But don't medallion owners also hire drivers? Not all of them care about their employer's reputation.
Thus, surely some negligible——but still tangible——fraction of cab drivers, working for Uber or not, will at some point rape a customer no matter what but with Uber the chances to collect evidence and identify the driver after the fact is probably much better, making it likely for the abusing driver to be prosecuted. This in turn creates a deterrent. With a regular cab, unless the customer can identify the car s/he doesn't really know who the driver is. Further, all the bad driver needs to do is to cover the cab number and become practically anonymous.
Thus, surely some negligible——but still tangible——fraction of cab drivers, working for Uber or not, will at some point rape a customer no matter what but with Uber the chances to collect evidence and identify the driver after the fact is probably much better, making it likely for the abusing driver to be prosecuted. This in turn creates a deterrent. With a regular cab, unless the customer can identify the car s/he doesn't really know who the driver is. Further, all the bad driver needs to do is to cover the cab number and become practically anonymous.