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This is an interesting problem that I think some states in the US have at least partially solved.

The highways in Michigan, for example, are almost all set at 70 MPH (minus those around large cities like Detroit, a point I disagree with). The result has been a dramatic reduction in speeding. I'm not sure if road safety has improved or not since the change, but since I have taken the same way to/from work 5 days a week for 15 years, I can say I haven't seen any increase or decrease in accidents, personally. What I have noticed is a dramatic change in driving behavior. When the limit was 55 MPH, the majority of traffic was going at least 60 with a sizable minority of traffic working very hard to get around those doing 60.

From my personal perspective, 70 MPH feels fast enough. It probably feels that way because I'm not being tailgated at that speed, nor do I feel like I'd have to slow down to take a bend in the road at that speed (my understanding is that the highways in Michigan are designed to be driven safely at 75 MPH in reasonable weather conditions). By casual observation, most people are driving between 65 and 75 MPH outside of rush hour.