This interactive figure lets you experiment with five election methods and see how they behave under different conditions. Voters and candidates are assumed to have political opinions on a one-dimensional spectrum from left to right. (For the two-dimensional version, see the article on Voting Simulation Visualizations.)
Candidates: Position the candidates by dragging the triangles at the bottom. Initially only two candidates are running (red and green); to add more candidates, click the other triangles.
Voters: The big hump represents a normal distribution of voters, which is shaded to show the voters who have each candidate as their favourite. You can drag the voter distribution left or right. Double-click the voter distribution to change its shape (normal, bimodal, or uniform).
Text: The text at the top explains the outcome of a single election using the chosen voter distribution, candidate positions, and election method. The winner of this election is indicated by the coloured dot below the voter distribution, on the bar for the selected election method.
Methods: There is a bar for each voting method. Click in the empty space in a bar to select that voting method and position the center of opinion of the voters, shown as the coloured dot. Click on the name of the voting method to shade the entire bar according to the winner for all positions of the center of opinion (the colour of the dot along the entire spectrum).
The five election methods are:
- Plurality (also called "first past the post"): Each voter may vote for only one candidate. The candidate with the most votes wins. Voters are assumed to vote for the nearest candidate.
- Approval: Each voter may vote for any number of candidates. The candidate with the most votes wins. Voters are assumed to vote for all candidates within an acceptable distance.
- Borda: Each voter ranks the candidates in preference order. Candidates get points according to the ranks they are given, and the candidate with the lowest total rank wins. Voters are assumed to rank the candidates in order of increasing distance.
- Condorcet: Each voter ranks the candidates in preference order. If there is a candidate who would defeat all of the other candidates in one-on-one contests, that candidate wins. Voters are assumed to rank the candidates in order of increasing distance.
- Hare (also called "instant runoff" or "IRV"): Each voter ranks the candidates in preference order. Each ballot is assigned to its highest-ranked candidate, and if one candidate has more than half the ballots, that candidate wins. Otherwise, the candidate with the least first-ranked votes is eliminated, and the ballots ranking that candidate highest are reassigned to the next-highest non-eliminated candidate. The counting and elimination process is repeated until there is a majority winner. Voters are assumed to rank the candidates in order of increasing distance.