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Probability, Justice, and the Risk of Wrongful Conviction
The Mathematics Enthusiast Volume 12 Number 1 Numbers 1, 2, & 3 Article 5 6-2015 Probability, Justice, and the Risk of Wrongful Conviction Jeffrey S. Rosenthal Follow this and additional works at: https://scholarworks.umt.edu/tme Part of the Mathematics Commons Let us know how access to this document benefits ou.y Recommended Citation Rosenthal, Jeffrey S. (2015) "Probability, Justice, and the Risk of Wrongful Conviction," The Mathematics Enthusiast: Vol. 12 : No. 1 , Article 5. Available at: https://scholarworks.umt.edu/tme/vol12/iss1/5 This Article is brought to you for free and open access by ScholarWorks at University of Montana. It has been accepted for inclusion in The Mathematics Enthusiast by an authorized editor of ScholarWorks at University of Montana. For more information, please contact [email protected]. TME, vol. 12, no. 1,2&3, p. 11 Probability, Justice, and the Risk of Wrongful Conviction Jeffrey S. Rosenthal University of Toronto, Canada Abstract: We consider the issue of standards of proof in legal decisions from the point of view of probability. We compare ``balance of probabilities'' and ``beyond a reasonable doubt'' to the statistical use of p-values. We point out various fallacies which sometimes arise in legal reasoning. And we provide several examples of legal cases which involved probabilities, including some in which incorrect decisions were made and defendants were wrongfully convicted. Keywords: probability, statistics, p-value, balance of probabilities, beyond a reasonable doubt, standard of proof. Background and Context I am a professor of statistics, and most of my work is fairly technical and mathematical (see www.probability.ca/jeff/research.html). -
“Your Honor, This Was Not a Coincidence!”
Peter Grünwald March 2007 The Case of Lucia de Berk “Your Honor, this was not a coincidence!” • In 2004, the court of appeals convicted Lucia de Berk, a nurse from the Juliana Children’s Hospital in the Hague, to life On the (ab)use of statistics in the case against imprisonment for 7 murders and 3 Lucia de B. murder attempts. • De B. has been in prison for more than 5 Peter Grünwald years now, but has never confessed. CWI, Amsterdam • The case is now under review of the “Committee Posthumus-II” 2001 (september 16th) Juliana hospital notifies the police Menu –There were many more “incidents” during her shifts than during those of other nurses in her ward –Statistician calculates that the probability that something like this would happen by pure coincidence, is less than 1 in 342 million 1. The use of statistics –Trial gets (more than) substantial media attention 2003 Court convicts L. of 4 murders, 3 attempts • What the statistician did (evidence in first verdict) –Statistics is crucial part of the evidence • What went wrong (everything) –In appeal, experts for defense R. Meester (probabilist) and • The role of statistics in the final verdict M. van Lambalgen (logician) claim calculation is flawed 2004 Court of appeals convicts L. of 7 murders,3 attempts –Court says that this time, “statistics in the form of probability 2. Can we do better? calculations has not been used” –In fact, the court’s report has flawed statistics written all over it 2006 Prof. Ton Derksen writes a book about the case –Case goes to “Posthumus-II committee” –Richard Gill and myself write letter to the committee supporting Derksen’s statistical analysis Not a coincidence! - Evidence Seminar, University College London 1 Peter Grünwald March 2007 The Statistician’s Work 1. -
Probability, Statistics, and Justice
Probability, Statistics, and Justice Jeffrey S. Rosenthal Professor Department of Statistics University of Toronto jeff@math.toronto.edu www.probability.ca (Canadian Institute for the Administration of Justice, Annual Conference, October 10, 2013) (1/45) I'm a Professor of Statistics. A typical day's work: Therefore p − (d) + (d) α (βi ) = α (βi − `= d) 1=2 (d) 1=2 (d) 0 1=2 (d) 000 (d) d + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) ≈ α (βi )− p φ − − 2 2 1=2 (d) d 6I (βi ) (d) 1=2 (d) 0 2 (d) 000 (`(βi )I (βi )) −` − exp(−` (β )K (βi )=6) p × i 2 d I 1=2(β(d))` `K 000(β(d)) ×φ − i + i 2 1=2 (d) 6I (βi ) 1=2 1=2 d d 0 Then, since ` ≈ ` + `0 ≈ ` + `0 = ` + `` , we have that d1=2 0 d1=2 1 h `` µ(β(d)) ≈ − α+` + ` + × i 2d 1=2 d 1=2 (d) 1=2 (d) 0 1=2 (d) 000 (d) + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) α (βi )− p φ − − − 2 2 1=2 (d) d 6I (βi ) About Me . (2/45) A typical day's work: Therefore p − (d) + (d) α (βi ) = α (βi − `= d) 1=2 (d) 1=2 (d) 0 1=2 (d) 000 (d) d + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) ≈ α (βi )− p φ − − 2 2 1=2 (d) d 6I (βi ) (d) 1=2 (d) 0 2 (d) 000 (`(βi )I (βi )) −` − exp(−` (β )K (βi )=6) p × i 2 d I 1=2(β(d))` `K 000(β(d)) ×φ − i + i 2 1=2 (d) 6I (βi ) 1=2 1=2 d d 0 Then, since ` ≈ ` + `0 ≈ ` + `0 = ` + `` , we have that d1=2 0 d1=2 1 h `` µ(β(d)) ≈ − α+` + ` + × i 2d 1=2 d 1=2 (d) 1=2 (d) 0 1=2 (d) 000 (d) + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) α (βi )− p φ − − − 2 2 1=2 (d) d 6I (βi ) About Me . -
Probability, Justice, and the Risk of Wrongful Conviction by Jeffrey S
Probability, Justice, and the Risk of Wrongful Conviction by Jeffrey S. Rosenthal1 (September, 2014) 1 Background and Context I am a professor of statistics, and most of my work is fairly technical and mathematical2. But one day I wrote a book for the general public3, which did unexpected well, especially in Canada. I was then interviewed by the media about such diverse topics as lottery probabilities, public opinion polls, violent crime rates, sports statistics, and more, and was even involved in probing a major lottery retailer fraud scandal involving millions of dollars and criminal convictions4. I was also invited to give talks to all sorts of different groups, from insurance brokers to financial investors, from humour therapists to gambling addiction counselors. And then one day I was invited to speak to a prominent group of Cana- dian lawyers and judges. This invitation in turn led to others, and I ended up giving five different talks to five different groups of lawyers and judges (including the Irish Supreme Court and High Court justices) within a sin- gle year. This forced me to investigate the connection of probabilities and statistical analysis to the justice system, as I will now discuss. 2 Probability and Justice? What is the connection of probability and statistics to justice issues? Well, both topics involve evaluating evidence, i.e. determining whether the avail- able information is sufficient to draw certain conclusions. This perspective 1Professor, Department of Statistics, University of Toronto. Email: [email protected]. Web: www.probability.ca 2See: www.probability.ca/jeff/research.html 3Struck by Lightning: The Curious World of Probabilities, HarperCollins Canada 2005 and Joseph Henry Press 2006.