A Preferential Parking District Sign in Hollywood
Source: WhitleyHeights.com
Preferential parking districts (PPDs) are areas, usually in residential neighborhoods, where there are parking restrictions that residents can be exempted from by getting a permit. They usually spring up in situations where residents are angry about "spillover" parking from nearby businesses, and/or "outsiders" parking in front of their houses.
A good thing about PPDs is that they often introduce an element of pay parking. Residents buy permits to offset the City's cost of providing the district (which includes PPD application processing costs, signs, permit processing, etc.). A big drawback however, is that the area is essentially shut off to anyone else who might want to park there. This can harm local businesses that don't have a lot of off-street parking to offer their customers. It can also harm commuting students who may be parking in a neighborhood to avoid the higher costs of parking on campus.
Here's what I think should happen instead. Let me start off by saying that this will often be politically difficult, but I think it makes a lot more sense, and I hope that people will one day see the benefits of not gleefully guzzling the free parking Kool Aid.
Instead of a PPD, set up a parking market. This should include areas for both short-term and long-term on-street parking. The short-term parking can be handled by putting up meters. Yes, I'm advocating for putting up parking meters in front of people's houses and apartments in these situations. If you want to get really fancy, embed sensors in the ground under each parking space, then use the data on which spaces are occupied to set demand-sensitive prices that keep some spaces open at all times (hat tip to Shoup Dogg). For long term parking the solution is designating certain areas with signs on every block and selling permits, but not the same way a PPD sells them. These permits would be for sale to anyone, and their price would be based on demand so that they don't sell out instantly. They would also have to be renewed periodically.
This system insures that everybody who is willing to pay the market price for parking will have access to both short and long term parking. The prices are a disincentive to leave cars on the street (and hence to own an excessive number of cars) and this benefits alternatives to the car, which, with any luck, will some day make this discussion less relevant :)

