The optimal toilet seat rule

Back in 2016, I wrote a post about the 'toilet seat game' - was it better to leave the toilet seat up, or down? Economists research the really important questions, you see.

A while back, someone (I forget who) drew my attention to this 2011 article by Jay Choi (Michigan State University), published in the journal Economic Inquiry (ungated version available here). Choi develops a theoretical model of toilet seat etiquette, and then solves the model for the optimal rule (that is, the most efficient rule for the toilet seat). He finds that:

...the down rule is inefficient unless there is large asymmetry in the inconvenience costs of shifting the position of the toilet seat across genders. I show that the “selfish” or the “status quo” rule that leaves the toilet seat in the position used dominates the down rule in a wide range of parameter spaces including the case where the inconvenience costs are the same. The intuition for this result is easy to understand. Imagine a situation in which the aggregate frequency of toilet usage is the same across genders, that is, the probability that any visitor will be male is 1/2. With the down rule, each male visit is associated with lifting the toilet seat up before use and lowering it down after use, with the inconvenience costs being incurred twice. With the selfish rule, in contrast, the inconvenience costs are incurred once and only when the previous visitor is a member of different gender. The worst case under the selfish rule would occur when the sex of the toilet visitor strictly alternates in each usage. Even in this case, the total inconvenience costs would be the same as those under the down rule if the costs are symmetric. If there is any possibility that consecutive users are from the same gender, the selfish rule strictly dominates the down rule because it keeps the option value of not incurring any inconvenience costs in such an event.

He also notes in the conclusion that:

...the selfish rule is incentive-compatible in that it can be self-enforcing without any outside sanctions for violating the rule.

So, there you go. Follow the 'selfish rule', and maximise efficiency by leaving the toilet seat as it is when you are done. Unless you're William, of course. Or if the costs are asymmetric (Choi estimates that if the inconvenience costs for females are three times or more higher than the inconvenience costs for males, then the 'down rule' becomes the efficient alternative). Or if men sometimes have to use the toilet with the seat down. Or if some of the costs of the selfish rule blow back onto you (I don't mean it in that way - ewww, gross!), which is a situation that Choi didn't consider.

That's a lot of exceptions. I guess more work is required on this important research topic.

Read more:

• The toilet seat game