There are two factors that go into "innocent until proven guilty". One is basic reasoning: if you only know that a crime was committed, anyone is just as likely to have done it, so you need evidence to find the perpetrator. The other is the idea that it's worse to punish someone innocent than to let the guilty go unpunished.
The second part is quite interesting, because it would be suboptimal for rational agents. If humans were rational decision makers, the reaction to a crime should be chosen to balance out the damage, so that nobody can derive a benefit from criminal behavior. Then failure to punish would be equally severe as unjust punishment, and everyone should be treated according to their probability of guilt.
However, humans react much more strongly to losing something they already have than to not gaining it in the first place. So if you have a fine of $10,000 to distribute among 100 people with 1% probability of guilt, they will complain much more about the $100 they have to pay than when nobody pays anything, which means that one of them gets away with whatever crime deserved the $10,000 in the first place.
If the situation is different, e.g. when you are just deciding whether to write an article about some as yet unproven allegation, the same considerations don't necessarily apply. That doesn't make the general principle completely irrelevant, but it does mean that your standard of proof doesn't have to be quite as strict.
> If humans were rational decision makers, the reaction to a crime should be chosen to balance out the damage, so that nobody can derive a benefit from criminal behavior
Your example doesn't follow from this. In your example 99 innocent people are losing $100 because of a crime they didn't commit, and the perpetrator is making $9900 from their crime. So the perpetrator definitely still has profits from the crime if the punishment is spread out over multiple people.
Thanks for noticing that, I should have actually done the math instead of just relying on my intuition. Now I wonder what the actual optimal punishment strategy is.
The second part is quite interesting, because it would be suboptimal for rational agents. If humans were rational decision makers, the reaction to a crime should be chosen to balance out the damage, so that nobody can derive a benefit from criminal behavior. Then failure to punish would be equally severe as unjust punishment, and everyone should be treated according to their probability of guilt.
However, humans react much more strongly to losing something they already have than to not gaining it in the first place. So if you have a fine of $10,000 to distribute among 100 people with 1% probability of guilt, they will complain much more about the $100 they have to pay than when nobody pays anything, which means that one of them gets away with whatever crime deserved the $10,000 in the first place.
If the situation is different, e.g. when you are just deciding whether to write an article about some as yet unproven allegation, the same considerations don't necessarily apply. That doesn't make the general principle completely irrelevant, but it does mean that your standard of proof doesn't have to be quite as strict.