Singapore does this in a sense. In order to qualify for new, heavily subsidized public housing (so called "Build to Order" - BTO) you need to be married and be

Singapore does this in a sense. In order to qualify for new, heavily subsidized public housing (so called "Build to Order" - BTO) you need to be married and below the household income threshold (which is actually very high - $170,000 for a couple). Well the problem is demand massively outstrips supply, especially in highly desirable developments. So what do they do? They have a lottery. And because of the way Singapore lets you sell public housing at market rates after a period of time, it's a literal lottery - you can usually flip your unit for double after 5 years. So what happens? Lotteries are massively oversubscribed. Sometimes 10 to 1. And people have every incentive to enter the lottery because it's cheap ($50) but the pay out is huge. So as a result, plenty of young couple fail the lottery 3, 4, 5 times and then move to the resale market where prices are much higher. So instead of allowing the market to allocate housing based on who is willing to pay (with the proceeds going to the government who can use the money for other things), the price is kept low and allocation is based on a lottery. I'm not sure it's much better?