Let's say that instead of taxing carbon, we pay people a bonus for emitting a below-average amount of carbon (proportional to the amount that they are below average by). If the amount is in a certain range, it will be too small an amount for wealthy people to care about, but large enough for poorer people to do things within their means (e.g. carpooling) to try to get it.
The results would hit certain geographic areas much worse than others, and (if priced enough to change behavior) would also probably depress car sales, which are two reasons why the federal fuel tax has been flat for over 30 years.