Although it is indeed true that males may use one of two modes (seat up/seat down), there's probably a higher frequency of seat-up usage.
Ultimately, the efficiency is going to be determined by how the sex ratio of the users combined with the relative seat-up/seat-down ratio tabulated across all users.
However, it's always struck me that the simplest option is to leave the seat in the state that you put it. That way, there will never need to be an "unnecessary" seat movement - if the next person needs the seat up, and it's down, they can just put it up, but if you had put it down and they had to put it back up again, well, that's just rampant inefficiency right there - two people have wasted time and energy.
Given the number of bathrooms these days (particularly in hotels) that have two sinks - a his and hers option - it may be time we just started putting ni his and hers toilets. Then one seat can just stay down all the time (hell, glue it there if you like), and everybody's content.
I can't believe I'm discussing this.