1. Just because X (here, income distribution) creates a bias that we have to correct for doesn't mean that the bias created by Y (here, self-selection for lottery participation) isn't also problematic form a statistical perspective.
2. There are a lot of reasons to believe that, in the case where we compare charters to publics, that the volunteer selection bias is more problematic than the income distribution bias in public schools. Namely, we pretty much already know how to statistically control for the latter, but it's a lot more difficult to statistically control for the former.
So, you're wrong. Period. Voluntary selection bias exists. This is just a scientific fact. You have to correct for it in statistical studies. Period. End of story. Do other biases exist? Yes. Are they more important? No, because that's a stupid question. Any sort of selection bias is a threat to validity, and the entire point of a bias is that it's hard to know exactly the effect it's having until you correct for that.
But, and I stress this because you seem to be ignoring it, the important portion of all of my posts has NOTHING to do with selection bias!
In many states we don't even have a meaningful statistic upon which to make a comparison between chaters and non-charters because charters aren't taking the same standardized tests. So even after perfectly correcting for bias, we still have zero hope of actually comparing charters to publics.
Fundamental take-away: any school taking taxpayer money should be required to take the same standardized tests as public schools. Otherwise, any and all comparisons between them are bunk.
That you are right because you can claim that parents who are interested in their childs educations and apply to charter schools is the selection bias.
But this is not what this discussion is about. The claim being made was that charter school had an advantage because they got to pick the best kids and leave the rest for the public school system.
It doesn't and so the selection bias you keep insisting exist is really nothing compared to the one that exist in the public system where you are completely depending on how rich your parents are so they can live the right place and you are zoned for that.
Thats what parents do btw. Move to the good school districts. Those who can afford it. To any extent a lottery is selection bias it's simply not relevant or interesting for the premise of this discussion which is that the charter schools had an advantage.
They don't. Public schools in rich neighborhoods however do.