统计信息越来越有可能在法庭上提供。It may appear in civil cases (e.g., percentages of men and women employees in a gender discrimination case) or criminal cases (e.g., the defendant’s blood type matches that of a sample found at the crime scene and that blood type is found in only 20% of the population). Can jurors understand that information on their own, or must they rely on experts to explain its meaning? Even if jurors correctly understand statistical evidence, how do they combine that evidence with other, nonquantitative evidence?
与陪审员理解的其他领域相反(例如,陪审员对影响目击者识别准确性的因素的信念),直接回答这些问题的研究相对较少。这些研究可以分为两个广泛的类别。第一个主要集中于对统计证据的理解。第二个询问统计证据如何与其他非统计证据相结合。考虑在一起,陪审员即使是单一的统计证据也很难理解。当面对两个统计证据时,这种困难会增加。与贝叶斯规范相比,即使有关于如何使用此类证据的说明,陪审员也倾向于统计证据不足。然而,这种情况无法掩盖相当大的差异。
陪审员对统计证据的理解
“裸统计”(有时称为基本费率)是真实的数据,无论在特定情况下发生了什么。与数学上等效的证据相比,模拟陪审员并非被裸统计的说服力,这些证据取决于某些最终事实(即,解决案件的事实)。例如,在蓝色公共汽车问题中,一辆公共汽车驶过一条色盲女人的狗。被告A公司拥有该地区80%的公共汽车,A公司的所有公共汽车都是蓝色的。B公司拥有20%的公共汽车,其公共汽车是灰色的。这位色盲女人无法从灰色的巴士上告诉一辆蓝色的巴士,因此她不知道哪个公司的公共汽车越过狗。她起诉公司A关于该理论,因为公司A拥有该地区80%的公共汽车,因此有80%的公司有可能杀死了她的狗。在实验中,陪审员在一种情况下听说被告在该地区拥有80%的公共汽车,而另一种情况的公共汽车则听到80%准确的称重站服务员对被告公共汽车公司的识别。两组陪审员都认为,被告的蓝色巴士而不是B公司的灰色巴士杀死了狗。但是,只有听到服务员证词的陪审员才愿意针对巴士公司找到。 Jurors who simply heard the naked statistics (Company A owns 80% of the buses) do not find Company A responsible. Similarly, although learning that the defendant is responsible for 80% of the accidents in the county leads to high probability estimates that the defendant’s bus killed the dog, jurors are unwilling to find the defendant responsible.
Most research has examined “nonnaked” statistical information—information in which one’s belief about the ultimate fact (in the example above, whether or not a blue bus hit the dog) is linked to one’s belief about the evidence (the weigh-station attendant’s accuracy). Some research finds that the manner in which statistical information is presented may affect mock jurors’ use of the information. For example, incidence rate information presented in the form of a conditional probability (there is only a 2% probability that the defendant’s hair would match the perpetrator’s if the defendant were innocent) may encourage some jurors to commit the prosecutor’s fallacy. These jurors believe that there is a 98% chance that the defendant is guilty. If the same information is presented as a percentage and number (a 2% match in a city of 1,000,000 people, meaning 20,000 people share that characteristic), some others may commit the defense attorney’s fallacy. They believe the evidence shows only a 1 in 20,000 chance that the defendant is the culprit. These errors may be more likely when an expert, rather than an attorney, offers the fallacious argument. An attorney who makes such an argument in the face of expert testimony (e.g., when the expert explains Bayes’s theorem) runs the risk of backlash; the defense attorney’s fallacy combined with expert Bayesian instruction may increase guilty verdicts.
即使是统计证据的非恐惧介绍给陪审员构成挑战,尤其是当他们评估低概率事件时。比较DNA的发病率在10,000分中的0.1,100,000分之一或200,000分中的2个。从数学上讲,这些速率是相同的,但是从心理上讲,它们有所不同。在后两个案件中,陪审员更有可能为被告找到。为什么?第一个,部分发病率不包含被告以外的其他人可能与DNA相匹配的线索。其他每个费率都在其中至少包含一个示例,这鼓励陪审员考虑其他可能匹配的人。这种效果可能部分取决于更广泛的参考组的大小;在考虑500,000人的城市时,以100,000人中的发病率为100,000的示例要比考虑500个城镇时容易得多。
Jurors’ task becomes more difficult when they face both a random match probability (RMP) (e.g., there is a 1 in 1 million chance that the defendant’s DNA sample would match that of the perpetrator if the defendant is innocent) and a laboratory error rate (LE) (e.g., the laboratory makes a mistake in 2 of every 100 cases). The probability that a match occurred due either to chance or to lab error is roughly 2 in 100. Yet jurors who hear the separate RMP and LE (as recommended by the National Research Council) convict the defendant as often as those who hear only the much more incriminating RMP.
为什么陪审员将RMP和LE结合在一起?传统的解释指出了各种逻辑或数学错误。另一种解释表明,陪审员对统计证据的解释必然反映出他们对此类数据的期望。考虑到接受极少量的RMP估计值(十亿分之一)和相对较大的LE估计(100分之一)的陪审员,与接受相对较大的RMP估计(100分之一)和极小的LE估计(十亿分之一)相比。逻辑(例如,我们对更生动的证据更有说服力,例如十亿分之一)或数学(例如,我们对陪审员错误的平均概率解释)在这两种情况下都相同的预测。但是,相反,模拟陪审员更有可能在大型RMP中与小勒的条件搭配。同样,当出现极小的LE估计值时,它们更有可能被定罪,而没有RMP估算值,而不是仅显示极小的RMP估计值,而没有LE估计。这种差异可能反映出陪审员的预期,即随机匹配的可能性极小,实验室错误相对较大。
某些形式的统计证据(例如,子弹铅分析)表明,陪审员不仅必须考虑统计证据的可靠性,还必须考虑其诊断性(有用性)。The value of a forensic match (e.g., the defendant’s DNA profile is the same as that of blood found at the crime scene) depends on reliability of the evidence (did the laboratory correctly perform the test?) and also its diagnosticity (could the match be a coincidence?). One study gave the same information about hit rate and false-positive rate to all jurors. It varied a third statistical piece of information: the diagnostic value of the evidence. Some jurors learned that all sample bullets taken from the defendant matched the composition of the murder bullet, while no bullets taken from a community sample matched (strong diagnostic evidence). Others learned that the matching rate for the defendant’s bullets was the same as that for bullets taken from a community sample (worthless diagnostic evidence). Jurors who received the strong diagnostic evidence were more likely to believe the defendant guilty. However, this effect held only for mock jurors who were relatively confident in their ability to draw conclusions from numerical data. Jurors who were less confident did not differ across conditions. Furthermore, jurors who heard the worthless diagnostic evidence tended to give it some weight before they deliberated; deliberation eliminated the effect.
陪审员如何将统计证据与非统计证据相结合
陪审员如何结合做出决定的大量证据(不一定是统计)?已经提出了数学(例如概率理论)和基于解释的(例如故事模型)方法。专门检查统计证据使用的研究通常遵循一种数学方法,并将陪审员的概率(通常是被告犯罪的可能性)与使用贝叶斯定理计算的概率。
贝叶斯的定理规定了决策者应如何将统计证据与先前证据相结合。Prior odds (the defendant’s odds of guilt, based on all previously presented evidence) are multiplied by the likelihood ratio (the probability that the new evidence would match the defendant if he or she is guilty, divided by the probability that the new evidence would match an innocent person). The product is the posterior odds. For example, after opening statements and eyewitness testimony, a juror might believe that there is a 25% chance that the defendant is guilty. The prior odds are 25:(100-25) = .33:1. If the defendant and the perpetrator share a blood type found in only 5% of the population, the likelihood ratio is 1:.05 = 20. The posterior odds, then, are .33:1 x 20 = 6.67:1. The probability of guilt is 6.67/(6.67 + 1) or .87. In short, for this juror, Bayes’s theorem states that the probability of guilt should increase from .25 to .87.
只有少数研究将陪审员的决定与贝叶斯规范进行了比较,有时很难进行比较。一些研究没有要求先前的概率,而另一些研究则要求信念证据符合(而不是对内gui的信念)。大多数人认为陪审员以面值接受统计证据。鉴于这些警告通常与贝叶斯规范相比,陪审员没有统计证据。然而,这一总体发现掩盖了基本的复杂性。在许多研究中,先前的证据,统计证据或两者都相对强。在这种情况下,很难超越贝叶斯后概率(通常为0.90或更高)。同样,陪审员如何使用统计证据,往往会有很大的差异。也就是说,两个具有相同先前概率的陪审员可能会听到相同的统计证据,并具有截然不同的后验概率。这些差异可能部分基于影响统计证据价值的其他因素(例如,潜在的研究者不当行为)或其他因素(例如潜在的研究者不当行为)的预期。 But studies (reviewed above) of how jurors respond to statistical information by itself provide ample reason to suspect wide variation in jurors’ understanding. For example, jurors who claim to be comfortable with mathematics are more likely to be affected by statistical information than those who express discomfort. To further complicate matters, at least one study has found that later, nonprobabilistic evidence leads to a reevaluation of the quantitative evidence presented earlier.
指导是否可以帮助陪审员将统计证据与非统计证据相结合?研究提供了简单的说明。通常,它们包括统计学家关于贝叶斯定理的工作方式的证词。专家显示表或图表,显示了一些样本先前的概率,并且鉴于统计证据,相应的后验概率。通常,这些相对不教育的教学手段通常没有影响陪审员对证据的使用;收到指示的陪审员比那些没有的贝叶斯规范更接近贝叶斯规范。
参考:
- Koehler,J。J.和Macchi,L。(2004)。思考低概率事件:典范理论。心理科学,15,540-546。
- 莱维特(L.陪审团和陪审员决策的心理学。在N. Brewer和K. D. Williams(编辑)中,《心理学与法律:经验观点》(第365-106页)。纽约:吉尔福德出版社。
- Niedermeier,K。E.,Kerr,N。L.,&Messe,L。A.(1999)。陪审员对裸统计证据的使用:探索井的基础和含义。人格与社会心理学杂志,76,533-542。
- Schklar,J。和Diamond,S。S.(1999)。陪审员对DNA证据的反应:错误和期望。法律与人类行为,23,159-184。