Anti-Plurality
Table of Contents
The Positional MethodOne of the main disadvantages of the anti-plurality voting method is that voters are not allowed to distinguish between their top two choices. A more natural voting method would be to assign 1 point to a voter's top choice and half a point to their second-ranked choice. The bottom-ranked choice still would receive zero points. This method is called the Borda count. The Borda count was devised by Jean-Charles de Borda in 1770, and was used by the French Academy of Sciences beginning in 1784. This ended in 1800 when Napoleon Bonaparte, a year after Borda's death, insisted that his own method be used.
Let's consider how the Borda count works for the "milk, soda, juice" example.
Number of People |
Preference Order |
Milk |
Soda |
Juice |
6 |
M > J > S |
6 x 1 = 6 |
6 x 0 = 0 |
6 x 0.5 = 3 |
5 |
S > J > M |
5 x 0 = 0 |
5 x 1 = 5 |
5 x 0.5 = 2.5 |
4 |
J > S > M |
4 x 0 = 0 |
4 x 0.5 = 2 |
4 x 1 = 4 |
Totals |
6 |
7 |
9.5 |
Juice is the winner with 9.5 points.
Use the interactive diagram below to explore the Borda count. Can you create a profile so that the Borda count winner is different from the plurality or anti-plurality winner?
The Borda count is a popular method because it allows voters to express their full preference. However, the choice of 0.5 points for a second-place vote is somewhat arbitrary. On the next page we will discuss a generalization of the three methods we have seen so far called the positional method.
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Anti-Plurality |
Table of Contents |
The Positional Method |