In 399 BC, Socrates — the father of Greek philosophy — was put on trial for impiety and corrupting the youth of Athens. The jury was comprised of 500 men, who found Socrates guilty by a vote of 280 to 220. He was sentenced to death by drinking hemlock - and the rest, as they say, is history.
These days most jurisdictions utilise 12 jurors, a tradition that dates back to an ancient Welsh king, Morgan of Gla-Morgan, in 725 AD. He is said to have declared "For as Christ and his 12 apostles were finally to judge the world, so human tribunals should be composed of the king and 12 wise men”. Throughout history, the number 12 has held a mystical significance – the 12 tribes of Israel, the 12 signs of the zodiac, the 12 days of Christmas, 12 hours on a clock and even a baker’s dozen, which is, of course, 13. (Did you know that twelve plus one is an anagram of eleven plus two)?
In 1970, the US Supreme Court ruled that juries did not always have to be made up of 12 persons. Arizona allows an eight-member jury and Florida allows six but in a 1978 Georgia case, the Supreme Court ruled that a 5 member jury was too small.
Approximately 90% of people selected for jury duty in Queensland avoid it. Last year, 241 480 received jury notices but only 26 954 were summonsed to serve and just 6 972 were empanelled. These people are selected from those registered to vote on the electoral roll. For every juror who is empanelled on the jury about 35 notices have been sent out equating to around 416 for the entire 12 member jury. Of course, all potential jurors are subject to peremptory challenges by the counsels for both the prosecution and the defence (8 each in Queensland). To ensure a full jury of twelve is able to be empanelled, the Sheriff generally allows for at least 28 plus a few additional jurors in reserve to allow for those that may have personal reasons to be excluded from the case. Of course, there may be several trials occurring concurrently, so this number soon escalates!
The jury for the infamous OJ Simpson trial, consisted of 10 women and only 2 men. Interestingly, both prosecution and defence thought that female jurors would benefit their own case. Twelve jurors and 12 alternates were originally selected from a pool of 250 but over the course of the trial, 10 were dismissed leaving only four of the original jurors on the final panel of twelve. In many Commonwealth jurisdictions, if the court runs out of potential jurors the Court has the power to summon any person off the street to serve as a juror. This process is known as ‘praying a tales’, a legal Latin-French term, roughly translated as "praying that the number of jurymen be completed". Refusal to serve at this point can be considered contempt of court – which could lead to another trial!
In the US, jurors are interviewed to determine their suitability (a process known as Voir dire, translated as ‘tell the truth’). This procedure reminds me of the Secretary problem which involves optimal stopping theory. How many secretaries do you need to interview in order to get the best one for the job? Rather than interviewing every secretary and ranking them in order, there is an optimal strategy for finding the best one. If n secretaries are to be interviewed, you reject the first n/2.718 that are interviewed and give the job to the next one that is better than those previously seen. This has a success rate of about 1/2.718 or 37%. Why is the number 2.718 so important? It is in fact the number e (known as Euler’s number), although it was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.
For example, if there are 20 applicants for a job you would reject the first 20/2.718 applicants (about 7) and then give the job to the next applicant that was better than those 7. (I can hear the sigh of disdain from Human Resources departments everywhere). With jury selection, the challenge would be to select k jurors from a pool of n; the cut off would be n / ke 1/k . If we return to the OJ Simpson case; to select the 24 jurors required (including alternates) from a pool of 250 they would need to reject the first 10 interviewees and appoint the next 24 that were better than those discarded.
Now having mustered together a jury, the next consideration is just how accurate they are in making their decision? The first mathematical analysis on jury size was undertaken in 1785 by the Marquis de Condorcet who concluded that “More is better”, but this was only for majority verdicts. For unanimous decisions, and assuming each juror gets it ‘right’ say 80% of the time, the chance of a correct unanimous decision would be (80/100)12 which is about 1 time in 15.
In 2008, Helland and Raviv refined Condorcet’s model to account for the deliberations that take place after the first ballot. They assumed that the likelihood of a conviction was proportional to the votes on the initial ballot. If the first ballot is 11 to 1 to convict, then the odds of a conviction are 11 to 1. If it is 6 – 6 then there is a 50% chance of conviction. That resulted in the opposite conclusion for jury size that “Less is better”. Of course, accuracy depends on what the ‘right’ decision is and that really depends on the degree of alignment between the values of the jury and those of the society that it represents.
In 2012, an international panel of ten judges held a mock re-trial of Socrates and the decision was split 5 – 5, which acquitted Socrates of the charges. There was no sentence considered but not one of the judges said they would have considered the death penalty. I am sure that Socrates, if he could have been there, would have again responded with his famous quote “The unexamined life is not worth living”.
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