Blame Theory

by cousin_it 9y19th May 201016 comments

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EDIT: this post, like many other posts of mine, is wrong. See the comments by Yvain below. Maybe "Regret Theory" would've been a better title. But I'm keeping this as it is because I like having reminders of my mistakes.

Platitudes notwithstanding, "personal responsibility" doesn't adequately summarize my relationship with the universe. Other people are to blame for some of my troubles because, as Shepherd from MW2 put it, "what happens over here matters over there". Let's talk about it.

When other people's actions can affect you and vice versa, individual utility maximization stops working and you must use game theory. The Prisoner's Dilemma stresses our intuitions by making a mockery of personal responsibility: each player holds the power to screw up the other player's welfare which they don't care about. Economists call such things "externalities", political scientists talk of "special interests". You can press a button that gives you $10 but makes 10000 random people lose $0.01 each (due to environmental pollution or something like that), you care enough to vote for this proposal, other people don't care enough to vote against, haha democracy fail. 

When the shit hits the fan in a multiplayer setting, we clearly need a theory for assigning blame in correct proportion. For example, what should we make of the democratic credo that people are responsible for the leaders they have? Exactly how much responsible? How many people did I personally kill by voting for Hitler, and how is this responsibility shared between Hitler and me? The "naive counterfactual" answer goes like this: if I hadn't voted for Hitler, he'd still have been elected (since I wasn't the marginal deciding voter), therefore I'm blameless. Clearly this answer is not satisfactory. We need more sophisticated game theory concepts.

First of all, we would do well to assume transferable utility. To understand why, consider Clippy. Clippy is perfectly willing to kill a million Armenians to gain one paperclip. We can blame him (her?) for it all day, but it's probably safe to say that Clippy's internal sense of guilt isn't denominated in Armenians. We must reach a mutual understanding by employing a common currency of guilt, which is just another way of saying "convertable utils". You feel guilty toward me = you owe me dough. Too bad, knowing you, you probably won't pay.

Our second assumption goes like this: rational actions cannot be immoral. Given our knowledge of game theory, this sounds completely callous and bloodthirsty, but in the transferable utility case it's actually quite tame. You have no incentive to screw Bob over in PD if you'll be sharing the proceeds anyway. The standard procedure for sharing will be, of course, the Shapley value.

This brings us to today's ultimate conclusion: Blame Theory. Imagine that instead of killing all those Gypsies, the evil leader and the stupid voters together sang kumbaya and built a city on a hill. The proceeds of that effort would be divided according to everyone's personal contributions using the standard Shapley construction (taking into account each group's counterfactual non-cooperation, of course). You, dear reader, would have gotten richer by two million dollars, instead of hiding in a bomb shelter while the ground shakes and your nephew is missing. And calculating the difference between your personal welfare in the perfect world where everyone cooperated, and the welfare you actually have right now given that everyone acted as they did, gives you the extent of your personal guilt. You can't push it away, it's yours. Sorry.

Don't know about you, but I'm genuinely scared by this result.

On one hand, it agrees with intuition in all the right ways: the "naive counterfactual" voter still carries non-zero guilt because (s)he was part of the collective that elected a monster, and the little personal guilts add up exactly to the total missed opportunity of all society, and... But on the other hand, this procedure gives every one of us a new and unexpectedly harsh yardstick to measure ourselves by. It probably makes me equivalent to a serial murderer already. I've long had a voice in the back of my head telling me it was possible to do better, but Blame Theory brings the truth into sharp and painful focus. I'm not sure I wanted that when I set out to solve this particular problem...

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