Borda Count

Published by Mario Oettler on

Borda vote belongs to positional voting. Voters give each candidate points according to the rank in their preference list. The most preferred candidate receives the most points.

The winner is the candidate who receives the most points over all voters.

Method 1

In the original method, the lowest-ranked candidate receives 0 points, the next higher-ranked candidate 1 point, and so on. The most preferred candidate receives n-1 points, where n is the number of candidates. After all voters cast their votes, all points for each candidate are added. The candidate with the most points wins the election.

Let’s consider the following preferences.

Preference (2 points)AABBCC
Preference (1 points)BCACAB
Preference (0 points)CBCABA
Number of persons with this preference order605253
  • A receives 22 points in total.
  • B receives 23 points in total.
  • C receives 18 points in total.

The winner is candidate B.

Method 2

Another method of distributing points is to grant the least preferred candidate 1 point and the highest preferred candidate n points, where n is the number of candidates.

Method 3

Another method to distribute points is using fractions. The highest preferred candidate receives 1/1 points, the next candidate ½ points, the third-best candidate 1/3 points, and so on. The least preferred candidate receives 1/n points.


The problem with the Borda count is that it is not resistant to clone attacks. An alternative can increase its chances by creating a clone and thereby increasing the number of alternatives.

Suppose a population of 100 people where:

  • 66 people prefer A over B
  • 34 people prefer B over A

A would receive 66 points and B 34 points. Hence, A wins.

Now, B introduces a clone candidate B’.

  • 66 people prefer A over B over B’
  • 34 people prefer B over B’ over A

A receives 132 points, B receives 134 points and B’ 34 points. Thus, A wins the election.