Ethics on the Infinite Block

Suppose that you live at the first house on an infinitely long block. Each house has a single occupant, and as things stand, the well-being of the occupants is distributed in the following way: the occupant of every 10th house is happy, and the occupant of every other house is miserably unhappy.

God comes before you and presents you two offers that, if you accept, will make some people happy and some people unhappy. The first offer is such that the occupant of every 101st house will become happy, and every the occupant of every other house will be miserably unhappy. The second offer is such that the occupant of every 3rd house will become happy, and every the occupant of every other house will be miserably unhappy.

Supposing that you only have the well-being of others in mind, must you choose the second option and not choose the first? It is deeply intuitive that you should. The world seems to be better off if every 3rd person is happy than that every 101st person is.

Of course each option will leave an infinite number of people happy and unhappy. And there will be both an infinite number of people made happy and unhappy in each scenario that would not have been happy or unhappy in the other. Thus, there is no good sense in which more people will be happy under one option than another.

One might say that in such a case, we should pay attention not just to the numbers but to the structure. It is better that happiness should be structured in such a way that we come upon it more often, as we travel along a natural path. The second option makes happiness more common, even if it doesn't make any greater number of people happy. We might think that it is better for that reason.

However, this response is odd. We could produce the same distribution simply by moving people around. Suppose that God offers the following third option: he will move the currently happy occupants around so that there is one in every other house. Then he will pick one at random and make her unhappy. Ought you choose this option? The distribution is better, but some one additional person is unhappy. If you ought not, it is hard to see why you should choose the second option, if it were between nothing and it (or between the first option and it). If it is not better because of the number of people, or because of how their happiness is structured, it is unclear how it is better at all.

On the other hand, it seems to things strictly worse.