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NihilCredo comments on Punishing future crimes - Less Wrong
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Well, if having many time-travelers pre-punishing crimes is useful, then presumably having a single time-traveler pre-punish one crime is worth some fraction of that utility.
Only if (a) people know you did it, and why; and (b) you're not a one-shot time traveller, so that there is the potential for this kind of pre-punishment to happen again.
It can still be effective if they don't as I discuss here.
[Insert standard TDT argument about how by doing this, you're acausally increasing the number of other time traveling pre-punishers.]
However, your main point, that the effectiveness of this scales non-linearly with the number of punishers is correct. However, this appears to be more of an acausal co-ordination problem.
Your argument seems sound - basically, if criminals get enough apparently "random" misfortunes, people will eventually associate criminal = unlucky loser and be somewhat discouraged from that path, am I getting this right?
I would just note that "having a single time-traveler pre-punish one crime is worth some fraction of that utility" doesn't really seem to fit this system, since a single pre-punishment falls well under the 'random noise' threshold so its deterrence effect is effectively zero. (This isn't really a factual disagreement, it just depends on how you interpret "fraction of utility" in a context where one act is useless but, say, a thousand are useful; is the single act's utility zero or k/1000? Personally, I straight-up refuse to treat utility as a scalar quantity.)
I estimate acausal relationships between the behaviours of different individuals to be negligible.
There is no sharp "random noise threshold". A single act has some positive probability of increasing the amount of belief someone assigns to the proposition "crime doesn't pay". Rather the expected value of the change is positive.
That's why I called this an acausal coordination problem.