Should you leave the toilet seat up or down? Here's the game theory analysis of leaving the toilet seat down:
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.
Link - Thanks David R!
Reason 1) If you are in a relationship with a female, and you always put the seat down, if you return to your domicile, and the seat is up, you then know that some strange man was there.
Reason 2) If you are that strange man (noted in reason 1, above), if you always put the seat down, the cuckold will never know you've been there.
Source: Burgio KL, Engel BT, & Locher JL. Normative patterns of diurnal urination across 6 age decades. The Journal of urology. 1991;145(4):728-31.