Wednesday, July 30, 2008

The Economics of toilet seats

No, this is not about the industry that produce toilet seats, but rather about the habit for men to leave the toilet seat up. Hammad Siddiqi analyses this problem from a game theoretic point of view. Let me quote the entire abstract:

We model the toilet seat problem as a 2 player non-cooperative game. We find that the social norm of leaving the toilet seat down is inefficient. However, to the dismay of “mankind”, we also find that the social norm of leaving the seat down after use is a trembling-hand perfect equilibrium. Hence, sadly, this norm is not likely to go away.

It appears there is a literature on the subject: Jay Pil Choi argues that the selfish rule of leaving the toilet seat how one prefers it is the most efficient one. Any other rule (always up, or always down) inconveniences each member of one gender twice on each bathroom trip. With the selfish rule, one may not need to alter the seat, depending who came before, and never alters it after doing one's business. The always down rule is only efficient if the inconvenience to females is much larger than to males.

Hammad Siddiqi argues that a crucial element is missing from this analysis: conflict, or in other words game theory. One could do it like in a cooperative game, like Richard Harter. This assumes that members of a household minimize the joint cost of toilet seat moving. But what if they act selfishly, and possibly strategically?

Within a non-cooperative game, player can inflict penalties on others. In this case it would be females yelling at males for leaving the seat up. While leaving the seat always down remains inefficient, as in the two previous analyses, it is now a Nash equilibrium. There are often many such equilibria in a game, so this does not say much. But it is also trembling-hand robust, which means it is still the best strategy if the man (or the woman) sometimes forgets. Hammad Siddiqi concludes by asserting that if females realized that the always-down rule is inefficient, they would stop yelling and allow for a better strategy. There is hope.


Anonymous said...

I just love your blog. Monday you post about hyperinflation in Zimbabwe, yesterday about how to write a good title, and now this. It cannot get more eclectic!

Anonymous said...

The ads on the side bar are just hilarious. Imagine this on an Economics blog...

Anonymous said...

These papers are a bit simplistic, as results depend on parameter values and they ignore the fact that some households have an unbalanced gender distribution. In my case, I am the lone male in a four person household. Guess my optimal strategy, which is likely the most efficient as well.

T-Bone said...

I moved in recently with a roommate and he's got one of those fluffy covers for the top toilet lid. It cause the 2nd lid to not stay up unless I hold it. The action of holding it up while I do my thing messes up my normal bathroom technique.

As a result, I am always forgetting to zip my fly. I think I normally have one hand zipping up while the other flushes. But now I'm lowering the toilet seat while flushing, forgetting the zipping up part... Doesn't help that my mind is always somewhere else and I let mindless habit take over my actions.