But now you'll get an unstable system where candidates get kicked out all the time and are too populist because they don't expect to live long.
So add a low-pass filter. When the moving average of the candidate's support falls below the threshold and a definite other candidate's support is high enough, replace the incumbent with that challenger.
You might even increase the duration of the moving average with time, like the doubling trick in multi-armed bandits. The logic is that a candidate who has shown that he can weather the initial period without getting voted out can be trusted with more long-term decisions, i.e. actions speak louder than words.
Unrelated side note: when you are talking about a hypothetical politician, be aware of your choice of pronoun.
You might be the type of person who picks between he/she with a precise 50/50 split but I'm going to assume you are not that type of person. Similar to the way you seem to have assumed that if a person is a politician they are also a man.
Next ammendment: direct election of cabinet members.
Also, all changes to policies to be parameterized and adiabatic.
I guess some of that bleeds through: that I use "he" without reflecting on it because it wouldn't carry an implication of actual gender in my first language. I am definitely not assuming that politics is a men's only club.
"No heat, only work". I like that proposal :-)