reverse lottery

Of course you know about the lottery, where you can pay some small amount of money for a low probability of winning a large amount of money.  And lots of businesses have promotions along the same lines: e.g., if you buy our slightly-overpriced french fries, you might win a yacht.

However, I have never seen the reverse: we're giving out free french fries, except there's a small chance you'll have to pay us $1000.  Now, a potential customer might not have $1000, so let's lower the values here to get a simpler and fairer comparison between two potential offerings:

1. French fries cost $1.25, but one out of every five customers gets his for free.
2. French fries are free, but one out of every five customers has to pay a $5.00 fine.

There must be a reason why businesses never offer the second type of deal.  Is it just logistical?  Or is it that people would hate this, and a 1 in 5 chance of losing $5 is worse than just giving away $1.25.  It seems that this sort of deal would not be too difficult to arrange, so I have to imagine that businesses don't offer it because people don't like it.

This brings me to my main point: a lot of law enforcement works like this "reverse lottery", and I think we're underestimating just how much people hate this.  Our goal should be punishments that exactly offset the value of the crime, and a 100% chance of getting caught.  This makes enforcement prohibitively costly, but serves as an ideal.  (The other extreme, where you get away with criminal behavior almost all of the time, but if you get caught you and your family are tortured for 20 years then killed, sounds awful to anyone.)  Certainty itself has value, and this needs to be traded off against the cost of enforcement.

Disclaimer: I don't know anything about crime statistics, and I would hope there are experts who do know what happens as you vary the level of punishment and probability of getting caught.  I'm betting that, while keeping level of punishment times probability of getting caught constant, good things happen as punishment goes down and probability of getting caught goes up, and the only reason not to move further in this direction is cost of patrol.

This blog post arose from a discussion with Alex Jaffe.

(Another way to look at things is that in my ideal scenario, there is no crime — you simply pay for the damage you do.)