Mathematics is often thought of as being esoteric and nothing to do with the real world which, to be honest, is why it appealed to me when I decided to study maths at University. However, I am delighted to see that the subject of toilet seats (up or down?) has been tackled by Hammad Siddiqi in a paper called The social norm of leaving the toilet seat down: A game theoretic analysis. Some extracts give the flavour:
- 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.
Changing the seat position during an operation is beyond the scope of this paper and is definitely not recommended.
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.
Ars Mathematica first alerted me to this paper, but it has spread virally from blog to blog. I have alerted the Annals of Improbable Research so hopefully it will receive a wider audience. The editor contributes a weekly column in the Guardian; this week’s column is subtitled “The dangers of whisky and candlelight”.