Classroom games: candidate convergence.

• Author: Wilson, Rick K.
• Position: Teaching political economics

1. Introduction

   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 preferences can demonstrate the suddenness with which equilibrium can be changed and how quickly candidates will converge on the new equilibrium. Typically the exercise is run before introducing the concept of a median voter. Candidate behavior can be used as data to illustrate convergence to the median voter and to illustrate the power of equilibrium.

   The exercise can be run with any size class and in less than 30 minutes. Classes with more than 100 students will require more preparation time. The exercise usually goes through 15 distinct elections. The entire exercise can be carded out by a single person, although with large classes appointing election monitors to pass out material and to count ballots is helpful.

2. Instructor Procedures

   The materials needed for this exercise are limited and all of the preparations can be handled beforehand. All that is needed is

   * A spreadsheet or some other device to generate voter distributions

   * Index cards (enough so that everyone in the class has one index card).

   * A smaller set of index cards of a different color (enough for 10-20% of the number in the class)

   * Numbered poker chips (or some other randomizing device) numbered from 1 through the number in the class

   * An experimenter record sheet (see the Appendix)

   * Oral instructions to be read by the experimenter (see the Appendix)

   * An overhead projector for the student instructions or enough sheets with the printed student instructions (see the Appendix)

   * A student record sheet (optional)

   Preexperiment Preparations

   The elections take place on a single dimension made up of a whole number line ranging from 1 to 100. To begin preparations a distribution of voters needs to be constructed, index cards must be prepared, a random device must be designed and various forms should be assembled. The tasks prior to the experiment include the following:

   (i) Generate a distribution of voters. The easiest way to do so is to build a spreadsheet with rows equal to the number of students in the class. One column has numbers ranging from 1 to the number of students in the class. The second column assigns each cell (student) a whole number on the number line ranging from 1 to 100. Rather than assigning numbers along a uniform distribution, I use a skewed distribution either to the left or to the right. This number will constitute a student's "ideal" position in the campaign space. People can have the same number (preference) if there are a lot of students. Typically I choose numbers so that the position of the median voter is close to 65. The third column should copy the numbers from the second column. In this column 10% to 20% of the "ideal" positions should be changed so that the equilibrium is shifted. This can easily be done by changing the values of the high valued students (if the equilibrium is above 50) and assigning them low values. I typically try to shift the equilibrium by 25 or 30 points to the left. Highlight the numbers that have been changed. To make life easier, keep the numbers that are changed in sequence with the ID numbers. So, for 100 students in a class and if 20 ideal positions are changed, change IDs that range between 71 and 90. (1)

   (ii) Prepare the index cards. The index card needs two pieces of information: an 1D number and an ideal position. The ID is simply copied from the first column and placed in the upper-left corner of the index card. The ideal position is copied from the second column and put in the middle of the index card. The second, smaller set of index cards that differ in color should now have the ID copied from the first column and the new value from the third column of the spreadsheet. That set of cards needs to be generated only for those numbers that were changed (and highlighted).

   (iii) Substitute the colored index cards for cards with the same ID. If the first deck of ID cards is white and the second, smaller deck is blue, the final deck will have almost all white cards and some blue. The remaining small stack will have all white cards. This is done so that during the exercise it will be easy to swap cards (change preferences) for a small subset of the students.

   (iv) Prepare a randomizing device. I typically use numbered poker chips, but anything can be used. Plastic poker chips are cheap and can be numbered with a permanent ink marker. These chips can be drawn from a box, a hat, or anything else that is handy.

   (v) Prepare...