I worry about this sort of argument because (at least so far as I can judge from introspection and seeing what others say) that +1000 utility is likely to come from sources that get double-counted if you just add up all the sensible people’s +1000 values.
When I say “it would be much better for A to win rather than B” I don’t generally mean that I personally will benefit hugely, I mean that I think everyone will benefit a bit, and when I’m choosing how to vote I attempt to do so altruistically and not count my own interests as much more important than everyone else’s in the way that (alas) I generally do in the rest of my life. And that benefit to everyone doesn’t really get 10x more important if the number of people who, like me, are clever and wise and good enough to have noticed A’s advantages is 10x bigger. You can approximate my opinion by saying that I attach +1000 utility to A’s victory, but that doesn’t really mean that we want A to win because it will make me happy, and if there are a million people like me then we shouldn’t say that when A wins it means +10^9 utilons rather than +10^3, because if there were only a thousand people like me then the net benefit of A’s winning would still be about the same, not 1000x smaller.
I’m not objecting here to your characterization of the situation as prisoners’-dilemma-like; I agree. (Maybe more like the tragedy of the commons, but it’s the same kind of thing.) But casting it in terms of the utility gained by sensible voters seems like it might encourage miscalculation.