Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University...
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Transcript of Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University...
![Page 1: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/1.jpg)
Juror Understanding of Random Match Probabilities
Dale A. NanceCase Western Reserve University
August, 2007
![Page 2: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/2.jpg)
Focus of Presentation
• What we know about how jurors react to testimony reporting a match between the defendant and the perpetrator and presenting a “random match probability” (RMP)
• “Experiments” assessing juror reactions
![Page 3: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/3.jpg)
Eight Common Hypotheses About Cognitive Error by Jurors
• 1. The Prosecutor’s Fallacy• 2. Neglect of Lab Error• 3. Improper Combination Strategies• 4. Vividness• 5. Defense Attorney’s Fallacy• 6. Defense Attorney’s (Extreme) Fallacy• 7. The Inversion Fallacy• 8. Misaggregation
![Page 4: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/4.jpg)
1. The Prosecutor’s Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
![Page 5: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/5.jpg)
1. The Prosecutor’s Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
“The chance that the accused in innocent is 1 in 40,000, so the odds that he is guilty must be 39,999 to 1.”
What the Jurors Think
![Page 6: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/6.jpg)
2. Neglect of Lab Error
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
![Page 7: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/7.jpg)
2. Neglect of Lab Error
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
“The chance that the accused, though innocent, would be implicated by either coincidence or lab error is 1 in 40,000.”
What the Jurors Think
![Page 8: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/8.jpg)
3. Combination Errors (Averaging)
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
“The chance of a false positive lab error is about 1 in 1,000.”
What the Expert Says
![Page 9: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/9.jpg)
3. Combination Errors (Averaging)
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
“The chance of a false positive lab error is about 1 in 1,000.”
What the Expert Says
“The chance that the accused , though innocent, would be implicated by a coincidental match or lab error is 1 in 20,500.”
What the Jurors Think
![Page 10: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/10.jpg)
4. The Vividness Hypothesis
“The chance of a coincidental match with an innocent man is one in a billion.”
What the Expert Says
![Page 11: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/11.jpg)
4. The Vividness Hypothesis
“The chance of a coincidental match with an innocent man is one in a billion.”
What the Expert Says
“One in a billion! That’s all I need to know. Hang the bastard!”
What the Jurors Think
![Page 12: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/12.jpg)
5. The Defense Attorney’s Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000. Yes, out of 12,000,000 adult men, about 300 will match.”
What the Expert Says
![Page 13: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/13.jpg)
5. The Defense Attorney’s Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000. Yes, out of 12,000,000 adult men, about 300 will match.”
What the Expert Says
“If 300 men will match, then this DNA evidence tells us nothing. I should just decide the case on the eyewitness evidence.”
What the Jurors Think
![Page 14: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/14.jpg)
6. The Defense Attorney’s (Extreme) Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000. Yes, out of 12,000,000 adult men, about 300 will match.”
What the Expert Says
![Page 15: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/15.jpg)
6. The Defense Attorney’s (Extreme) Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000. Yes, out of 12,000,000 adult men, about 300 will match.”
What the Expert Says
“If 300 men will match, then the chance the accused is guilty must be only 1 in 300.”
What the Jurors Think
![Page 16: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/16.jpg)
7. The Inversion Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
![Page 17: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/17.jpg)
7. The Inversion Fallacy
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
“The chance that the accused in guilty is just 1 in 40,000. This prosecutor must be from Durham.”
\
What the Jurors Think
![Page 18: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/18.jpg)
8. Misaggregation
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
![Page 19: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/19.jpg)
8. Misaggregation
“The chance of a coincidental match with an innocent man is 1 in 40,000.”
What the Expert Says
“Without the DNA evidence, I would place the odds of guilt at 2:1 against. With this DNA evidence, the odds of guilt are about 2:1 for.”
What the Jurors Think
![Page 20: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/20.jpg)
8. Misaggregation: How Bad Is It?For a RMP = 1 in 40,000, and considering
only the chance of:
• Coincidental match, posterior odds should be 40,000 times the prior odds:
• Coincidental match or lab error (at a rate of 1 in 1,000), posterior odds should be about 1000 times the prior:
• Coincidental match, lab error, or other sources of error (like police planting of evidence), assessed by the average juror at about 1 in 50, the posterior should be about 40 times the prior:
PRIOR → POST. ODDS ODDS
1:2 → 20,000:1
1:2 → 500:1
1:2 → 20:1
![Page 21: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/21.jpg)
8. Misaggregation:What Can Be Done About it?
• 1. Give RMP testimony in the form of probabilities focused on the defendant, rather than frequencies focused on the population:
– “The probability that defendant would match if he were innocent is 1 in 40,000.”
rather than
– “1 in 40,000 people in the population share this DNA profile.”
![Page 22: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/22.jpg)
8. Misaggregation:What Can Be Done About it?
• 2. Give testimony explaining the RMP by showing results of hypothetical Bayes’ Rule calculations. For example, with RMP= 1 in 40,000 and ignoring other sources of error:
Prior Probability → Posterior Probability 1/10 of 1% → 97.56% 1% → 99.75% 20% → 99.99% 50% → 99.99% 70% → 99.99%
![Page 23: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/23.jpg)
8. Misaggregation:What Can Be Done About it?
• Incorporating information about lab error rates into the calculation produces lower posterior probabilities:
Prior Prob. → Post. Prob. Post. Prob. (ignoring lab error) (incorp. lab
error)
1/10 of 1% → 97.56% 49.42% 1% → 99.75% 90.79% 20% → 99.99% 99.59% 50% → 99.99% 99.90% 70% → 99.99% 99.96%
![Page 24: Juror Understanding of Random Match Probabilities Dale A. Nance Case Western Reserve University August, 2007.](https://reader036.fdocuments.in/reader036/viewer/2022081518/55146742550346b0158b4bba/html5/thumbnails/24.jpg)
Conclusions
• Pro-prosecution fallacies: extant but correctible by argument or by restrictions on form of RMP presentation
• Pro-defense fallacies: extant but of declining importance as RMP becomes very small
• Pro-defense error (misaggregation): serious but
potentially amenable to Bayesian instruction