How about get rid of medallions and let a free market exist? Uber is going to provide it if they don't, in fact, that restriction on the market-- artificially for political purposes-- is what made Uber possible.
Uber's, taxis and other cars get to use Manhattan streets for free. The real estate those streets sit on is perhaps the most valuable in the entire world, and the maintenance for those streets is paid for via property taxes. I'm all for a free market, as long as players in the game aren't freeloading.
The problem is that once the medallions were created, they represent a property right, and the Fifth Amendment Taking Clause prevents the government from eliminating them without compensation. And, it's hard to see the argument for spending $16 B to do so.
On the positive front, once Uber switches to robot drivers in the next decade, yellow taxis will probably go away forever, and the medallion system can be eliminated.
Then, the city can be compensated via congestion pricing for the traffic that on-demand cars generate.
I highly recommend checking out Move NY for the most credible congestion pricing plan under consideration: http://iheartmoveny.org/
