Qualifying the NYC Housing Lottery
https://www.nytimes.com/2019/01/11/realestate/better-than-the-powerball.html
Due to New York City’s notoriously high rent prices, many people enter the city-run affordable housing lotteries for a chance to win affordable (i.e. below market-price) and rent-stabilized homes. With over 10s of thousands of people applying every day, there were over 4.6 million applicants in 2018 alone, all vying for one of the 7,857 available apartments. However, this number is almost a 300% increase from that in 2012, when there were 2,741 apartments up for grabs. As detailed in the articles listed above, the chances of winning the housing lottery in NYC was 1 in 592 (0.168%) in 2018, as compared to 1 in 1000 in 2016—a 168% increase. To enter these lotteries, residents must pass certain requirements, from income qualifications to interview processes.
The nature of the candidate screening process for these lotteries reminded me of the concept of matching markets and market clearing prices. Since every candidate has high valuations for low-cost housing, the city adds restrictions and qualifications in lieu of “prices” to reduce the amount of buyers, or the size of the constricted set. For example, as mentioned in the articles, New Yorkers who earn less than $120,615 for a single person, or $199,650 for a family of 6, can enter the lottery. This disqualifies many applicants, if either they surpass this threshold or cannot provide work history or tax record paperwork to substantiate their claims. Furthermore, some housing developments give priority to people who meet certain criteria, such as government workers, homeless people, or people already living within the neighborhood. Through the interview process, the New York City Housing Authority is also able to filter through the applicant pool on the basis of family size and hardships experienced. However, because the demand for these apartments is so great, a perfect matching is hard to prescribe to this bipartite graph, where houses are on one side and buyers are on the other. Even after assigning various qualifications to the buyers (or “pricings” to houses), it is hard to decrease the applicant pool to the point in which the number of buyers equals the number of houses; it is almost guaranteed that there will be a constricted set. Because of this, the city relies on a lottery system to delegate which people get which houses.