The Borda Count Method in Elections

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  • 0:02 Borda Count Introduction
  • 1:35 Working Through Borda Count
  • 3:57 A Larger Example
  • 5:39 Lesson Summary
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

Have you ever wondered how a winner is determined when you must rank the choices in a voting scenario? This lesson covers the Borda count method of determining a winner in preferential elections.

Borda Count Introduction

Have you ever had to vote for something by ranking the order in which you would prefer the outcome? For example, if you had to vote on a type of office party, you might be asked to rank all the choices in order of what you prefer most, next and least. This is called preferential voting, a type of voting in which voters number the candidates in the order they prefer them.

Let's say your office party ballot had three choices: formal, casual and beach. If everyone ordered these choices by preference, you would end up with lots of different combinations of number one, number two and number three.

How do you determine which choice wins? Is it always going to be the choice that gets the most number one votes? That is where the Borda count method comes in to help. The Borda count method is a simple process whereby points are given to each choice based on the ranking, with the lowest spot receiving one point, and each consecutive spot up the ranking receives one more point until you are at the top. Mathematically, we could say that the first place position gets N points, with N being the number of choices on the ballot. Second place receives (N - 1) points and so on until the last place selection receives just one point.

After all the points are assigned, the choice with the most points wins, regardless of whether it received the majority vote for first place. Let's see how this works using our office party example.

Working Through Borda Count

If your office has 40 employees voting on this issue, the results might look like this.

Preference Schedule

This is a preference schedule, a chart showing the results of preference voting.

Notice that there are six different combinations for preferential voting with three choices. One person might select the formal party for first place and the beach for second, but another might prefer the formal party first and a casual office party second. It is due to these differences that the Borda count really comes in handy. Each vote and each rank selected is assigned a value so that an overall score can be achieved.

For a three choice ballot, the top rank place will equate to three points, second place is two points and third place will earn one point. We can write a formula to easily count up the points for each option:

  • Formal: 3 ( ) + 2 ( ) + 1 ( ) =
  • Casual: 3 ( ) + 2 ( ) + 1 ( ) =
  • Beach: 3 ( ) + 2 ( ) + 1 ( ) =

Now we can look at the preference schedule to determine how many times each option was chosen at each rank. So, formal was chosen as first place a total of ten plus five times, so 15. Formal was chosen second here and here, so ten times total. Finally, formal was chosen last place a total of 15 times. For the formal option, we now have: 3(15) + 2 (10) + 1(15) = 80 points. Did you notice that the 15 votes for first place were multiplied by three, the highest number of points assigned? In this way, the votes are weighted to take into account people's preference for each choice.

Finishing the point totals, we see that casual was chosen first 20 times, second eight times and third 12 times; for a total score of 88 points. The beach option was chosen first five times, second 22 and third 13 times, for a total of 72 points. In this election, the casual office party wins because that option has the highest point value.

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