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(simple prediction model)
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We divide the population into two categories: those that would rape you if they had the chance, and those that wouldn't. You can guess which category any given person will fall into, if you want, with a certain degree of success; for simplicity's sake, we'll assume that if you correctly spot a non-rapist 90% of the time, you also correctly spot a rapist 90% of the time. You pay a cost if you decide to guard against rape when dealing with a non-rapist.
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You also pay a cost for getting raped, of course. If you choose to guard against a rapist, your guard will either be successful, in which you pay no cost, or it may fail, in which case you pay the full cost of being raped.
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6.0%Odds of encountering a rapist
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75.0%Odds of predicting who is a rapist or non-rapist
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100Cost of falsely guarding against rape
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10000Cost of being raped
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50.0%Success rate of guarding against rape
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394Expected cost of always being on guard
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398.5Expected cost of being on guard when you think it's necessary
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600Expected cost of never being on guard
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Therefore,always be on guard against rape.
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A Guide to Create Realistic Numbers
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Odds of encountering a rapist:Between 6% and 33%, over a lifetime. 6-14% of men indirectly admit to raping someone, or attempting to do so.
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Odds of predicting who is a rapist:Low. Obvious rapists are easily avoided, so there's evolutionary pressure to appear normal. Assuming perfect normality, the odds of correctly predicting who is a rapist are on par with their incidence in the population. Imperfect normality leads to a higher probability, of course, in proportion to how obvious rapists are in the general population.
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Success rate of guarding against rape:Low. ~80% of rapes are done by someone known to the victim, suggesting the offenders took their time to establish trust and get the victim to drop their guard, or waited for a momentary lapse.
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Sources:http://www.torontopolice.on.ca/sexcrimes/sas/statistics.php
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http://freethoughtblogs.com/zinniajones/2012/09/rapists-dont-look-like-rapists-continued/
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http://yesmeansyesblog.wordpress.com/2009/11/12/meet-the-predators/
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http://www.rapecrisis.org.uk/commonmyths2.php