The initial apparent advantage of the medallion system is that it gives the regulators quite a lot of control over what cab operators do and it's easy to imagine that power might be used to do good.
We don't to limit competition for that. All we need to do is spend 50% of medallion fees on inspections (with the remainder going to general wasteful NYC spending, e.g. redistributing wealth based on random chance [1]).
In a comment on this topic a couple of years ago, I did some calculations showing that by spending only 50% of the yearly medallion fee, we could subject every taxi to an undercover inspection every single day.
That's a little harsh - yes, a lottery is involved, but only because the supply falls far short of the demand. The lottery is conducted only among eligible people anyway (or at least, ineligible people are filtered out after the lottery), and only low-income people receive the apartments in the end.
We don't to limit competition for that. All we need to do is spend 50% of medallion fees on inspections (with the remainder going to general wasteful NYC spending, e.g. redistributing wealth based on random chance [1]).
In a comment on this topic a couple of years ago, I did some calculations showing that by spending only 50% of the yearly medallion fee, we could subject every taxi to an undercover inspection every single day.
http://news.ycombinator.com/item?id=1650659
[1] http://www.nyc.gov/html/hpd/html/apartment/lotteries.shtml