12 KiB
The Grim Calculus
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Author: u/totorox92 Because I want to Know*
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URL: https://www.reddit.com/r/rational/comments/3v7dol/the_grim_calculus/
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Score: 7
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Created: 2015-12-02T22:38:28
Post:
So Im writing a story, and I need to explain to someone why letting a bad guy go is desirable.
Subject A has a 99% chance of killing 1,000 people, and a 0.1% chance of saving the lives of 1,000,000 people. Since the net lives is +10 (.99*-1000=-990 + .001*1000000=1000) letting him go is the right choice, morally and rationally. Or am I not understanding how the logic behind such a decision is supposed to go?
Comments:
u/Roxolan [+20] Head of antimemetiWalmart senior assistant manager (23 minutes later)
It is indeed the right choice, assuming that
those are the only two options available to you, and
you can trust your numbers.
It's an easy enough choice to make in a clear-cut dilemma, but the complexity of real life (or fiction) rarely provides those. Is your protagonist certain that subject A has at least a 0.1% chance of saving those lives, and not, say, 0.08%?
(PS: two * on reddit will put all text between them in italics, unless preceded by a \.)
u/totorox92 [+8] Because I want to Know (an hour later)
Thanks! And yes, the numbers (which these are only a simple approximation of) are derived from magic which is at least 99.99% accurate. I was just making sure I was treating the problem correctly.
u/ArgentStonecutter [+4] Emergency Mustelid Hologram (13 hours later)
And there's no other action you can possibly take that will save those million people, that has a higher probability than one in a thousand?
u/khafra [+1] (17 hours later)
Is your protagonist certain that subject A has at least a 0.1% chance of saving those lives, and not, say, 0.08%?
Uncertainty about the exact probability of an event devolves to just normal uncertainty about the event. A rational agent will have a probability, not a fuzzy range of probabilities.
Where the uncertainty would come in, for me, is in the knock-on effects. As a simple example, if everyone starts letting murderers go free because they're likely to save more lives than they take, you may end up with rich people going on shooting sprees, then paying it off with anti-malaria bed nets or whatever.
u/None [+16] (20 minutes later)
How accurately do you know that information? Your orders of magnitude are different enough that significant digits are relevant in the extreme.
Which people will die or be saved, and their own future anticipated contributions are also relevant.
Would not the better answer be to jail Subject A, and then do for yourself whatever action Subject A would have taken to save the one million?
u/blazinghand [+13] Chaos Undivided (55 minutes later)
I mean, if you want letting a bad guy escaping to be desirable, just make it more acceptable than that. You're the author, you can write the story. Maybe the bad guy isn't a murder, but he's otherwise a criminal-- he's a thief or something-- but he uses his stolen money to save people's lives. Like a modern day Robin Hood or something. Now, if you're a cop or a superhero maybe you have to arrest this guy, but there's a moment of privacy and you can let him escape and say he overpowered you. He'll continue stealing but he'll save more lives. Do you do it? Now there's an interesting dilemma, and one that a typical reader will understand!
If you have to go with the "murder vs lives saved" thing, again, frame it narratively in an interesting way. Maybe the guy you're saving is a famous general, and he has a gambit to bring the civil war to a close, a gambit that involves launching a big offensive in an urban area....
"Listen to me," he growls, and you can hear every smokey oily cigar this man has smoked in the timbre of his voice. He's a mountain of a man, not what you expected for a filthy rebel. "I know we're enemies, boy, and I know you want to take me back to your headquarters. We all know what happens then. Your bosses, those men in charge, they execute me, and this war goes on."
You're trying your best not to listen to him, of course. Seditious treason spews from the rebel leaders' lips, and he continues, "killing me won't stop the war. Millions will die no matter what, boy. I'm not running the revolution personally, I'll just be another martyr. Cut me down and there are many who will take my place. The war drags on, and more people die."
"Let me go, though, and I can finally bring peace to Olaron. I've got a plan, one last push through to knock down your comms towers and take out King Baston. It won't be pretty, and innocent guys, guys like you and I, are gonna die in the process. But you know what? It just might work. Baston's the last of his line. With him dead, it's the end to the monarchy, and we'll finally have control of this damn country. The war will end tomorrow, and the millions fated to die in the next few years will live instead."
"I'll be honest with you, boy, it's a long shot. Less than a 1% chance of succeeding. Normally, I would never try something like this, but Baston never comes out of the palace. This is the first time he'll be outside in over a year. It's the only chance we have to end this thing, before it swallows up another generation of you kids..."
See, now there's a guy who maybe you'd let murder a thousand people! Just maybe! Framed like that, murder a thousand to MAYBE save a million, well, that's not unthinkable. Maybe you won't agree with what the protagonist does, but you'll be able to relate, see?
u/FuguofAnotherWorld [+5] Roll the Dice on Fate (23 hours later)
Unless that 0.1% chance comes up then the readers (and also many of your supporting characters) will use this to come to the conclusion that the character is too smart for his own good and this whole math-based morality thing is stupid. Conversely if the 0.1% chance does come up, then it's an arse pull by the writer and unconvincing as well. If you want to get people to agree with that lesson, I would suggest you do it another way as the only people who will agree with you now are the people who are already convinced of that methods' correctness.
Further, if this guy (who is the sort to kill 1000 people) survives the second event, he has a much higher than base rate chance to kill many more people.
u/Kodix [+5] (5 hours later)
Keep in mind that humans aren't perfectly rational by default, and it's pretty hard to get there. The math you propose is okay in theory (with the caveats that others have already mentioned - that's a pretty different order of magnitude, and the information needs to be damn near perfect at that point), but in practice, intuitively, the returns on a gamble need to be roughly twice the losses.
What I mean is that letting a person who has a 50% chance to kill a person a 50% chance to save two people is barely positive for most people, and many probably wouldn't do it. If the character in your story actually lets go someone who has 50/50 chances of saving/killing a person, they will seem.. odd to most readers, even though that's mathematically neutral.
(I'm referring to small amounts of people to avoid scope insensitivity - it may "feel" different when the stakes are larger, too.)
u/djscrub [+8] (31 minutes later)
Is the person making this calculation supposed to be well-versed in game theory? If so, this construction is quite rudimentary and probably won't be believable to knowledgeable readers. You might want to look into Bayes' Theorem.
For a less technical analysis, the Hand theorem is a principle of law that is used to make this kind of determination.
Note also that many people don't see preventable deaths as having the same moral weight as murders. If this guy has a high chance to be Hitler and a low chance to be Norman Borlaug, even if the math checks out, a lot of people would still not consider it to be worth the risk. For an analysis of the way people treat preventable harm as less significant than deliberate harm (from the point of view that they are wrong to do so), I recommend Peter Singer's seminal essay "Famine, Affluence, and Morality."
u/IomKg [+3] (a day later)
Personally i don't know if that ratio is that good actually.. to compare, lets say someone offers you a bet, you roll a dice with 10 faces, if you roll higher 3 or higher you win. now you have the option, either you put 1000$ and do this once and get 2000$ or lose the 1000$ if you lose. alternatively you can do the same thing, but need to win 20 times in a row. if you win you get 1024001$, if you lose you get nothing.
technically the second one gives you 1$ more than the first option, but unless you have the option to repeat the bet many times the first option is much more relevant because you may actually end the day with 2k$, as opposed to almost for sure lose 1k$.
unless the person that gets to take this decision is building a procedure because every day he catches a bunch of bad guys with similar odds and thus statistically will get the benefit of these odds over time i would probably suggest not letting the bad guy go.
u/Khaos1125 [+3] (2 days later)
Even assuming your numbers are correct, you still risk weakening existing precedents. Other people may be more willing to commit crime knowing that people much worse then them have seemingly escaped punishment.
A big reason why the law is so effective is it's a credible precommitment to punish despite other factors (such as this grim calculus). When you decide to take this calculus into account, you let off every rich person who says 'Let me skip jail time and I'll donate $50k to buying mosquito nets. Surely the 25 lives saved by the mosquito nets outweighs the need to punish me for something that can no longer be changed anyways'.
Beyond that, by playing by these kind of rules, other bad guys can win by pre-committing to things like...
"If you send me to jail, my henchmen will kill 100 people indiscriminantly."
"If you don't give me 50 million dollars and a helicopter, I'll blow up this school". (Valuing a life at $5 million dollars, I'd expect this logic to lead to many almost bombed schools, and huge numbers of bankrupt municipalities).
etc. If you fold to any credible blackmail, as this simple arithmetic strategy suggests, then you very strongly incentivize criminals to follow that route in the future, which has substantial negative utility.
It may actually be worse then this, because it's in the 'bad guys' best interests to make sure their threats are taken seriously, so a winning strategy on their part may be Commit Atrocity -> Demand Ransom while threatening another Atrocity.
A character acting on this example of 'the grim calculus' would be hugely mistaken in my mind. It's a classic Chesteron's Fence Scenario. He's acting on what he knows for sure, while ignoring/giving no weight to the reasons the cultural norms exist in the first place.
u/None [+4] (14 minutes later)
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u/Roxolan [+3] Head of antimemetiWalmart senior assistant manager (an hour later)
You're right. But if the protagonist has enough time and knowledge to do actual QALY math, I have serious doubts that they can't also figure out a way out of the dilemma.
u/loonyphoenix [+2] (11 hours later)
In isolation, if no other factors are involved, I'd say the calculation is correct. However, I think it's impossible for it to be in isolation. Maybe letting go a criminal will set an undesirable precedent, the person will surely do something besides kill 1,000 people or save 1,000,000 people -- they might steal something, incite a rebellion, steal $1,000,000, break out other criminals... Conversely, the person might do something productive. I don't think it's possible to plausibly engineer a situation where a character needs to make a choice like this, without having anything else to consider.
u/Anderkent [+2] (16 hours later)
This is never going to be convincing to anyone because no one can believe those kind of numbers. People reason about these kind of things intuitively, and the intuition is skewed towards correct decisions in situations that are actually likely to occur, rather than very unlikely thought experiments.