Tinkeln nicht Sprinkeln

by Henry on December 6, 2006

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 Unpublished (available “here”:http://mpra.ub.uni-muenchen.de/856/ as PDF). Don’t bother with the obvious jokes about trembling hand equilibria – the author has made them already. Via “Mark Thoma”:http://economistsview.typepad.com/economistsview/2006/12/that_settles_it.html.

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Ars Mathematica » Blog Archive » Finally, Some Real Applications
12.07.06 at 1:25 am



Kieran Healy 12.07.06 at 12:07 am

Martin Hollis has a related discussion somewhere, in the context of seeing a sign reading “Gentlemen lift the seat” in a British Rail train toilet. He wonders whether it’s a coercive rule (“Gentlemen! Lift the seat or else!”) or a public reminder to conform to a Parsonian norm (“Proper gentlemen lift the seat”).


LJ 12.07.06 at 12:30 am

This has Ig Nobel written all over it.


Elliot Reed 12.07.06 at 12:55 am

Interesting discussion, but the analysis doesn’t account for the costs to women who get up in the middle of the night to use the bathroom and wind up in the water because the toilet seat is up and it’s hard to remember to check in the middle of the night.


ogged 12.07.06 at 1:55 am

I thought the Germans had already solved this problem.


ben wolfson 12.07.06 at 2:24 am

Clever readers might detect in the post title an allusion to the Teutonic way of pissing, ogged.


ben wolfson 12.07.06 at 2:26 am

And to think you subverted my work to make your shoddy point.


Michael Mouse 12.07.06 at 6:19 am

The analysis is deficient in modelling my household, at least. As well as one adult female and one adult male, it contains one infant and one cat.

The adults have reached a stable agreement to leave both seat and lid down after every use, since any other solution would impose undesirable externalities on the other household members (risk of them gaining access to the bowl), and the adults are committed to giving such externalities full consideration.

(And since the phrase “toilet aerosols” was drawn to my attention I have vastly preferred to have the lid down before flushing anyway.)


Matt 12.07.06 at 9:17 am

That approach wouldn’t work at my place, Michael M., since I’ve trained my cat to use the human toilet. He likes the seat down but the lid, obviously, needs to be up. (He can’t flush yet, unfortunately. He does, however, pea a bit like a German, it seems.)


Eric 12.07.06 at 10:56 am

I’m glad that now that the problem of poverty has been solved we can turn our attention to more critical issues of concern to certain men.


Matt 12.07.06 at 11:39 am

Didn’t you notice, eric? Poverty was beaten late last night. It was too late to get in the morning papers, I guess.


marcel 12.07.06 at 12:05 pm


astrongmaybe 12.07.06 at 12:38 pm

I knew someone (in Germany, natch) who, after years of arguments with his wife, solved this problem by finding a urinal in a dumpster and building it into the bathroom of his new house. Everyone was happy.

When I first went there (Germany), I thought it was all some kind of cutesy joke, all those stickers in the toilets (in English) saying “Stand Up for Your Rights, Sit Down for your Piss”. But they really mean it.


CJColucci 12.07.06 at 12:57 pm

OK, I can more or less intuitively follow the math, but I’m not up on the jargon. What is this “trembling hand” business?


Bear 12.07.06 at 1:49 pm

This analysis ignores the significant cost of having the seat down when an unconsiderate friend Ralph is over. In that case, one can assume that the unpleasantness of being the first to sit following Ralph might outweigh the cost of changing the position of the lid. If Ralph is over sufficiently often, it may even tip the balance to a policy of always leaving the seat up. (For anybody doing the math, make sure you include the higher probability of Ralph standing, since he is a drunk after all.)

Of course, if this is a men’s bathroom, the unfortunately high frequency of “Ralphs” in the population ought to encourage an all up strategy, at least among non-Ralphs. I actually have a business plan in mind related to this case.


Henry 12.07.06 at 2:35 pm

“trembling hand” is a means (proposed by Reinhard Selten if me memory is correct) of eliminating certain irrational Nash equilibria by making a game into a perturbed game in which there is a tiny chance that a player will make the wrong move, and seeing which equilibria still work.


Scylla the Cat 12.07.06 at 8:45 pm

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