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The way you are wording it to yourself makes it seem like it's impossible to avoid 100% killing one innocent person, and infinite costs approach 100% never killing one innocent person, but never reaching that perfection. That is not the case. There is a price ceiling on avoiding killing an innocent person. That is the cost of putting them in a jail cell for 90 years (upper limit) as an alternative to the death penalty. What is the cost for jailing someone for 90 years? Let's say it's 10 million dollars. That is 4 cents per person in the USA.

Jailing the offender also prevents them from killing/raping/etc because now they are in jail. Really a false comparison here. I think all the countries of the world overwhelmingly have voted in favour that this cost is worth it. The countries that did not, made it very hard to execute prisoners anyways and very rarely use it.

According to (https://www.marketplace.org/2017/05/19/how-much-does-it-cost...), it's above $31,000 per inmate per year (up to $60,000/year). That's $0.000095 per person per inmate per year. Assuming an average of 33 not-executed-but-would-have-been inmates per year, and that they actually live 45 years in jail (because they're not all going to live 90 years there), that's 1,485 inmates at any one time (my math may be wrong).

That works out to about $0.14 per year per citizen, or $0.37 per household (assuming all my math is more or less correct)

I agree with your analysis that it's not a lot of money. I will ponder this.

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