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Other Voting Methods

• Elections in the United States  • Other Voting Methods  • The Math 

Assume that five members of a city council get to decide which of three candidates—A, B, or C—will be the new council president. Initially, they decide to use the plurality method, but that didn’t work: two council members chose A, two chose B, and one chose C. They therefore hired an election consultant, who explained some other possibilities.

 

Plurality 

Borda, Condorcet 

Weighted Voting 

Approval 

Amandala 

A

A-B-C

A: 4
B: 3
C: 3

A, B, C

Benji 

A

A-C-B

A: 5
C: 4
B: 1

A, C

Chuck 

B

B-C-A

B: 5
C: 4
A: 1

B, C

Daria 

B

B-A-C

B: 4
A: 3
C: 3

A, B, C

Emil 

C

C-B-A

C: 10
B: 0
A: 0

C

The table above shows how the five council members (Amandala, Benji, Chuck, Daria, and Emil) voted.

Borda Count 

The Borda count method allows voters to rank the candidates in order from best to worst. Candidates earn points depending on how they were ranked by each voter. Under the most common system, an election with n candidates gives n points to the top-ranked candidate, (n – 1) points to the second-ranked candidate, and so forth, with only 1 point going to the lowest ranked candidate.

For this election, there are three candidates, so the top ranked candidate receives 3 points, the second receives 2 points, and the third receives 1 point. For instance, Amandala orders the candidates A-B-C, so A gets 3 points, B gets 2 points, and C gets 1 point. If the other candidates receive points in the same way from the other voters, the results are 10 points for A, 11 points for B, and 9 points for C. Therefore, B would win if the Borda count method were used.

Weighted Voting 

In weighted voting, each candidate is given a certain number of points to divide among all of the candidates. For this example, each voter was allowed to divide 10 points among three candidates. As you can see, Amandala liked A best, so she gave 4 points to A; but, she would have been happy enough with B or C, so she gave each of them 3 points. On the other hand, Emil really liked C but disliked A and B, so he gave all 10 points to C. When the points are totaled, A received 13 points, B received 13 points, but C received 24 points! If this weighted voting scheme were used, it would be a landslide victory for C.

(Note that the Borda count method is just a specific case of weighted voting. Each voter divides 6 points among 3 candidates in the ratio 3:2:1.)

Condorcet Method 

The Condorcet method uses pair-wise comparisons. That is, each candidate is compared to every other candidate, and the candidate who wins the most of these comparisons wins the election.

Again using the rankings from the second column, the following results are tallied:

  • A vs. B: 3 of the 5 voters ranked B higher than A
  • A vs. C: 3 of the 5 voters ranked C higher than A
  • B vs. C: 3 of the 5 voters ranked B higher than C

Because B won 2 comparisons, C won 1, and A won 0, B would win the election if the Condorcet method were used.

Approval 

Under the Approval method, each voter identifies the candidate(s) that would be acceptable, and the winner is the candidate who is approved by the most voters.

As shown above, 3 of the voters approved of A, 3 approved of B, but all 5 approved of C. Therefore, C would win the election if the Approval method were used.

For an explanation of some other voting systems, visit the Electoral Reform Society or Mt. Holyoke College’s Proportional Representation Library.


Elections in the United States   • Other Voting Methods   • The Math 


 

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