Carrots vs. Sticks in affecting behavior

Instead of charging extra ('congestion pricing') to drive your car during rush hour, how about giving me a reward (a lottery ticket) for driving using less congested routes? That's a clever idea that is being tested by a Stanford professor:

"[…]So this spring, with a $3 million research grant from the federal Department of Transportation, Stanford deployed a new system designed by Dr. Prabhakar’s group. Called Capri, for Congestion and Parking Relief Incentives, it allows people driving to the notoriously traffic-clogged campus to enter a daily lottery, with a chance to win up to an extra $50 in their paycheck, just by shifting their commute to off-peak times. The program has proved so popular that it is to be expanded soon to also cover parking.[…]" (from The New York Times)

This is a really cool idea! I wonder if we can try it here in the city of Boston!

But what would it actually mean? In my experience, cars flow through openings and alternate routes in perfect proportion to the time it takes and the convenience it has. There are no 'secret routes" to avoid traffic, because enough people know them that the 'invisible hand' guides just enough people to each option so as to make everyone arrive more or less at the same time.

That means I think that the reward has to be for taking routes that are clearly inferior. Perhaps if I am trying to get from the BackBay to the FInancial District, I might take Storrow drive, or go directly through the city streets. I am guessing that during rush hour those two obvious routes are equally congested. But if I instead got on the Mass Pike and took that to the Leather district, that might be rewarded.

So a cool idea, but I wonder what actual traffic experts would say about it!