DyslexicPoster agree, the idea that kids currently in private schools moving into state schools will be good for the state schools is pie in the sky. My kid who went through private school did do partly because he had special educational needs that the private school could meet as a matter of course, but that could only have been met in the state school he'd otherwise have gone to if I had been extremely sharp-elbowed and advocated for him non -stop. Not only did I not want to do that (it might well have meant me going part time at work, so less tax revenue, too) but also I didn't like the idea that any extra teacher attention or resources I secured for him would likely have meant less for other children. If I'd had to send him there, though, you had better believe I would have done whatever it took to get his needs met.
At the same time, the presence of another well -supported kid or middle-class parent would not have benefited the school at all - being a school in a solid middle-class area near a university, it had those in droves already.
As for voting based on who I think likely to improve state schools, I've always done that anyway. (It would be interesting, in fact, to survey how people with kids in private school prioritise state education spending as a factor, compared with people with the same income but no kids in private school. I wouldn't mind betting a small amount that the former group prioritises state education spending higher, even if you don't exclude voters with kids in state school from the other group. Private school parents may not be on average earnings, but spending that amount of money on education when you could instead choose to spend it on cars, holidays, pension etc is generally a strong statement of education being important to you. I know most people couldn't afford private education, but at the same time, there are a lot of people who could if they really wanted to, choosing not to because they prioritise other things. I've seen it here often, usually as people saying they "can't afford" private school after saying enough to make clear that they are in a better position to do so than I've ever been. It's their right, of course, but I sometimes feel part of what spreading the "private school parents are all rich" meme does for people is help them avoid facing the fact that they're not prioritising their children's education as highly as they might, which if they faced it would make them, rightly or wrongly, feel guilty. There, I've said it ;-) )