Then I only need to make the condition slightly stronger: “Any slight tendency to aggregation that doesn’t beg the question.” Ie, that doesn’t place a mathematical upper limit on disutility(Specks) that is lower than disutility(Torture=1). I trust you can see how that would be simply begging the question. Your formulation:
Contrary to what you think, it doesn’t require unbounded utility. Limiting the lower bound of the range to (say) 2 * disutility(torture) will suffice. The rest of your message assumes it does.
For completeness, I note that introducing numbers comparable to 3^^^3 in an attempt to undo the 3^^^3 scaling would cause a formulation to fail the “slight” condition, modest though it is.
@Neel.
Then I only need to make the condition slightly stronger: “Any slight tendency to aggregation that doesn’t beg the question.” Ie, that doesn’t place a mathematical upper limit on disutility(Specks) that is lower than disutility(Torture=1). I trust you can see how that would be simply begging the question. Your formulation:
D(Torture, Specks) = [10 * (Torture/(Torture + 1))] + (Specks/(Specks + 1))
...doesn’t meet this test.
Contrary to what you think, it doesn’t require unbounded utility. Limiting the lower bound of the range to (say) 2 * disutility(torture) will suffice. The rest of your message assumes it does.
For completeness, I note that introducing numbers comparable to 3^^^3 in an attempt to undo the 3^^^3 scaling would cause a formulation to fail the “slight” condition, modest though it is.