In big liberal cities, the most politically acceptable form of new housing—apartments officially designated as affordable—isn’t sold to the highest bidder or rented to the first tenant willing to pay the going rate. It’s given out by lottery. This fact deserves a lot more scrutiny than it gets.

Instead of simply allowing enough apartment construction to keep up with employment and population growth, New York, Boston, San Francisco, Los Angeles, and many other cities have restricted housing development but simultaneously offered developers tax credits, zoning changes, and other incentives to include below-market-rate units in their projects, which have in many cases been made available to the public via lottery.

Last year, New York City’s Department of Housing Preservation & Development o

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