From DC Common Lottery Board September 2015 minutes - https://ms-dc.s3.amazonaws.com/docs/clb-meeting-minutes-91415.pdf

Algorithm Analysis: My School DC tested the algorithm design that uses a single
random lottery number for each applicant, regardless of the number of school
selections. We wanted to confirm that design this summer with our own data, since
we now have two years of the common lottery under our belt. Our contractor ran
5,000 lottery simulations using real DC data and compared match results using single
random numbers (SRN) and multiple random numbers (MRN). Both SRN and MRN
maintained the overall match rate of about 72%, but SRN matched about 400 more
students (2% of applicants) to their #1 choice than MRN did. Based on the results of
that analysis, the design with the SRN remains preferable and My School DC will not
be recommending an algorithm change to the Common Lottery Board for the 2016
lottery.