a. Intuitively, fun per person feels like it is upper bounded (just like utility of money). I cannot imagine what kind of fun for one person could compensate a month of torture. We will fix X and play with N
b. The difficulty seems to arise from the fact that the mechanical answer is to set e.g., X=1, N = ceil(Y + epsilon) (where minus Y is utility of the torture), yet this intuitively does not feel right. Some thoughts on why:
Scope insensitivity. We have trouble instinctively multiplying fun by many people (i.e., I can picture one day of fun very clearly, but have trouble multiplying that by millions of people, to get anywhere near compensating for a month of torture). So the mechanical answer would be correct, but our brains cannot evaluate the fun side of the equation “intuitively”.
Bias towards “fairness”. Having one person suffer and others have fun to compensate doesn’t feel right (or at least assessing this trade-off is difficult)
Bias towards negative utilitarianism. We instinctively prefer minimizing suffering than maximizing utility.
c. When we scale things down the question seems easier. Suppose we set X = an amazing week of fun I will remember for the rest of my life, bringing me joy to think about it again and again. Now I ask how much torture I would put up for that. This is a question I feel I can intuitively answer. I would trade, say Y = 10 seconds of extreme pain for X (assuming no permanent physical damage). To move to 1 month of torture we need to assess how the utility of a torture session scales with its duration. If it scaled linearly, 1 month of torture is ~2.6 million seconds of torture, which means we should set N= ~260’000 for X defined above. I feel that after a few days, the scale is sub-linear, but it may be super-linear before that (when you start moving into the permanent psychological damage area). I cannot seem to come up with an answer I am comfortable with.
2) As pointed out by Nornagest, If I give you my utility function (mapping all possible pains and pleasures to a number), I’m not sure how you could tell whether pain and pleasure are being measured “on the same scale” or not?
1) A few thoughts:
a. Intuitively, fun per person feels like it is upper bounded (just like utility of money). I cannot imagine what kind of fun for one person could compensate a month of torture. We will fix X and play with N
b. The difficulty seems to arise from the fact that the mechanical answer is to set e.g., X=1, N = ceil(Y + epsilon) (where minus Y is utility of the torture), yet this intuitively does not feel right. Some thoughts on why:
Scope insensitivity. We have trouble instinctively multiplying fun by many people (i.e., I can picture one day of fun very clearly, but have trouble multiplying that by millions of people, to get anywhere near compensating for a month of torture). So the mechanical answer would be correct, but our brains cannot evaluate the fun side of the equation “intuitively”.
Bias towards “fairness”. Having one person suffer and others have fun to compensate doesn’t feel right (or at least assessing this trade-off is difficult)
Bias towards negative utilitarianism. We instinctively prefer minimizing suffering than maximizing utility.
c. When we scale things down the question seems easier. Suppose we set X = an amazing week of fun I will remember for the rest of my life, bringing me joy to think about it again and again. Now I ask how much torture I would put up for that. This is a question I feel I can intuitively answer. I would trade, say Y = 10 seconds of extreme pain for X (assuming no permanent physical damage).
To move to 1 month of torture we need to assess how the utility of a torture session scales with its duration. If it scaled linearly, 1 month of torture is ~2.6 million seconds of torture, which means we should set N= ~260’000 for X defined above. I feel that after a few days, the scale is sub-linear, but it may be super-linear before that (when you start moving into the permanent psychological damage area). I cannot seem to come up with an answer I am comfortable with.
2) As pointed out by Nornagest, If I give you my utility function (mapping all possible pains and pleasures to a number), I’m not sure how you could tell whether pain and pleasure are being measured “on the same scale” or not?