It's called a legal obligation. I know landlords only like using that word when it comes to things that benefit them, but in some cases renters do in fact have rights, and you are in fact legally obligated to abide by them. If you get 400 applicants and decide to take someone with higher income that's one thing. If you do what a lot of landlords do and keep properties posted until they find someone with a preset income threshold and refuse to even consider voucher tenants? Scum of the earth.