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Wednesday, December 06, 2006

That Settles It

I need to send this to my first ex-wife:

Game theory and toilet seats, by Chris Dillow: With this being Pre-Budget day [in the UK], you're probably expecting serious economic analysis. So here's a paper: "The social norm of leaving the toilet seat down: a game theoretic analysis." The gist:

We show conclusively that the social norm of leaving the toilet seat down after use decreases welfare ... social norms are not always welfare-enhancing.

There's probably more proper economic analysis in this paper than we'll get from Brown today.

I don't care if it's been over twenty years, I win. However, Chris left something out. From the abstract of the paper:

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.

Here's a bit more from the introduction:

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 outperforms 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 is 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...

    Posted by on Wednesday, December 6, 2006 at 07:49 PM in Economics, Miscellaneous | Permalink  TrackBack (1)  Comments (37)

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    For all you game theorists out there, Hammad Siddiqi (2006): The social norm of leaving the toilet seat down: A game theoretic analysis. Unpublished (available here as PDF). Don’t bother with the obvious jokes about trembling hand equilibria – the auth... [Read More]

    Tracked on Wednesday, December 06, 2006 at 09:15 PM


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