The federal government underwrites affordable housing in part by providing tax credits to developers who build affordable housing. The Texas Department of Housing and Community Affairs parcels out these tax credits in Texas. A lot rides on TDHCA's decisions and competition for the tax credits is fierce.
This Statesman article on TDHCA's scoring system is interesting because it explains how NIMBYism is baked into TDHCA's evaluations. Although projects are scored on several criteria, local opposition (or support) carries a lot of weight. The scoring system effectively counts local reaction twice: it weights letters from neighborhood associations and it weights letters from the legislators who represent these neighborhoods, who, naturally, can be counted upon to do their constituents' bidding. There is a 52-point swing between unqualified opposition and unqualified support, a big deal given the maximum score is 226. (Although I am calling this "TDHCA's system," in fairness I should note that it is merely implementing statutory standards.)
It's worth stressing that these are not zoning cases. Tax-credit subsidized housing can only be built where zoning allows it. Developers, in other words, merely propose multi-family projects for parcels of land that the city has already determined are suitable for multi-family housing. Concerns about traffic, noise, overcrowding, etc. should have been resolved when the parcel was zoned.
Weighting the neighborhood's approval and the approval of its proxy is of course bad policy. Homeowners are notoriously risk averse. Their risk aversion causes them sometimes to oppose a project that has a remote chance of depressing property values even though it has a better chance of raising property values. The premise of the tax-credit program is that cities need more affordable housing. Politicians like to talk about affordable housing in the abstract but ultimately it has to be built somewhere, which means that neighborhood opposition has to be discounted rather than emphasized. Unless, that is, we are happy to relegate it to neighborhoods that are already full of affordable housing, which is the effect of current policy.
I also want to point out that the TDHCA's system institutionalizes a sort of "ward courtesy" at the state level. The Texas Legislature attempted to reform that system this session, but Perry vetoed it for murky reasons. (Texas Housers has a detailed account.) The proposed reform would have entrusted the decision to support or oppose the project to the local elected body rather than a single legislator, probably in the sound belief that councilmembers are more likely to make reasonable decision in the aggregate than individually.