DNA shows who soiled the commons (a crappy analysis)

This American Life featured a story on PooPrints, a company that DNA tests dog dropping to determine which dog left a mess. Economists often talk about the tradegy of the commons, and anyone who has stepped in dog poop knows that commons (open shared green space) become less valuable when filled with dog poo.

So in what situation will PooPrints work? First since it costs $30 to register a dog and next for each test you need to pay $50 to have the sample matched against the database of registered dogs. To work you must have an area where only certain dogs go (like a gated apartment or condo) and an organization where people can actually get people to register their dog.

So when will PooPrints be worth it? To make it simple we could assume everyone is a dog owner and that no poo goes unmatched. In that cases the reduction in poo would have to be worth $30 for it to be approved in a vote. A more complex case could consider when both dog owners and no-dog owners have to pay and there are cases where the poo is not matched. In that case the difference in utilities from the amount of poo with PooPrints (Upp) minus the utility with no PooPrints (Unp) is greater than $30 times the percentage of people with a dog (d) plus the % of times there is no match (nm) times $50 we also subtract out the case where there is fine if the dog is matched which will happen 1-nm% of the time (one fomplex had $100 fine so we will use that).

Upp - Unp > d*$30 + nm*$50 - (1 -nm)*$100