Candidate Competition Demo

You can use this demo to investigate candidate competition and the spatial model of voting.

Start by clicking on the "Add Candidate" button. You will see the position of candidate Alex appear in the figure and table, and you can click or drag Alex to another position.

When you think Alex is ready to face some competition, click on the "Add Candidate" again to add Billy.

As you move Alex and Billy to different positions, the table will update to show you their new vote shares.

If Alex is losing the election, find a new position so that they win. If Billy is losing, find them a new position so that they win instead.

Then keep repeating this process, leaving the winner at the same position and finding a new position for the loser so that they become the winner.

Can you find a position for one of the candidates that guarantees they will always win no matter what the other candidate's position is? What is it?

The heights of the vertical bars represents the share of voters at each position. In the original scenario, there are an equal number of voters at each position: voters are uniformly distributed.

Use the dropdown button to change the distribution from uniform to unimodal, where there are more voters in the middle positions and fewer at the ends.

Does this change whether or not there is a position that can guarantee a win?

Go ahead and try the bimodal and random distributions, too. Does this change your answer?

Change the distribution back to uniform, then add a third candidate. Can Chris get the most votes to win the election?

What happens now if you keep repeating the process in which one of the losing candidates finds a new position to win the most votes? It may sometimes be the case that only one of the losing candidates can find a new winning position.

Does this process ever stop? Does your answer depend on the distribution?

You can add up to five candidates. Does your answer depend on the number of candidates?

Candidate Competition

Further reading