Voters sometimes vote for seemingly less-qualified candidates. To explain this fact, we develop a political agency model with sequential elections in which a voter elects a politician among candidates with different competence (valence) levels, considering that politicians’ representation of voters’ preferences depends on their competence levels. We show that a negative relationship exists between politicians’ competence and their representation when a future challenger is likely to be incompetent and the reward for politicians is small. We also highlight voters’ private information on how they evaluate candidates’ competence, demonstrating that voters’ demand for incompetent candidates can be a self-fulfilling prophecy.