The Corner

Game Theory & Toilet Seats

Discuss amongst yourselves:

The issue of whether the toilet seat should be left up or down after use seemingly generates a lot of passion among the parties concerned, however, scientific inquiries into the matter are almost non-existent. Notable exceptions are Choi (2002) and Harter (2005). Choi (2002) argues that the rule of leaving the toilet seat down after use is inefficient in the sense that there is at least one other rule that outperform this rule. The unit of analysis in Choi (2002) is the household and the efficient rule is defined as one that minimizes the total cost of toilet seat operations per household. Choi (2002) does not model the issue as a situation of conflict, hence ignores the game theoretic aspects of the problem. Harter (2005) models the situation as a cooperative game and proposes a contract that splits the costs of toilet seat operations evenly among the parties. Both papers agree that the social norm of leaving the toilet seat down in inefficient in the sense that it does not minimize the total cost of toilet seat operations per household. However, both papers fail to address an important concern: If a female finds the toilet seat in a wrong position then she will most probably yell at the male involved. This yelling inflicts a cost on the male. Based on this omission, women may argue that the analysis in these papers is suspect.

In this paper, we internalize the cost of yelling and model the conflict as a non-cooperative game between two species, males and females.We find that the social norm of leaving the toilet seat down is inefficient. However, to our dismay, we also find that the social norm of always leaving the toilet seat down after use is not only a Nash equilibrium in pure strategies but is also trembling-hand perfect. So, we can complain all we like, but this norm is not likely to go away.

All hope is not lost though. An important issue regarding social norms is whether they are created to increase welfare. Are they society’s response to market failures? One such norm is tipping for service quality. Azar (2003) has shown that the norm of tipping increases social welfare. In this paper, we show conclusively that the social norm of leaving the toilet seat down after use decreases welfare and by doing that we hope to convince the reader that social norms are not always welfare enhancing. Hence, there is a case for scientifically examining social norms and educating the masses about the fallacy of following social norms blindly.

Update: My productivity guy writes:

Subject: Trembling hands and toilet seats 

This might look like a game theory article to the untrained eye, but the math is WAY too simple.  What, no lemmas, or fixed point theorems in hemi-continuous space?  Derb would know better (although perusing any such article would probably strengthen his opinion that economists are idiots).

But in case you’re wondering, there really is such a thing as a “trembling hand equilibrium.”  And every equilibrium strategy in an accepted game theory article must of course be “sub game perfect.”

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