Classroom Games: Candidate Convergence

Abstract

This article details an experiment that is easily run in the classroom. It demonstrates how two candidate elections quickly converge to an equilibrium. It points out that the equilibrium is centered on the median voter. Finally, it illustrates what happens when preferences or institutions change. Material associated with conducting the experiment is provided, as is supplemental material for classroom instruction. A critical part of teaching political economy is getting students to understand the link between voter preferences, candidate position taking, and vote aggregation rules. While in the abstract it is easy to understand that candidates will often converge to the median voter, the ease with which candidates respond is not often grasped. This exercise mimics multiple elections with candidates holding no information about the distribution of voter preferences. Parallels are also drawn to one-dimensional spatial location models. The median voter model is one of the basic building blocks for political economy. The model assumes that voters have single-peaked preferences over a single policy dimension. This means that each voter has a single preferred position that can be mapped onto the policy dimension and the voter's utility decreases as a function of distance from that preferred position. Candidates seek election by proposing a policy position that will be implemented if elected. Voters then compare the utility they get from the policy position proposed by each candidate. In a two-candidate model the median voter's position is in equilibrium and candidates converge to the equilibrium. The simplicity of the model and its unique equilibrium allows those teaching various aspects of political economy to quickly cut through the complexity of political elections. This classroom experiment has three goals. The first is to demonstrate that competitive elections quickly drive candidates to adopt winning positions. Second, the exercise points to the stability of an equilibrium. This is especially useful for students who feel that an equilibrium is a fuzzy concept with little explanatory power. In this exercise candidates who deviate from the equilibrium are quickly punished. Third, the exercise introduces a feature common to many political systems: redistricting. This can be thought of as a change in the preferences of some voters. Simple changes in student