ITT we discuss scientifically how to arrive at the optimal state using economics, game theory, and statistics.

Represent a terrible candidate having $q$ probability being elected each election. Suppose the terrible incumbent has a constant advantage through corruption, represent this as a fixed constant $\gamma, \gamma > 1, \gamma * q < 1$. Suppose that each terrible incumbent has a fixed disadvantage in being elected each term, represent this as $\beta, 0 < \beta < 1$. The modifier chance of a incumbent terrible candidate over time will thus be $q_{t} = q * (\gamma * \beta) ^ {t - 1}$ . Thus as long as the corruption is sufficiently outweighed such that $\gamma < 1 / \beta$ then $q * ( \gamma * \beta ) ^ {t -1} \rightarrow 0, t \rightarrow \infty$. Furthermore since $p_{t} + q_{t} = 1$ we can see $p_{t} \rightarrow 1$. Hence as long as the country isn’t corrupt, a good candidate will have a higher chance of holding office over time.