>Around my house, I solved the seat problem. As a rule, not only do I (and everbody else) put the seat down afterwards, but also the lid. Therefore, if I have lean over and lift the seat (with the lid), so does everybody else have too at least lift the lid. Beside, that is why it is there.

We never had this problem, not that I remember. My wife probably tried to get me to put the seat down (since I was outnumbered 4:1), and it probably worked for a number of years. Now with only one girl still with us, we don't care. Whoever comes into the toilet gets the seat into the position they want, and leaves it as they like. Nobody complains.