If people vote as if their individual vote determines the vote of a non-negligible fraction of the voter pool, then you only need ν=O(1/N) (averaged over the whole population, so the value of the entire population is νN=O(1) instead of ν=O(1), which seems much more realistic.
So voting blue can make sense for a sufficiently large coalition of “ordinary altruists” with ν≫1/N who are able to pre-commit to their vote and think people outside the coalition might vote blue by mistake etc. rather than the “extraordinary altruists” we need in the original situation with ν=O(1). Ditto if you’re using a decision theory where it makes sense to suppose such a commitment already exists when making your decision.
If people vote as if their individual vote determines the vote of a non-negligible fraction of the voter pool, then you only need ν=O(1/N) (averaged over the whole population, so the value of the entire population is νN=O(1) instead of ν=O(1), which seems much more realistic.
So voting blue can make sense for a sufficiently large coalition of “ordinary altruists” with ν≫1/N who are able to pre-commit to their vote and think people outside the coalition might vote blue by mistake etc. rather than the “extraordinary altruists” we need in the original situation with ν=O(1). Ditto if you’re using a decision theory where it makes sense to suppose such a commitment already exists when making your decision.