# Solution Library

# Citizen Candidate Model with the Given Electoral Rule to Find Candidate Equilibrium

**Question**

Assume a citizen candidate model with the following electoral rule. Voters rank the candidates and give their first two ranked candidates a weight of I. and all other candidates a weight of zero. The candidate with the highest total score wins the election. If more than one candidate has the highest score, a lottery determines the winner. Voters have ideal points which are uniformly distributed on the [--1, 1] interval. As is standard in the citizen-candidate model, the benefit of winning the election is b > 0 and the cost of running is c > 0. Assume that b > 2c.

(a) Show that there cannot be an equilibrium with only one candidate.

(b) Is it an equilibrium to have two candidates, both with ideal points at zero? Prove your answer.

(c) Is it an equilibrium to have two candidates, both with different ideal points which are equidistant from zero? Prove your answer.

(d) Under what conditions on b and c, if any, will three candidate with ideal points at zero be an equilibrium?

(e) Contrast the results of this model to the citizen candidate model with simple plurality rule studied in class. What accounts for the different predictions about divergence of candidate platforms.

**Summary: **This question belongs to political economy and discusses about a citizen candidate model with the given electoral rule and discusses equilibrium of candidates.

**Total word count: **720

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