People don't like to touch toilet seats in public restrooms, so they don't get raised by men before they pee. A lot of the time the urine stream trails off so that the last dribble will fall over where the front of the seat would be. So to avoid getting drops of piss splashed on the surface where someone might sit down, they put the open part of the horseshoe shaped seat. The pee will then fall on the bowl rim and floor instead of the seat.
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Not sure,that's a good question. Though it would seem less sanitary to have the horseshoe shaped then full.
People don't like to touch toilet seats in public restrooms, so they don't get raised by men before they pee. A lot of the time the urine stream trails off so that the last dribble will fall over where the front of the seat would be. So to avoid getting drops of piss splashed on the surface where someone might sit down, they put the open part of the horseshoe shaped seat. The pee will then fall on the bowl rim and floor instead of the seat.