"What's the worst that can happen?" goes the optimistic saying. It's probably a bad question to ask anyone with a creative imagination. Let's consider the problem on an individual level: it's not really the worst that can happen, but would nonetheless be fairly bad, if you were horribly tortured for a number of years. This is one of the worse things that can realistically happen to one person in today's world.
What's the least bad, bad thing that can happen? Well, suppose a dust speck floated into your eye and irritated it just a little, for a fraction of a second, barely enough to make you notice before you blink and wipe away the dust speck.
For our next ingredient, we need a large number. Let's use 3^^^3, written in Knuth's up-arrow notation:
- 3^3 = 27.
- 3^^3 = (3^(3^3)) = 3^27 = 7625597484987.
- 3^^^3 = (3^^(3^^3)) = 3^^7625597484987 = (3^(3^(3^(... 7625597484987 times ...)))).
3^^^3 is an exponential tower of 3s which is 7,625,597,484,987 layers tall. You start with 1; raise 3 to the power of 1 to get 3; raise 3 to the power of 3 to get 27; raise 3 to the power of 27 to get 7625597484987; raise 3 to the power of 7625597484987 to get a number much larger than the number of atoms in the universe, but which could still be written down in base 10, on 100 square kilometers of paper; then raise 3 to that power; and continue until you've exponentiated 7625597484987 times. That's 3^^^3. It's the smallest simple inconceivably huge number I know.
Now here's the moral dilemma. If neither event is going to happen to you personally, but you still had to choose one or the other:
Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?
I think the answer is obvious. How about you?
I would suggest that torture has greater and greater disutility the larger the size of the society. So given a specific society of a specific size, the dust specks can never add up to more suffering than the torture; the greater the number of dust specs possible, the greater the disutility of the torture, and the torture will always add up to worse.
If you're comparing societies of different size, it may be that the society with the dust specks has as much disutility as the society with the torture, but this is no longer a choice between dust specks and torture, it's a choice between dust specks+A to torture+B, and it's not so counterintuitive that I might prefer torture+B.
As for why I have such an odd utility function as "torture is worse tin a larger society"? I'm trying to derive my utility function from my preferences and this is what I come up with--I'm not choosing a utility function as a starting point.
Any utility function runs into a repugnant conclusion of one type or another. I wonder if there is a theorem to this effect, following from transitivity + continuity. Yours is no exception.
For example, in your case of disutility of torture growing larger with the size of the society, doesn't the disutility of dust specks grow both with the number of people subjected to it and the society's size? If not, ho... (read more)