Is "medallion" a requirement for this search? I think a lot of cities that use this system merely call them licenses. I'm not sure that whether you call the system one of medallions or one of licenses makes them qualitatively different if the principle is that a) only a limited number can ever be issued creating artificial scarcity; b) that scarcity and resulting high cost create a protected group of suppliers; c) the city has a financial interest and even duty to shield the market from competitors and innovation.