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Borda Voting

Borda Voting is the simplest ordinal voting method. It is also a rating method, since each candidate gets rated with a numbered ranking.

The elector lists the options he/she likes in a specific order, and each option gets a score according to its position. Options listed first get a higher score, so you may specify that you like candidate X more than Y just by listing Y after X.

Suppose for instance there are four options n=4: then the first option in the list gets n-1 = 3 points, the second options n-2 = 2 points, the third option n-3 = 1 point and the last one gets no points at all. So, listing “B A C D” means:

B gets 3 points
A gets 2 points
C gets 1 point
D gets 0 points

Typically, in Borda method, electors are asked to list all the candidates in order to lower (but not to erase) the risk of abuses from insincere voters (see next section).

At the end, the total score for each candidate is counted and displayed as a percentage. The Borda method is theoretically very attractive, since it is relatively easy to understand and gives great expressive power to the user (effectively allowing him/her the possibility to rate the candidates in order of preference).

However, in practice, the Borda method is a rather poor method since insincere voters can easily abuse it. A simple example that shows why this is the case is reported below. If you want to use an ordinal method, which is solid against insincere votes, you should look at the Condorcet method.

Shortcomings of the Borda method

Consider an election with four candidates A, B, C and D and the sincere electoral ballot.

3: B A C D
2: A C B D

(Three votes for “B A C D” and two votes for “A C B D”). The result is:

A: 12 points
B: 11 points
C: 7 points
D: 0 points

In this case A wins over B since the last two voters, which preferred B to A, nevertheless liked A enough to put it as second choice. So, being sincere made their candidate lose the election.If B voters knew that their least preferred candidate D didn’t have any hope to win, they could have listed it over A:

1: B A C D
2: A C B D
2: B D C A

Now the result of the election would have been:

B: 11
A: 8
C: 7
D: 4

Strategically voting the weak candidate D over A made the B candidate win. Stealing points from a strong candidate and transferring them over a weak candidate is a good strategy to make middle candidates to win. So being sincere is not encouraged by the Borda method. In other words, the Borda method is not robust against insincere voters.

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