It has been determined that keeping not just the seat but the lid closed while flushing minimizes the amount of harmful bacteria that gets into the surrounding air, on toothbrushes and such places we don't want it. There was a mythbusters about that in addition to other health studies. Closing the lid also keeps other stuff from falling in the bowl. Someone left a terlet lid open and a plugged-in hair dryer fell into it, boiled the water for a while, which helped sanitize the bowl but ruined the hair dryer and was generally unsafe electrically. Two errors; leaving lid open and leaving hairdryer plugged in.