I don't have the citation, but I remember this quote:
"The easiest way to make people stupid is to limit their degrees of freedom"
Cars really only have 2 degrees of freedom: linear acceleration and radial acceleration. In traffic, these DoFs go down by a lot. You ability to de/accelerate linearly is very limited by the cars behind you and in front of you. Your turning also goes down to nearly a binary choice of 1 lane left/right.
Get people 4-wheeling and the stupid is very much still there, but just to get back to a main road, you have to use your noggin a fair bit more. Folks tend to think things through and weight choices more.
The social dynamics are themselves a dimension. Social network graphs can behave as fractals. In a gymnasium filled with people, there is a significant 'fractallyness' to the social network. In traffic, the fractallyness is very limited to just about all the people in the road near you. The social graph, though more fluid in a traffic jam than a pep-rally, is still fairly small.
3Blue1Brown has a great video on the dimensionality of fractals [0] that is useful here. I'm just going to spitball, but I'd bet that the dimensionality of the social graph of a traffic jam is really close to 1.
So in the end, the DoFs of a traffic jam are probably very close to 3, but just a bit over. Say, 3.14-ish. ;)