Some interesting stuff here, including links to more studies showing similar results in different countries.
The summary is that the reason motorists break more laws is that speeding is so common.
I don't think this is because motorists are all evil and cyclists are all saints. Probably, the reason motorists break speed limits is that it can be relatively difficult to keep cars below the speed limit. It's all too easy to absentmindedly speed up. It's also, perhaps becuase of this, widely seen as socially acceptable to break the speed limit (speaking anecdotally).
One interesting thing here, which may not surprise regular readers of Fuck Cars, is that better cycling infrastructure leads to less lawbreaking by cyclists. As is often the case, it's the design of roads and cities that changes behaviour, not abstract appeals to road users to be sensible!
If there were no cars, there’d be a hell of a lot more bikes. I’d still want rules. Like which side of the road one should be riding their bike, etc.
Before cars, there were a hell of a lot more bikes (and pedestrians, horses, and horse-drawn carriages) and yet we didn’t need rules.
Stop signs and traffic lights were invented specifically because cars were uniquely dangerous. (Or rather, they were invented to shift the blame for the danger from the cars to the infrastructure.)
There were a hell of a lot less people then too, plus a lot less traveling.
You still need laws for bicycles regardless of the presence of cars.