Sticking It To The Man

This morning while riding the U-bahn to class no one died--or appeared to be dead--but I did have my ticket checked by one of the subway personnel. This morning only marks the second time I've had my ticket checked, meaning that if past experience can be trusted I will only get checked once a month on average. My immediate thought was that if the probability of my ticket being checked is so low, why on earth would I ever purchase a ticket? (As a bit of background for those unaware readers, Germany has an "honor system" for its public city transport; there are no turnstiles, but if passengers are discovered on public transport without a ticket they will be fined.) For the strictly rational members of Homo economicus, a simple expected value calculation is all that is needed to decide the appropriate course of action. If the expected value of the fine is less than what I would pay for the ticket, then I'd be financially better off by not purchasing a ticket and playing the odds.

To find the expected value of the fine, one merely multiplies the probability of being caught with the value of the fine (≈50 €). In my case, the equation is thus:

( 1/30) * -50€ = -1.67 €

In other words, the expected fine I would expect to receive on any given day is less than 2 €. But what is that compared to the daily cost of a ticket?

Well, because the monthly ticket costs about 50 € it actually has the same daily cost as the fine--in fact, in my case, the ticket is the fine. In other words, if I were caught without a ticket, they would force me to buy the ticket I should have bought anyways. One really needn't do a probability calculation to see that a purely rational actor would never buy a ticket under these conditions. He or she has nothing to lose and a small chance to be better off by being a literal free-rider.

Of course, my probability distribution is a function of the train I ride on to town--many other trains are checked far more frequently than mine. Nonetheless the lesson is clear: unless the amount of the fine is raised or the chances of getting caught increases, gaming the system would be a rational choice under my circumstances.

Good thing my ticket is already paid for, I suppose.