"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?
Fascinating question. No matter how small the negative utility in the dust speck, multiplying it with a number such as 3^^^3 will make it way worse than torture. Yet I find the obvious answer to be the dust speck one, for reasons similar to what others have pointed out - the negative utility rounds down to zero.
But that doesn't really solve the problem, for what if the harm in question was slightly larger? At what point does it cease rounding down? I have no meaningful criteria to give for that one. Obviously there must be a point where it does cease doing so, for it certainly is much better to torture one person for 50 years than 3^^^3 people for 49 years.
It is quite counterintuitive, but I suppose I should choose the torture option. My other alternatives would be to reject utilitarianism (but I have no better substitutes for it) or to modify my ethical system so that it solves this problem, but I currently cannot come up with an unproblematic way of doing so.
Still, I can't quite bring myself to do so. I choose specks, and admit that my ethical system is not consistent yet. (Not that it would be a surprise - I've noticed that all my attempts at building entirely consistent ethical systems tend to cause unwanted results at one point or the other.)
For those who would pick SPECKS, would you pay a single penny to avoid the dust specks?
A single penny to avoid one dust speck, or to avoid 3^^^3 dust specks? No to the first one. To the second one, depends on how often they occured - if I somehow could live for 3^^^3 years, getting one dust speck in my eye per year, then no. If they actually inconvenienced me, then yes - a penny is just a penny.