Do school vouchers work?

My biggest issue with vouchers is that I honestly don't believe the schools are the problem. Parents are. I think the children being sent to private are much more likely to have parents who are more involved with their education whereas it's more of a coin-toss with the parents of kids in the public school system. The voucher system may have a positive effect on the individual children's education to some degree, but I really don't think it does anything to address the root of the problem which is at the home.

The main problem with school vouchers is that there are never going to be enough issued to satisfy the needs of the community. This has been the main complaint about the voucher program in Washington, D.C. Why is one child more deserving than another?