The conundrum of toilet seat placement has been professionally investigated.
When mathematicians (I'm one) decided to tackle the problem of toilet seat
placement, I got interested. The results of applying game theory to the
question of "Leave up or down?" are interesting.
Assumptions had to be made, of course: The female performs more toilet
operations because of a smaller bladder, but the male drinks more beer. Not
considered was potential prostate problems.
Mathematical calculations demand the seat be left in its last-used position.
Researchers, however, conclude that the seat should be placed down after
toilet use. It turns out female hectoring is more compelling than science.
Other possible considerations, such as esthetics, sanitation, and pet
hydration were ignored.