No, Paul can be wrong about only psychopaths pushing the button.
How confident is Paul about that? Oh right, “quite”. Is that a credence of 80%? 95% 99.99%?
How much more strongly does Paul prefer living in a world with psychopaths to dying? Oh right, “very”. Is that a utility of 2x? 100x? 10000x?
What is Paul’s prior credence that he is a psychopath according to the button’s implementation? 0.1%? 1%? 5%? 50%?
… and so on for other variables that are required for every logical decision theory. In the original post it doesn’t make sense to ask what various logical decision theories answer when the question has only vague terms that are compatible with any answer.
Of course Paul could be wrong, and then you need to calculate probabilities, which is a trivial calculation that does not depend on a chosen decision theory. But the problem statement as is does not specify any of it, only that he is sure that only a psychopath would press the button, so take it as 100% confidence and 100% accuracy, for simplicity. The point does not change: you need a good specification of the problem, and once you have it, the calculation is evaluating probabilities of each world, multiplying by utilities, and declaring the agent that picks the world with the highest EV “rational”.
No, Paul can be wrong about only psychopaths pushing the button.
How confident is Paul about that? Oh right, “quite”. Is that a credence of 80%? 95% 99.99%?
How much more strongly does Paul prefer living in a world with psychopaths to dying? Oh right, “very”. Is that a utility of 2x? 100x? 10000x?
What is Paul’s prior credence that he is a psychopath according to the button’s implementation? 0.1%? 1%? 5%? 50%?
… and so on for other variables that are required for every logical decision theory. In the original post it doesn’t make sense to ask what various logical decision theories answer when the question has only vague terms that are compatible with any answer.
Of course Paul could be wrong, and then you need to calculate probabilities, which is a trivial calculation that does not depend on a chosen decision theory. But the problem statement as is does not specify any of it, only that he is sure that only a psychopath would press the button, so take it as 100% confidence and 100% accuracy, for simplicity. The point does not change: you need a good specification of the problem, and once you have it, the calculation is evaluating probabilities of each world, multiplying by utilities, and declaring the agent that picks the world with the highest EV “rational”.