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In the 2015 Nevada Legislature the Taxi Cab companies successfully lobbied for changes in the law which they saw as giving them an advantage over Uber and Lyft but which actually gives Uber and Lyft passengers many more advantages in a car wreck.
Nevada law says a driver's or passenger's failure to use a seatbelt can't be used against them in a lawsuit. BUT, if you are riding in a taxi, but not an Uber or Lyft vehicle, your failure to use a seat belt can be used against you.
Also, taxis do not provide uninsured/underinsured motor vehicle coverage to their passengers but Lyft and Uber has to provide $1,500,000 in uninsured/underinsured motorist coverage to its passengers. Thus if you are in a Lyft or Uber vehicle and some uninsured or inadequately insured driver runs into you and hurts you, you have this great coverage with Lyft and Uber but not with a regular taxi.
Likewise, if you are riding in a taxi and the taxi driver is at fault for a collision, the taxi company only has to have $15,000 in liability insurance to any one person, whereas Lyft and Uber have to have $1,500,000 in liability coverage.
So from an insurance standpoint Uber and Lyft appear to have the advantage over taxis.
It is hard to say what your chances of injury are riding in cab versus riding in an Uber of Lyft vehicle. Cab drivers tend to be full-time drivers supporting themselves and their families on their earnings from driving a cab. Uber and Lyft drivers are usually part-timers willing to work for less because they can set their own hours. Generally cab driver need to be finger printed as part of their licensing process whereas Uber and Lyft resist that requirement. But if you are in a wreck in Nevada, your legal position is much better if you are in a Lyft or Uber vehicle rather than a taxi.