On the whole issue of the connection between a propensity to burgle (or "burglarize" for our American friends) and propensity to rape:
The whole area of conditional probability consistently causes huge confusion in courtrooms among lawyers and juries alike, and most likely has had significant impacts on judicial outcomes. Take for example the argument: "Only x% (small percentage) of burglars or other non-violent property offenders go on to rape someone at a future time, so just because Mr A has been shown to be a burglar, he has only a statistical x% probability of being a rapist". This argument is in fact completely invalid, as it's based on the wrong application of probability theory.
The relevant statistic to know in this example would be this: given that someone is raped, what is the probability that her rapist has a prior history of burglary or similar non-violent offences? This is a totally different statistic, and is calculated using Bayesian theories of conditional probability. It might well be that the correct conditional probability in this case could be very high (viz the 80%-ish stat from above).
A very high-profile casualty of this failure to understand conditional probability was the OJ Simpson case. I can't recall the exact probabilities used in the trial, but what happened went like this: Simpson had previously pleaded guilty (well, nolo contendere, technically) to physical abuse & battery against his wife - the subsequent murder victim Nicole Brown Simpson. Simpson's defence attorney warned the jury not to be be swayed to believe that, since OJ had previously beaten his wife, he was more likely to be her murderer. His defence counsel (Johnny Cochrane, if I remember correctly), told the jury something like this: "Over 1,000,000 men have been convicted in the USA over the past 10 years of spousal abuse. Of these 1,000,000, only around 400 have gone on to subsequently be convicted of murdering their spouse. That equates to just 0.04%! So just because my client hit his wife (which he's ashamed of etc etc), you CANNOT go from that crime to a belief that he killed her - the statistics simply would not support such a position".
Many jury members post-trial stated that they were impressed by the compelling logic of this argument, and that it was one of the more significant things that helped them decide to acquit. But the logic was TOTALLY wrong - and the prosecution not only neither picked up on it nor corrected it, but actively REINFORCED it with statements such as "a slap is a prelude to homicide".
The question that the jurors SHOULD have been assessing was this: What are the statistical chances that a man murdered his partner or ex-partner, given that a) she'd been murdered by SOMEONE, and b) the man had previously been convicted of abusing her? The statistics showed a radically different probability to that implied by OJ's defence team (and, inexplicably, also by the prosecution) - and one that heavily implicated OJ.
The correct conditional analysis, broken down into smaller steps, goes like this: First, we need an additional statistic: how many women in the USA in a comparable demographic bracket were killed by all different sorts of perpetrators in those previous ten years? The answer- if one excludes known prostitutes that were killed by their pimps or johns and women in the drugs trade that were killed by their dealer or customer - is around 55,000. That's for all of the USA, where there were on average 120,000,000 women in the population over this period.
Now we take that statistic and apply it to our sample group of 1,000,000 battered women. Scaling down ((1 million / 120 million) x 55,000), we might statistically expect around 458 women from our sample group to be murdered in total over the ten year period.
So, now we have a statistical total number of women in our sample group who were killed (458). But we also know that 400 men were convicted of murdering their partner/ex-partner within this group. By extension, 400 of these women were killed by a partner/ex-partner with a prior conviction for physical abuse against them. So, the answer to the crucial question is this:
If a woman in the US was murdered, and her partner (or ex-partner) had previously been convicted of her battery, there's a statistical 87% chance (400/458) that her partner/ex-partner was the perpetrator.
This 87% (or a very similar percentage) was the probability that actually should have been placed before the jury in their deliberation of OJ's guilt. Had the prosecutors known anything about correct application of conditional probability, things might possibly have turned out different - in spite of all the other strange and unique things about this trial.
PS the actual numbers that I've used here are purely from recollection. I don't claim that they are strictly accurate, but I am certain that they are very close to representing the true probabilities.
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