Balaji Prabhakar and the mystery rewards

Last week, the Times ran a gee-whiz article about Stanford computer scientist Balaji Prabhakar and his pilot program to reduce the number of people driving to campus. With a three million dollar (!) grant from the US DOT, it implements a lottery where people who choose not to drive during peak hours get credits which can be used to "win random cash rewards from $2 to $50 over and over again."

Whenever I enter a random drawing - that I actually care about, as opposed to paying a dollar for a charity raffle - I always want to find out what the odds are that I'll win. Interestingly, the Stanford pilot gives no indication of the odds that a driver will actually win one of these payouts. It makes me wonder how many economists, investors and statisticians signed up for the thing.

This is a more recent version of a pilot that Prabhakar and his colleagues ran in Bangalore, where commuters from downtown to the suburban call centers received similar random cash rewards for shifting to a less congested time. Interestingly, in that earlier version they were all bus passengers, and got rewarded for taking the bus.



The Stanford team did publish a paper (PDF) describing the Bangalore pilot, in which they go into detail about the reward system on Page 4:

Reward pyramid: The scheme has a pyramidal reward structure with four levels, as shown in Figure 9. The reward amounts are Rs. 500, Rs. 2,000, Rs. 6,000 and Rs. 12,000 in levels 1, 2, 3 and 4, respectively. The total sum of money in the pyramid is Rs. 96,000, distributed equally among the four levels. (Note that this amount is roughly equal to the total cost of extra fuel per week which was estimated at Rs. 15,000 per day.) Thus, there are 48 prizes worth Rs. 500 each, 12 worth Rs. 2,000, 4 worth Rs. 6,000 and 2 worth Rs. 12,000. Each level has a minimum number of credits needed for qualifying at that level. This number is 3, 7, 12 and 20 for levels 1, 2, 3 and 4, respectively. A commuter who qualifies at one level automatically qualifies at all lower levels.

In other words, the only way to know your chance of winning any given prize is to know which level you've achieved and how many other people are in each level. You could, of course, write a computer program to tell the commuter what the odds are for each level on a given day, but why bother if nobody cares?

In figure 3, it is revealed that there were 8000 commuters registered in January 2005. With 66 rewards, the chance of winning any reward is one in 121, which is pretty good as far as lotteries go. With one lottery a week, it is likely that any given commuter will win the ₨500 reward within three years. If we assume that each commuter works with ten other commuters, any given commuter will know someone who has won within three months.

My guess is that these odds were high enough to get people to change their behavior on the basis of feeling alone. That's pretty impressive. I have serious problems with the framing of the issue and concerns about the application of this idea, which I'll raise in future posts.