High School

Consider the model from Section 10.3. Suppose the voter has an affinity for the incumbent, so if the incumbent is reelected, the voter receives an additional payoff. This could be because the incumbent is charismatic or because the voter and incumbent share the same political party or ethnicity.

From the analysis in footnote 2, if the voter believes that low-ability incumbents choose effort level \( e_l \), then, conditional on seeing a good outcome, the voter believes the incumbent is of high ability with probability \( p \cdot r \cdot (1 - p) \). If the voter observes a bad outcome, they are certain the incumbent is of low ability.

What is the expected utility of electing the challenger?

Answer :

The expected utility of electing the challenger can be determined through analyzing conditional probabilities and payoffs related to the voter's perception of the incumbent's abilities and outcomes.

Expected utility of electing the challenger: This scenario involves a voter's affinity for the incumbent affecting their decision-making based on the incumbent's abilities and outcomes. When the voter believes a low ability incumbent chooses effort, and seeing a good outcome, they perceive the incumbent to be of high ability with a probability of [latex]p[/latex].

However, if a bad outcome is observed, they are certain the incumbent is of low ability. In such a case, the expected utility of electing the challenger can be calculated based on these conditional probabilities and payoffs.