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Notes -
Is it not actually more favorable? When we’re talking about ‘low probability of very bad outcome’, the way most sensible people make decisions is to disregard differences in badness and focus on actual probabilities of suffering them.
Assuming the potential payoff is the same, then no, the 1 in 500 scenario is worse. .002 * 50 = .1 years of lost freedom. .01 * 5 = .05 years of lost freedom. Twice the expected negative value.
Mathematically, going from 1 in 100 chance of 5 years to 1 in 20 chance of 2 years, the first one is a better risk. But I suspect most people would hesitate more at the 2nd one. What's sensible, I guess that depends on how you like to structure your risk, how many times you plan to take said risk, expected positive value, lots of factors really. But from a public policy perspective, it's more important to understand how criminals (mostly young men) structure their risk. Probably not utilizing game theory, so increasing enforcement rather than penalties makes sense.
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