The Borda Count Method

For the Borda Count Method, each candidate (or alternative) gets 1 point for each last place vote received, 2 points for each next-to-last point vote, etc., all the way up to N points for each first place vote (where N is the number of candidates/alternatives). The candidate with the largest point total wins the election.

For instance, in a 4 candidate election, each 4th place vote is worth 1 point, each 3rd place vote is worth 2 points, each 2nd place vote is worth 3 points, and each 1st place vote is worth 4 points.

The Borda Count Method, or some variation of it, is often used for things like polls which rank sporting teams or academic institutions.


The mayor of Smallville is being chosen in an election using the Borda Count Method. The four candidates are Paul (the town barber), Rita (head of the town council), Sarah (Superintendent of Education), and Tim (former District Attorney).

500 registered voters cast their preference ballots. The results are summarized in the preference schedule below.

 

# of

Voters

Place

130 120 100 150
1st P T T S
2nd R R R R
3rd S S P P
4th T P S T

 

There are various ways of performing the calculations needed to determine the winner of a Borda Count election. Perhaps the most straightforward way is to set up a 'calculation template' and then insert the appropriate numbers from the preference schedule. For instance, the 'calculation template' for the election above would be:

 

Paul: 4( ) + 3( ) + 2( ) + 1( ) =
Rita: 4( ) + 3( ) + 2( ) + 1( ) =
Sarah: 4( ) + 3( ) + 2( ) + 1( ) =
Tim: 4( ) + 3( ) + 2( ) + 1( ) =

 

To see why this works, notice that:
the column with '4( ___ )' is where each candidate's 1st place votes are entered
(for a 4 candidate election, each 1st place vote is worth 4 pts);
the column with '3( ___ )' is where each candidate's 2nd place votes are entered
(for a 4 candidate election, each 1st place vote is worth 3 pts);
the column with '2( ___ )' is where each candidate's 3rd place votes are entered
(for a 4 candidate election, each 3rd place vote is worth 2 pts);
the column with '1( ___ )' is where each candidate's 4th place votes are entered
(for a 4 candidate election, each 4th place vote is worth 1 pt).
Adding all the resulting products gives us the Borda Count total for each candidate.

Usng this 'template' technique, the first step is to write out the 'calculation template' based on the number of candidates in the election. Next, fill in the blanks and, finally, do the arithmetic.

Let's complete the work for the Borda Count election of Smallville's mayor.

FILL IN THE BLANKS IN THE CALCULATION TEMPLATE.

  • Determine the number of first place votes for each candidate and place these numbers appropriately in the 'calculation template'. answer
  • Determine the number of second place votes for each candidate and place these numbers appropriately in the 'calculation template'. answer
  • Determine the number of third place votes for each candidate and place these numbers appropriately in the 'calculation template'. answer
  • Determine the number of fourth place votes for each candidate and place these numbers appropriately in the 'calculation templete'. answer

DO THE ARITHMETIC. answer

Who wins the election using the Borda Count Method? answer


see another example


The Borda Count Method uses all the preference information in the preference schedule. When using the Plurality Method, all of the information in the preference schedule not related to first place is ignored. This is a powerful theoretical argument in favor of the Borda Count Method over the Plurality Method.

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