High occupancy vehicle lane math top-up

I think mathematics supports that at some volume of cars or traffic density, shifting some people/cars from regular highway lanes to the high occupancy vehicle lane improves traffic for everyone.

My perception is that during the 20th century HOV lanes always went to multi-person cars. Change this to allow some other cars to travel that way, improving traffic.

Reaching that mathematically optimal balance of high occupancy vehicle lane and regular highway could be accomplished with giving people the option to say they want to travel in the high occupancy vehicle lane, and then having a stochastic algorithm sometimes permit them to use it.

Improve this with the computer displays already at cars. A computer could do a stochastic lane assignment amongst interested drivers directing some to the high occupancy vehicle lane even if they were single drivers. The computer display in the car just says "High occupancy vehicle lane approved"

At some tension with this idea however is the use of high occupancy vehicle lanes as a nice, already-exists place to host driverless cars. I would rather see the driverless cars getting the light-traffic lane thus getting people to their preferred destinations faster, as a way of stimulating the development and adpotion of self driving cars.