Most probably no. First, let's assume that perfect law-abiding, self-driving cars exist. One one hand they would eliminate incidents caused by inattentive driv

Most probably no. First, let's assume that perfect law-abiding, self-driving cars exist. One one hand they would eliminate incidents caused by inattentive driving, on the other hand they would in fact create incidents where attentive driver in the right of way would yield for an inattentive driver. Change in total incidents would depend on proportion of these events. Anecdotal evidence is anecdotal, but in my own experience number of incidents I have avoided simply yielding when having right of way is much higher then the number of incidents I have gotten into due to my own mistake. Second, actual "self driving" cars are far from that, especially in their interaction with other drivers. Third, there second order effects. E.g. a car quickly, unexpectedly maneuvering could cause other car to break sharp, which could end up in an accident where the original car is not even involved. With an increase of cars behaving differently than the local custom such accidents are bound to happen. Most probably we are going to see an increase in the number of accidents with proliferation of semi-autonomous vehicles before that number starts to dwindle.