One of the common point of contention between males and females of western household is position of toilet seat - or so I am led to believe from movies, sitcoms and magazine articles. That the women of the house want seat down and men of the house want seat up is at the root of the problem. From first glance, problem is balanced since each party prefers position opposite of another. However, since women typically rule the households, default position is supposed to be seat down, and it's man's job to raise the seat, do the needful, and put it down again, failing which argument ensues. Inherent female bias in this is not hidden, but alas, not questioned either, reasons of which are related to how to deal with women and discussing these is detrimental to my potential relationships with them!
What I would like to propose is to show by simple mathematics that the best strategy for each is to leave toilet seat 'as is' after his/her work rather than leaving the seat in default position. Let's start with simple household with one man and one woman. Chances that last person to toilet was either, and next person to toilet will be either, are assumed to be fifty-fifty for simplicity. Computations can be worked out similarly for n men and m women with unequal probability of going to loo.
If no default position is set then expected workload per visit to loo is half unit. A man may either find it up, and do no work, or down, and have to raise it. He will leave is raised after use. Ditto for woman (no work for down position and one unit work for up position). Average work is half per visit with both working equally.
If either of default position (seat up or down) is set, then there is expected workload of one unit per visit. Consider seat down as default. When woman visits, there is no work required. When man visits there is two unit of work (raising, putting down) required. With half probability each, expected workload per person is one unit. However all of this is done by man.
Hence optimal rule is to leave as is after use, however generally used rule of seat down makes men do all the work. See the bias? But then, you know.
For western style toilet, I've felt the need for smaller mini-flush for urinal purposes so as not to waste as much water as is currently used.
And what's with vomiting/crying in bowls as they show in Hollywood movies? How can one even look into that water and bowl? Never really got my head around it. Why not use wash basins like we do here in India?