Psychopathy is strongly associated with poor impulse control and low self-reflection. If Paul is considering logical decision theories, rational choice, and their possible ramifications given his own mental makeup then he is substantially less likely than baseline to be a psychopath, which generally make up on the order of 1% of the population.
Does he have some prior evidence that he is a psychopath? If not, then his prior should be on the order of 0.2% or so. Willingness to press the button would otherwise be his only evidence, which he is “quite confident” about. What numerical value should he put for “quite confident”? Let’s say 90% (much more than that should be described more like “very” or “extremely” confident). So that would bring a baseline prior up to the order of 2%.
Now he “very strongly” prefers living in a world with psychopaths to dying. Is that 5x in utility? 100x? 10,000x? Well, dying is a pretty bad thing but I’d use some stronger term than just “very strongly” for 10,000x so let’s go with something on the order of 100x.
Well, this is awkward. For outcomes of pressing the button we’ve got a credence of 2% for being a psychopath and −100 utility, versus 98% for not being a psychopath and +1 utility. This is a net −1 utility, but the numbers are only order of magnitude estimates so the expected value could easily be much more positive or negative! It doesn’t really matter which decision theory he uses, Paul just doesn’t have enough information.
Yeah, in order to keep the problem statement clean I do think that one should specify that Paul does not have access to autobiographical memory or other self-knowledge for the duration of his time with the button making his decision. If he did, then he could use his self-knowledge to determine if he was a psychopath or not and use that information to supplement the piece of information from ‘would I choose to push the button’ to inform his prediction of whether he is indeed a psychopath and thus will be killed by pushing the button.
Psychopathy is strongly associated with poor impulse control and low self-reflection. If Paul is considering logical decision theories, rational choice, and their possible ramifications given his own mental makeup then he is substantially less likely than baseline to be a psychopath, which generally make up on the order of 1% of the population.
Does he have some prior evidence that he is a psychopath? If not, then his prior should be on the order of 0.2% or so. Willingness to press the button would otherwise be his only evidence, which he is “quite confident” about. What numerical value should he put for “quite confident”? Let’s say 90% (much more than that should be described more like “very” or “extremely” confident). So that would bring a baseline prior up to the order of 2%.
Now he “very strongly” prefers living in a world with psychopaths to dying. Is that 5x in utility? 100x? 10,000x? Well, dying is a pretty bad thing but I’d use some stronger term than just “very strongly” for 10,000x so let’s go with something on the order of 100x.
Well, this is awkward. For outcomes of pressing the button we’ve got a credence of 2% for being a psychopath and −100 utility, versus 98% for not being a psychopath and +1 utility. This is a net −1 utility, but the numbers are only order of magnitude estimates so the expected value could easily be much more positive or negative! It doesn’t really matter which decision theory he uses, Paul just doesn’t have enough information.
Yeah, in order to keep the problem statement clean I do think that one should specify that Paul does not have access to autobiographical memory or other self-knowledge for the duration of his time with the button making his decision. If he did, then he could use his self-knowledge to determine if he was a psychopath or not and use that information to supplement the piece of information from ‘would I choose to push the button’ to inform his prediction of whether he is indeed a psychopath and thus will be killed by pushing the button.