It may not be fair, but the people who don't die because of that effect won't complain.
Whether the prize played a role in their decision is something only they can say (and then you might not believe them).
So I find this question useless, because it cannot be answered. The mechanism I sketched is generally plausible, though.
Do you actually propose that they did violent things because they got the prize?
Possible, but not terribly plausible, IMO. And the examples proffered so far (Obama or Kissinger) certainly don't fit that pattern.
I find that not impossible to argue, but incredible, and would want to see supporting evidence.
For the former, Henry Kissinger.
There are examples of the latter, as well.
With 2 members of the committee resigning in protest, it seems not everyone with power to award it was so morally corrupt.
Also there was a 1,200+ page Senate investigation into the use of torture by the previous administration.
Neither method really provides any useful intelligence. The difference is victims of torture can go on ‘60 Minutes’, victims of targeted drone strikes can’t.
Awards don't just exist to award the individual.
In polarizing times, where the instinct is to create more conflict as a path to resolving conflict, what many of the Peace Prize winners have done, is to remind everyone that alternate non-obvious paths exist.