I think you have to take the 5k. The only way it doesn’t leave everyone better off and save lives is if you don’t actually believe your prior of >99%, in which case update your prior. I don’t see how what he does in another room matters. Any reputational effects are overwhelmed by the ability to save thousands of lives.
However, I also don’t see how you can cooperate in a true one-time prisoner’s dilemma without some form of cheating. The true PD presumes that I don’t care at all about the other side of the matrix, so assuming there isn’t some hidden reason to prefer co-operation—there are no reputational effects personally or generally, no one can read or reconstruct my mind, etc—why not just cover the other side’s payoffs? The payoff looks a lot like this: C → X, D → X+1, where X is unknown.
Also, as a fun side observation, this sounds suspiciously like a test designed to figure out which of us actually thinks we’re >99% once we take into account the other opinion and which of us is only >99% before we take into account the other opinion. Dr. House might be thinking that if we order 15k of either medicine that one is right often enough that his work here is done. I’d have to assign that p>0.01, as it’s actually a less evil option than taking him at face value. But I’m presuming that’s not the case and we can trust the scenario as written.
I think you have to take the 5k. The only way it doesn’t leave everyone better off and save lives is if you don’t actually believe your prior of >99%
I’m not sure how much work and what kind of work the following color does:
You, having carefully tested many patients, being a highly skilled, well-educated diagnostician [is 99% confident one way.] Yet your colleague, the blinkered fool, [is 99% certain the other way]. Well, it need hardly be said that someone here is failing at rationality. [...] You should be able to take one another’s estimates into account, share evidence, revise your estimates, reach a probability you both agree on.
I’m not sure what the assumptions are, here. If I have been using Testing of Patients while my colleague has been practicing Blinkered Folly, by which I mean forming truth-uncorrelated beliefs, taking his estimate into account shouldn’t change my beliefs since they’re not truth-correlated. He has no useful evidence, and he is impervious to mine.
But let’s say we’re playing a game of prisoners dilemma with payouts in two currencies. I can add either 5k malarian dollars or 10k birdfluian dollars to a pot which will be evenly shared by both (since we share the value of healing the sick), while my colleague has the reverse choice. The expected utilities if I’m right and he’s wrong are 99*5k + 1*0k = 4950 and 1*10k + 99*0k = 100. I maximize by defecting. By a similar calculation, my colleague maximizes by cooperating but is too foolishly blinkered to see this.
I guess your point is that if we have commitments available, I can do better than my 5k and his 0k malarian dollars by humoring his delusions and agreeing on $10,000m + $10,000b, which he wants because $10,000b is “better” than the 5k he could get by defecting.
So: sometimes you can act real stupid in ways that bribe crazy people to act even less stupid, thereby increasing social utility compared to the alternative. Or, said another way, people act “rationally” from the perspective of their wrong beliefs—the payoff matrix in terms of malarian dollars reflect the utility of the patients and the rational doctor whereas the payoff matrix in terms of birdfluian dollars reflects the utility of blinkered doctor, where “utility” means “behavior-predicting abstraction” in case of the blinkered doctor.
If it is common knowledge between the two doctors that both practice Epistemic Rationality and Intellectual Virtue but collect disjoint bodies of evidence (I think this goes against the stated assumptions), one doctor’s confidence is evidence of their conclusion to the other doctor, and they should both snap to 50% confidence once they learn about the other doctor’s (previous) certainty. In that scenario it’s a straightforward game of prisoner’s dilemma, the exact same as before except with half the payoffs.
The closest I have come to studying decision theory for irrational agents is reinforcement learning in Markov Decision Processes. Maybe you can argue in favor of epsilon-greedy exploration, on the argument that getting the medicine will not be the last thing the doctors will experience, but then we’re veering into a discussion about how to make and select maps rather than a discussion of how to select a route given the map the article author has drawn.
Also, as a fun side observation, this sounds suspiciously like a test designed to figure out which of us actually thinks we’re >99% once we take into account the other opinion and which of us is only >99% before we take into account the other opinion. Dr. House might be thinking that if we order 15k of either medicine that one is right often enough that his work here is done. I’d have to assign that p>0.01, as it’s actually a less evil option than taking him at face value. But I’m presuming that’s not the case and we can trust the scenario as written.
I think you have to take the 5k. The only way it doesn’t leave everyone better off and save lives is if you don’t actually believe your prior of >99%, in which case update your prior. I don’t see how what he does in another room matters. Any reputational effects are overwhelmed by the ability to save thousands of lives.
However, I also don’t see how you can cooperate in a true one-time prisoner’s dilemma without some form of cheating. The true PD presumes that I don’t care at all about the other side of the matrix, so assuming there isn’t some hidden reason to prefer co-operation—there are no reputational effects personally or generally, no one can read or reconstruct my mind, etc—why not just cover the other side’s payoffs? The payoff looks a lot like this: C → X, D → X+1, where X is unknown.
Also, as a fun side observation, this sounds suspiciously like a test designed to figure out which of us actually thinks we’re >99% once we take into account the other opinion and which of us is only >99% before we take into account the other opinion. Dr. House might be thinking that if we order 15k of either medicine that one is right often enough that his work here is done. I’d have to assign that p>0.01, as it’s actually a less evil option than taking him at face value. But I’m presuming that’s not the case and we can trust the scenario as written.
I’m not sure how much work and what kind of work the following color does:
I’m not sure what the assumptions are, here. If I have been using Testing of Patients while my colleague has been practicing Blinkered Folly, by which I mean forming truth-uncorrelated beliefs, taking his estimate into account shouldn’t change my beliefs since they’re not truth-correlated. He has no useful evidence, and he is impervious to mine.
But let’s say we’re playing a game of prisoners dilemma with payouts in two currencies. I can add either 5k malarian dollars or 10k birdfluian dollars to a pot which will be evenly shared by both (since we share the value of healing the sick), while my colleague has the reverse choice. The expected utilities if I’m right and he’s wrong are 99*5k + 1*0k = 4950 and 1*10k + 99*0k = 100. I maximize by defecting. By a similar calculation, my colleague maximizes by cooperating but is too foolishly blinkered to see this.
I guess your point is that if we have commitments available, I can do better than my 5k and his 0k malarian dollars by humoring his delusions and agreeing on $10,000m + $10,000b, which he wants because $10,000b is “better” than the 5k he could get by defecting.
So: sometimes you can act real stupid in ways that bribe crazy people to act even less stupid, thereby increasing social utility compared to the alternative. Or, said another way, people act “rationally” from the perspective of their wrong beliefs—the payoff matrix in terms of malarian dollars reflect the utility of the patients and the rational doctor whereas the payoff matrix in terms of birdfluian dollars reflects the utility of blinkered doctor, where “utility” means “behavior-predicting abstraction” in case of the blinkered doctor.
If it is common knowledge between the two doctors that both practice Epistemic Rationality and Intellectual Virtue but collect disjoint bodies of evidence (I think this goes against the stated assumptions), one doctor’s confidence is evidence of their conclusion to the other doctor, and they should both snap to 50% confidence once they learn about the other doctor’s (previous) certainty. In that scenario it’s a straightforward game of prisoner’s dilemma, the exact same as before except with half the payoffs.
The closest I have come to studying decision theory for irrational agents is reinforcement learning in Markov Decision Processes. Maybe you can argue in favor of epsilon-greedy exploration, on the argument that getting the medicine will not be the last thing the doctors will experience, but then we’re veering into a discussion about how to make and select maps rather than a discussion of how to select a route given the map the article author has drawn.
I wasn’t going there, but I like the thought =)