## Tuesday, October 15, 2013

### Benefitting some and harming none

Consider the principle that if an action benefits some and harms none, then it's permissible. Now imagine a lottery run by uniformly choosing a random number between 0 and 1, with each number equally likely. There are infinitely many tickets, each bearing a different number between 0 and 1. Each ticket has been sold to a different person (there are lots of people in this story!). At night, I steal all the tickets. I then rearrange them in the following way. I get all the tickets numbered between 0 and 0.990, and my best friend gets all the tickets numbered between 0.990 and 0.999. I then redistribute the remaining tickets to all the people who bought tickets. So by morning, my friend and I have all the tickets numbered between 0 and 0.999, but everybody who had a ticket still has a ticket, and the ticket she has is just a good as the one she had before. I have made it pretty sure that I would win, but I haven't lowered anybody else's chances at winning.

Bracketing contingent considerations of public peace and of positive law, it seems that:

1. I have harmed none—no one's chance of winning has gone down.
2. I have benefited some myself and my friend—our chances of winning have gone up.
3. I have done wrong.
4. Thus, an action that benefits some and harms none can still be wrong.

One might object. Suppose ticket number 0.458 wins. Previously it was assigned to Mr Smith. Now it's mine. Haven't I harmed Mr Smith? Maybe but maybe not. Let me fill out the case by saying that there is no fact of the matter as to who would have won had I not shuffled the tickets. In the story, we live in a very chaotic universe, and any activity—be it stretching one's arms in the morning or shuffling tickets—affects the random choice of winning number. There is no fact about what that random choice would have been had things gone differently. Thus just because ticket 0.458 wins and it was Mr Smith's before my night-time activity one cannot say that I have harmed Mr Smith. (Molinists won't like this. But surely whether I have harmed anybody shouldn't depend on the truth values of Molinist conditionals.)

Michael Rabenberg said...

I think the principle that an act which harms no one and benefits someone is permissible admits of pretty straightforward counterexamples. Suppose I attempt utterly unsuccessfully to harm innocent stranger Bob, and in so doing inadvertently benefit him a bit. What I do is wrong.

Alexander R Pruss said...

I think a risk of harm is a harm.

Alexander R Pruss said...

Or else one can simply modify the principle: "An act which is known for sure to harm no one and to benefit someone is permissible." And the case I gave may still work against that.

Heath White said...

This strikes me as having the intended effect of Hilbert's Hotel, namely that an actual real-numbered infinite is impossible.

William said...

Most governmental laws regarding real-life lotteries specify that every person's chances be the same. So, the law defines the proposed redistribution as legally unfair, because (I suppose) your chances are not the same as everyone else's.

A case where the law makes better sense than the math I think.

Alexander R Pruss said...

The law doesn't prohibit buying multiple tickets, though.

I set it up as theft, but you could even do this as a consensual swap. Since all tickets are on par, nobody could reasonably object to your proposed swap.

In fact, even more amusingly, you could set the case up so that you swap each person's single ticket for two tickets, while still pocketing enough tickets to be pretty sure to win. Who could object? :-)

Richard Davis said...

Maybe you harm a group of people, without harming any single person in the group. There will be certain groups of infinitely many people such that you've decreased the probability that some or other person from that group will win.

Richard Davis said...

This seems to be true at least of any group which consists of all the contestants except for you and your friend and zero to finitely many others.

Alexander R Pruss said...

Yeah, though they might not be "natural" groups. They might be completely arbitrary groupings, like the group of all people who have an even number of hairs. Do such groups have a common good?

Richard Davis said...

Good point.

It seems to me, though, that any group whatsoever has a common good. For instance, suppose there are two sets S1 and S2 such that their members can be paired one-for-one so that each element of any given pair is qualitatively identical to the other element of the pair. Let there be one exception to this: a single pair whose elements are not qualitatively identical. Now suppose one element of that anomalous pair (in fact, the element from S1) is better than the other element (the element from S2), and you are asked to choose between the two sets S1 and S2: which will cease to exist? It seems that we should choose for S2 to cease to exist rather than S1. So the fact that one element of S2 is worse than one element of S1 exposes S2 to danger: it introduces a possible situation in which S2, rather than S1, will be selected to be removed from existence. In this way, the existence of a poorer element in a given set endangers the continued existence of that set. So this makes it seem that for any group whatsoever, any bad-making feature whatsoever of any member of that group harms the group. It should not be possible for a group to be harmed, however, unless the group has a common good.

Here's another argument: If not just any group of people has a common good, then there will be a sorites series from the groups that do have a common good to the groups that don't. If there is such a series, then there are some intermediate groups of people for which it is indeterminate if they have a common good. But definitely, God cares about a certain good at least slightly iff it exists. So if there are groups for which it is indeterminate whether they have a common good, then it is (in certain cases) indeterminate whether there is a certain good which God cares about even slightly. So if some groups lack a common good, then it is indeterminate whether God exhibits certain token states of caring at least slightly. One might think this is a strange result.