The article focuses on two children, one of whom lives right across the street from a good school and one who doesn't. The kindergarten only has 32 places, only 16 of which are reserved for local children, with the other 16 giving everyone equal access. Since there are lots of ties, the lottery is important.
An early education in the meaning of ‘no’
"The system seems deeply regrettable to her parents, Jen and Doug Bowen-Flynn. But to Marie and Markel Wade of Dor chester, it is a blessing. They, too, live steps away from an elementary school. If school assignments were based on proximity, they would have no choice but to send their children to Winthrop Elementary, which has lower test scores and a less polished reputation.
(Our papers on the design of the Boston school choice mechanism here.)