (Hans et al., 2011; originally developed by National Science Board, 2004; 2006). We used Drummond and Fischhoff’s (2015) Scientific Reasoning Scale (SRS) to measure scientific reasoning skills. Weller et al.’s (2012) Numeracy Scale (WNS) measured proficiency in reasoning with quantitative information. The NFC-Short Form (Cacioppo et al., 1984) measured need for cognition. We developed a 20-item multiple-choice comprehension test for the mtDNA scientific information in the cases (modeled on Hans et al., 2011, and McAuliff et al., 2009). Participants were shown 20 statements related to DNA evidence and asked whether these statements were True or False. The test was then scored out of 20 points. Results For this project, we measured calibration to the scientific evidence in a few different ways. We are building a full model with these various operationalizations to be presented at APLS, but focus only on one of the calibration DVs (i.e., objective understanding of the mtDNA evidence) in the current proposal. We conducted a general linear model with total score on the mtDNA understanding measure as the DV and quality of scientific evidence condition, decision aid condition, and the four individual difference measures (i.e., NFC, ATS, WNS, and SRS) as predictors. Contrary to our main hypotheses, neither evidence quality nor decision aid condition affected juror understanding. However, the individual difference variables did: we found significant main effects for Scientific Reasoning Skills, F(1, 427) = 16.03, p <.001, np2 = .04, Weller Numeracy Scale, F(1, 427) = 15.19, p <.001, np2 = .03, and Need for Cognition, F(1, 427) = 16.80, p <.001, np2 = .04, such that those who scored higher on these measures displayed better understanding of the scientific evidence. In addition there was a significant interaction of evidence quality condition and scores on the Weller’s Numeracy Scale, F(1, 427) = 4.10, p = .04, np2 = .01. Further results will be discussed. Discussion These data suggest jurors are not sensitive to differences in the quality of scientific mtDNA evidence, and also that our attempt at helping sensitize them with Fuzzy Trace Theory-inspired aids did not improve calibration. Individual scientific reasoning abilities and general cognition styles were better predictors of understanding this scientific information. These results suggest a need for further exploration of approaches to help jurors differentiate between high and low quality evidence. Note: The 3rd author was supported by an AP-LS AP Award for her role in this research. Learning Objective: Participants will be able to describe how individual differences in scientific reasoning skills help jurors understand complex scientific evidence. 
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