Why not create community 'owned' housing, similar to a worker co-op, where poorer communities collectively 'own' the location. Everyone pays area-rental fees, but each month rented = 1 share ownership. Once the mortgage is paid off, the rent goes towards buying more rental properties and rinsing/repeating. A % of all rents is divided out by shares to each renter or ex-renter. A % could also go to LeBron's public school as a donation.

Obviously the longer you stay at a place and the smaller the place the more shares you'd have in the place. Shares could also = voting rights on properties/etc... More votes = louder voice.

Think of it as privatized (not government-ran) socialism in the real estate market.

If the property values go up, other people will buy the houses surrounding the collective, forcing the collective to pay more for housing and thereby raising the rents.