Well, the student would get a voucher for the amount that would be spent on him/her (the per child amount) and he/she could use it anywhere. But any difference in that amount and the "cost" would be left to the parents. So if they got a $2 voucher and the private school charged $3, the parent would have to pay the extra $1 (obviously I'm not using real figures! LOL)
It is one argument that it would cause too many people to leave the public school (especially in poor neighborhoods) and therefore the school would suffer. Another argument is that it would force schools to get there act together, listen to what parents want, teach the children and "compete" for students, thereby making all schools better.
Just depends on which argument you are listening to. There are also different variations ...I mean like you could use the voucher to pick a public school of your choice too...just take your dollars to the public school of your choice...you wouldn't have to use the voucher at a private school.
The competition aspect is still the "positive" arguement to this. The "negative" is that people would generally pick there own neighborhoods, if the schools didn't have huge differences in quality...so for convenience they would stay in their own neighborhood. Thus having prodominantly white and non-white schools again....so the "segregation" argument comes into play.
In places where this has been tried (I heard about one recently, but don't remember where) they found the schools were more segregated, but all the schools improved academically (the ones in poorer neighborhoods too and sometimes by a larger extent because they needed more work), so the argument is, which is more important...segregation, or the education level.
This is a quick synopsis...it is very detailed and I surely haven't hit all the big points.
My personal opinion is that vouchers would help more than hurt, and that improving all schools is more important than keeping them racially balanced BUT that does not mean I want the schools segregated...I like for my kids to be around other races. It's just hard to artificially make people go outside their "group" and it's a tough call for me how to make that better and don't know if it is worth it if all could benefit if that wasn't such a concern. When I was in school we had a pretty balanced racial mix, but the different races still "mostly" hung out with others of their race. I mean, I had black friends but most of my friends were white, and the same was true for the black students (back then there weren't a lot of other races at my school, but my city is much more diversified now)
Anyway, that is my understanding...I lean toward one side over the other (I guess you can tell) but I do see the other side and am not saying that I couldn't be wrong.

Oh and just saw the other post...I forgot about the religious argument...like I said, it gets very complicated! LOL