Logic dictates that you leave it the way you like it. If everyone did that, then the toilet seat would be in each user’s preferred position in proportion to their frequency of use.

As usual, logic and etiquette only have the faintest connection. There are any number of arguments I could give for why you should leave the seat down — from midnight surprises to the visibility of splashbacks — but in fact, the only real reason is convention. If you leave the seat up, in any toilet facility that a woman may use, then you’ll be considered uncivilised… even if it’s illogical.