voting methods

Many Ways to Pick a Winner

We are all used to voting for whoever we want to win, with the person receiving the most votes declared the winner. This system works pretty well when there are only two candidates, but when there are more it creates some problems.

What is one problem that might happen when more candidates run?

In order to get more information from voters, a better way to hold an election is to allow voters to rank order the candidates rather than just pick their favorite. This shows not only who you want to win, but also who you want to lose (and everyone in-between).

A Preference Ballot would look something like this:

When all of the preference ballots are counted, the results are placed in a preference table. The numbers at the top represent the number of people who have a ballot that looks like the one below that number.

If the four candidates were Fred, Wlima, Barney, and Dino…

A Preference Table would look something like this:

Number of Votes 210 185 315 901st choice F W B W2nd choice W F F D3rd choice B D W F4th choice D B D B

Who should win this election?

This is the method that many people are most comfortable with. In this method, the person with the most 1st place votes wins (so only look at the 1st row to determine the winner.

In this example, Fred has 210 votes, Wilma has 185+90=275 votes, and Barney has 315 votes. Therefore, Barney wins the election.


In a Borda Count, the different places are assigned different point values. Last place gets 1 point, and it increases by 1 point every time you go up one place (i.e. 2nd to last equals 2 points, next best place equals 3 points, etc.) The person with the most total points will win the election.

This is an example of the Borda count in action…

Here are the totals in this example: Fred=4*210 +3*500 +2*90 = 2520 pts Wilma = 4*275 + 3*210 + 2*315 = 2360

pts Barney = 4*315 + 2*210 + 1*275 = 1955

pts Dino = 3*90 + 2*185 + 1*525 = 1165 pts Fred wins the election


P. 735-736; #2, 3, 5, 7, 8, 11, 12

In this method, you find the candidate with the fewest number of 1st place votes and eliminate them from the race. All the votes in that column move up one place (the 2nd place votes now become the 1st place votes)

This process continues until someone has a majority (or there is a tie)

In this example, Dino has the fewest 1st place votes, so he is removed from the race, and the votes in that column move up one place.


Fred now has the fewest first place votes, and is the next to go.

Number of Votes 210 185 315 901st choice F W B W2nd choice W F F F3rd choice B B W B4th choice

Since Wilma now has 210+185+90 = 485 votes, she has a majority and is declared the winner of the election.

Number of Votes 210 185 315 901st choice W W B W2nd choice B B W B3rd choice4th choice

Election-swaying.com. Slapupsidethehead.com

In this method, you compare candidates two at a time and see who would win in each column. The candidate who would be victorious with a majority of the voters would win that comparison.

Each comparison victory is worth 1pt. Each tie is worth ½ pt. Whoever has the most points wins the election.

In this example, there will be 6 different comparisons. The number is determined by n(n-1)/2, where n is the number of candidates.


Between Fred & Wilma, Fred wins in 525 votes, while Wilma wins in 275 votes, so Fred beats Wilma (and gets 1 pt).


Between Fred & Barney, Fred wins in 485 votes, while Barney wins in 315 votes, so Fred beats Barney (and gets 1 pt).


Between Fred & Dino, Fred wins in 525 votes, while Dino wins in 275 votes, so Fred beats Dino (and gets 1 pt).


Between Wilma & Barney, Wilma wins in 485 votes, while Barney wins in 315 votes, so Wilma beats Barney (and gets 1 pt).


Between Wilma & Dino, Wilma crushes Dino with 800 votes to Dino’s none, so Wilma defeats Dino soundly (and gets 1 pt).


Between Barney & Dino, Barney gets 525 votes to Dino’s 275, so Barney defeats Dino (and gets 1 pt).


The final totals in this election are:

Fred = 3 pts Wilma = 2 pts Barney = 1 pt Dino = 0 points

So Fred wins the election.

Hipster-election-2004.gif. Toothpastefordinner.com

P. 735-737; #12-14, 19-22, 24-30

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