The reason the lottery is there is that you don’t have to specify N. Sure, if you do, it makes the scary infinities go away, but it seems natural that you shouldn’t improve your expected outcome by adding a limit on how much you can win, so it seems that the outcome you get is at least as good as any outcome you could specify by specifying N.
True, “seems natural” isn’t a good guideline, and in any case it’s obvious that there’s something fishy going on with our intuitions. However, if I had to point to something that’s probably wrong, it probably wouldn’t be the intuition that the infinite lottery is at least as good as any finite version.
The reason the lottery is there is that you don’t have to specify N. Sure, if you do, it makes the scary infinities go away, but it seems natural that you shouldn’t improve your expected outcome by adding a limit on how much you can win, so it seems that the outcome you get is at least as good as any outcome you could specify by specifying N.
True, “seems natural” isn’t a good guideline, and in any case it’s obvious that there’s something fishy going on with our intuitions. However, if I had to point to something that’s probably wrong, it probably wouldn’t be the intuition that the infinite lottery is at least as good as any finite version.