As a european 4 way stops seem really inefficient to me. If the intersection isn't that busy a 2 way stop (or no stop at all) favouring the more frequently used road is the obvious choice. If it's a busy 4 way stop however, can you really keep track of when other cars arrived at the stop? And if it's busy enough that you have to yield to the car to your right, chances are that everyone has a car to their right - so vague negotiation between drivers is required. Nobody wins in that scenario.

Also, roundabouts are the superior 4 way stops.

Figuring out who goes next is not remotely as difficult as you have made it out to be. Where I used to live, I would go through two four-way stops twice each day during peak traffic. There are generally two scenarios when you approach the intersection. In light traffic, you get to the intersection and nobody else is waiting to cross, or it is obvious who got there first. In moderate traffic, you will queue up behind one or possibly two cars. Once you get to the front of the queue, you wait for the cars on your left and right that are already at the front of the queue, and then you go. This is simple because each direction of traffic alternates, and it is reasonably fast because the queues are very short.

The real worst case scenario is that during light traffic four cars approach simultaneously, but not only is this extremely rare, but it is not really even a problem when it happens.

In my personal experience I have had far, far more problems in US cities on two-way stops when I am bicycling and a driver incorrectly yields when they have right of way.

I suspect that most Americans feel the same way about roundabouts that, say, Germans feel about 4-way stops. But please remember that roundabouts require more land and much more capital investment. The tradeoffs in the US are different.

Sounds like a high frequency traffic light, but less explicit.

Well, admittedly my experience with 4 way stops is nonexistent (never saw one in europe) and it may simply be a case of not being used to them, but I consider give-way intersections, 2 way stops, roundabouts and finally traffic lights as superior solutions - pretty much in that order and depending on how busy the intersection is. The goal should be to reduce breaking and full stops.

Except on the “compact real estate” axis. A plain intersection is always going to be smaller.

(Cattlemen Rd in Sarasota)

For the first year or two perhaps, but I wonder if the long term pay-offs might be worth it.