I think that limiting, at the very least, to people who actively WANTED to be a lawmaker would solve several of your problems.
This, however, leads to the tragedy of the commons problem that it’s in each faction’s interest to increase the number of it’s members who WANT to be lawmakers to increase the chance that one of them is selected.
This, however, leads to the tragedy of the commons problem that it’s in each faction’s interest to increase the number of it’s members who WANT to be lawmakers to increase the chance that one of them is selected.