@MontereyJack,
This is somewhat illogical for most cases, I would suggest, for the following reason:
The person who has just used it is the least likely to need to use it again, first. (Save in the exceptional case of advanced diarrhoea or other unpleasant medical condition)
And so on balance of probability, and assuming a reasonably even spread of genders (this is not an allusion to the size of your butts, ladies), it would surely make more sense to leave the seat in the opposite mode to the one just employed.