In the anti-plurality system, instead of voting for their top choice, voters vote against their bottom choice. So a voter with preference order "A>B>C" would cast a vote for A and B, but not for C. In effect this penalizes C by allowing the voter to increase the totals of all the other candidates.
In terms of the representation triangle, each candidate receives votes from all regions except those in which they are bottom ranked. In the picture below, A is top-ranked in the darkly shaded regions and middle-ranked in the lightly-shaded regions. We add up the scores in all four of these regions to compute A's total.
If we consider the "milk, soda, juice" example, milk still gets 6 votes, but now juice gets 9 and soda gets votes from all 15 voters. Thus it would seem that even though milk is plurality winner, all of the voters find soda at least somewhat acceptable. We say that soda is the anti-plurality winner. In the interactive window below, experiment with the anti-plurality method. Can you come up with other profiles where the plurality and anti-plurality winners are different?
While the antiplurality method does allow voters to express more of their preferences, it does not allow them to distinguish their top choice for their lower-ranked choices. With anti-plurality, every candidate except the bottom-ranked one is treated equally. A famous voting method that allows the voter to distinguish between all of their choices is the Borda count.
Plurality |
Table of Contents |
The Borda Count |