## 1. The Voting and Ranking Methods

Below you will find the Control Panel applet. This applet is used to create and edit preference schedules. It also has a Voting Methods section that you can use to find the winners using the various voting methods described in the text.

Give it a try. You will soon figure out that you can use this program to check answers to exercises. That's fine, just remember, you are going to have to show how you got the answers!

If you have trouble with this applet, then check out the Control Panel Help.

The program above is responsible for determining the schedule that is used by other programs on this page. First, there is the Ranking Methods program. Ranking the candidates means finding not just the first place winner, but second, third, etc.

To use the Ranking applet, first set the preference schedule in the Contril Panel applet above. Then click the appropriate button to see the ranking of the candidates. Note that ties now must be indicated with parentheses. For example, if (AD)(CB) appears in the box, then A and D are tied for first place and C and D are tied for second. D(AC)B indicates that D is first, A and C tied for second, and B was third.

## 2. Comparing Two Similar Ranking Methods

It has been my experience that students often have trouble distinguishing Recursive Plurality from Extended Plurality with Elimination. The next applet is designed to demonstrate the differences between these two ranking methods. First we quickly review the two techniques.

### Recursive Plurality

The candidate with the most first place votes is put in the top spot. Then you remove that candidate from the ballots and rewrite the preference schedule. The candidate with the most first place votes in the new schedule is put in second place, etc. So, you build the ranking from the top down. Each time a candidate is ranked you remove her from the ballots, so the numbers of first place votes for the remaining candidates change.

### Extended Plurality with Elimination

Here the ranking is built from the bottom up. The person with the fewest first place votes is ranked last. Then that candidate is removed from the ballots, so if they had any first place votes, these now go to someone else. The candidate who now has the fewest first place votes is second from last, etc.

The next applet illustrates these two methods by showing the preference schedules and the rankings step by step. Once again, the schedule is taken from the Control Panel applet above. The Start button reads the schedule, and displays it on the left and right sides. The Step button executes one iteration of each method, shows the slot filled in the ranking by that iteration, and displays the new preference schedules.