Many accidents happen in Taxis and ride share vehicles. Determining fault of these accidents is much the same as determining fault in all other types of motor vehicle accidents.  Accidents require an investigation into who acted negligently.  Assuming you're the passenger in an Uber, Lyft, or Taxi and that vehicle is struck by another vehicle (the driver of which was at fault), the other driver’s insurance will be responsible for paying for injuries.  If your ride share driver is at fault, your driver's insurance would have to pay.