The move coincides with secondary school "national offer day", the day when local authorities send letters to families telling them where their child will go to secondary school.
In a letter to the acting chief schools adjudicator, Dr. Elizabeth Passmore, Balls requested she report on whether or not random allocation is a fair system.
Passmore will also look into whether or not twins are being split up because of random allocation.
She will have to submit her findings on both issues by 1 September 2009.
Balls said that random allocation could be a legitimate way of determining a school place in tiebreak situations.
But he said he does have sympathy with parents who feel the system is arbitrary, random and hard to explain to children.
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