Toilet Fan

The unpleasent smells manufactured during the human waste-disposal process originate between the horizontal surface of the human in question and the bottom of the toilet bowl itself. In this volume, there is often a mix of air and water.

The water, and associated U-bend acts as an effective seal, it's there to prevent sewer smells coming into the house, but in this case it can be viewed as PREVENTING the smell leaving. The air volume above the water is where the most concentrated smells are to be found. While the human is present, this is actually quite well sealed, however, it may be displaced and spread around the place by movement, diffusion and ultimately dumping a few gallons of water into it. If we can vent the smelly air between water and human when it's at it's most concentrated then we will have an effective strategy toward preventing the smell diffusing about the place.

To do this we need an air intake, this should be at the back under that rim thing toilets tend to have. This should lead to an air pump. In the circumstances, it should be at least tolerant of water, so a diaphragm pump might fit the bill. We are moving the most concentrated air, so we don't need big volumes. This should pump air from the toilet bowl past the U-bend water trap into the air space that occupies the waste pipe most of the time*. Add a couple of non-return valves for obvious reasons and we're good.

This pump could be switched with a lid/weight on seat switch, but I propose it be left on continuously. That way the toilet will gradually attract and dispose of dust etc. And, the net influx of air into the toilet might encourage any errant male-generated droplets to land in, rather than near the toilet.

*domestic waste pipes are usually vented outside the house. In the UK this is vented high up in the air at the top of the roof. Here in Philadelphia, it's vented on the sidewalk 5ft from the front door. Which is why the whole place stinks of shit for the entire summer.