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Should lifetime prisoners be incentivized to kill themselves?

The death penalty has various serious problems and lifetime imprisonment is really really expensive.

I guess we should be happy every time someone so thoroughly bad we want them out of society forever (like a serial murderer) does us the favour of killing themselves. Nothing of value is lost, and the justice system saves money. Right?

It seems to me it logically follows that we should incentivize such suicides. Like: 5000 dollars to a person of your choice if you're dead within the first year of your lifetime sentence, wink, wink, nudge, nudge.

It feels very wrong and is clearly outside the overton window. But is there any reason to expect this wouldn't be a net benefit?

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Why should this be limited to prisoners? We can probably come up with actuarial tables that estimate everyone's net benefit to the society. If someone's projected to cost the government X by the time they are dead, why not offer them a loan of 0.25X right now with the stipulation that if they default on it, they get to send 0.25X more to whomever they want, but are executed afterwards?