New Jersey has very strange rules determining who has the right-of-way at rotaries / roundabouts when there aren't signs to clarify:

There are no set rules for driving into, around and out of a traffic circle in New Jersey. Common sense and caution must prevail at all times. In most cases, the circle's historically established traffic flow pattern dictates who has the right-of-way. If a major highway flows into and through the circle, it usually dominates the traffic flow pattern and commands the right-of-way. Traffic control signs, such as stop or yield signs, at the entrances to the circle also govern which motorist has the right-of-way. Never enter a traffic circle without checking all signs and determining the intentions of the motorists already moving within the circle.

Whenever a motorist is in doubt concerning who has the right-of-way in a circle, he/she should exercise extreme caution and remember the basic rules governing any uncontrolled intersection: The vehicle to the left yields the right-of-way to the vehicle approaching from the right.

The New Jersey Driver Manual, 2020

Having right of way depend on the "historically established traffic flow pattern" means that anyone who approaches an unfamiliar one doesn't know what the rules are. Which is definitely not how you should set up your traffic system!

Additionally, the second paragraph says drivers already in the rotary should yield to drivers entering, which is the opposite of the system everyone else has standardized on.

I encountered this several years ago, but at the time the only source I found was a dead link from Wikipedia. NJ has revised their manual, however, and post of the 2020 version, so I've updated Wikipedia.

On top of all that, NJ is apparently so embarrassed about this that they won't allow you to copy text from the manual:

If I were in charge of this for NJ, I would announce that we were going to switch to the standard "entering traffic yields" system in some number of months, and ask people to submit any locations that should be considered for alternative signage ahead of that change.

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I suspect this is one of those things which works way better than it sounds.

First, what fraction of people actually remember their state's official rotary rules? Presumably most follow the signs or the conventions of other motorists anyway. If the signs or conventions ever disagree with the official rules, I expect the signs/conventions to win. And usually, I expect that do-what-everyone-else-does is a better driving safety rule than follow-the-rules - for instance, if most of the traffic is way over the speed limit, then driving slowly is dangerous.

Second, social convention in general tends to work better-than-it-sounds, and some of the reasons for that carry over here. If a particular rotary circle happens to have bad visibility in one place, or one road coming in is much larger than another, that naturally turns into a social convention in a more fine-grained way than most laws.

I'm not sure that it ends up net-better having no official rules, but it's a case where I'd at least be cautious about High-Modernism-ing in and implementing new rules.

what fraction of people actually remember their state's official rotary rules?

Almost everywhere has standardized on a rule where the people already in the rotary have right of way. I'd expect that in areas with a lot of rotaries, 85%+ of the drivers know this (including knowing it implicitly).

if most of the traffic is way over the speed limit, then driving slowly is dangerous

It's legal to drive well below the speed limit, which can put you at a very high delta two other cars, and I agree that can be unsafe, but driving at the speed limit? I'm having trouble thinking of any places where the average speed is so much higher than the limit that the safety benefits of being closer to the speed of other cars would outweigh the safety benefits of slower driving.

It's a case where I'd at least be cautious about High-Modernism-ing in and implementing new rules

I don't know; traffic flow seems like a place where clear rules have generally worked extremely well, and NJ is pretty much the only place not using the standard rule?

I'm having trouble thinking of any places where the average speed is so much higher than the limit that the safety benefits of being closer to the speed of other cars would outweigh the safety benefits of slower driving.

Some parts of Route 2 in MA seem this way to me. Some of the stretches between I-95 and I-495 have a speed limit of 40-45 but an average speed of 65-70.

 

The MA drivers manual says to never drive over the speed limit (of course), but it also says to drive at the speed of traffic and not slow down cars behind you if you are in the second lane of a highway (p104). The intersection of these guidelines is unclear.

Some parts of Route 2 in MA seem this way to me. Some of the stretches between I-95 and I-495 have a speed limit of 40-45 but an average speed of 65-70.

Funnily enough, I drove this yesterday, and also happened to have a conversation with my kids about speeding. I tried driving exactly the speed limit, in the right lane, and while pretty much everyone was passing me, the speed delta was pretty low and it didn't feel unsafe. I agree this is not how people usually drive that road, though.

The MA drivers manual says to never drive over the speed limit (of course), but it also says to drive at the speed of traffic and not slow down cars behind you if you are in the second lane of a highway (p104). The intersection of these guidelines is unclear.

My reading is that driving in the right lane, at the speed limit, is the maximally legal option?