School Choice and Racial Balance

I like Peterson's idea:

To achieve racial balance, let  parents choose their school, and let oversubscribed schools admit students by  lot. If parents of all races and ethnicities seek admission to a particular  school at the same rate, then a lottery will ensure that the school's social  mix reflects that of the school district, the very goal Seattle said it tried  to achieve.

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School Choice and Racial Balance
By PAUL E. PETERSON
July 24, 2007; Page A15
http://online.wsj.com/article/SB118524106566875763.html

Schools that admit students on the basis of race run afoul of the Constitution, wrote Chief Justice John Roberts in the recent Supreme Court case, Parents v. Seattle. Over-subscribed schools may not use race as a tie-breaker when deciding which students to admit.