Example

A vacation club is trying to decide which destination to visit this year: Hawaii (H) or Anaheim (A). Their votes are shown below:

	Bob	Ann	Marv	Alice	Eve	Omar	Lupe	Dave	Tish	Jim	Erika
1st choice	A	A	H	H	A	H	H	H	H	A	A

These individual ballots can be combined in a table showing the number of voters in the top row that voted for each option:

Number of votes	5	6
1st choice	A	H

Notice that by totaling the vote counts across the top of the preference schedule we can recover the total number of votes cast: [latex]5+6=11[/latex] total votes.  Since there are only two choices and Hawaii has won the majority (~55%) of the votes, then Hawaii is the winning destination.

Example

The following table illustrates the results of a four-way race for Psychology Club President.  Notice that while Araceli received the most votes, no candidate received a majority (more than 50%) of the vote.  Using the plurality method, Araceli would win the election.

	Percentage of the Vote
Liam	26%
Sophia	19%
Araceli	30%
Enrique	25%

However, there are some potential problems with the plurality method.  Suppose, for example that all of the voters who chose Sophia and Enrique actually prefer Liam (over Araceli) as their second choice.  Then, while Araceli would still have the most first place votes, Liam would actually be preferred over Araceli by 70% of the voters.  One way to address this issue is to consider all of the voters' preferences.

Example

Consider again our vacation club.  They have decided to consider a third possible destination and so now they are trying to decide between: Hawaii (H), Orlando (O), or Anaheim (A). Their votes are shown below:

	Bob	Ann	Marv	Alice	Eve	Omar	Lupe	Dave	Tish	Jim	Erika
1st choice	A	A	H	H	A	O	H	O	H	A	A
2nd choice	O	H	A	A	H	H	A	H	A	H	O
3rd choice	H	O	O	O	O	A	O	A	O	O	H

  The individual ballots listed above are typically combined into one preference schedule (table below), which shows the number of voters in the top row that voted for each option.  You might notice that two of our six possible city-orders received no votes: OAH and HOA.  The four remaining orderings are listed in the preference schedule below under the number of votes each received.

	2	3	2	4
1st choice	A	A	O	H
2nd choice	O	H	H	A
3rd choice	H	O	A	O

  For the plurality method, we only care about the first choice options. Totaling them up: Anaheim: [latex]2+3=5[/latex] first-choice votes Orlando: 2 first-choice votes Hawaii: 4 first-choice votes Anaheim is the winner using the plurality voting method. Again, we notice that by totaling the vote counts across the top of the preference schedule we obtain the total number of votes cast: [latex]2+3+2+4=11[/latex] total votes.  Thus, we see that Anaheim won with 5 out of 11 votes, ~45% of the votes, which is a plurality of the votes, but not a majority.   Looking again at our preference schedule, we observe that while Anaheim received the most first place votes (five), the other six people prefer Hawaii over Anaheim.  It doesn't quite seem fair that Anaheim is the winning trip despite the fact that 6 out of 11 voters (~55%) would have preferred Hawaii! Hawaii vs Anaheim: 6 to 5 preference for Hawaii over Anaheim

	2	3	2	4
1st choice	A	A	O	H
2nd choice	O	H	H	A
3rd choice	H	O	A	O

  Since no option earned a majority (more than 50%) of first place votes, we can use the additional information included in our preference ballot to have a single run-off election.

Example

In the vacation club example, we would eliminate Orlando, since Anaheim and Hawaii both received more than two votes.

	2	3	2	4
1st choice	A	A	O	H
2nd choice	O	H	H	A
3rd choice	H	O	A	O

  Our revised table would look like this:

	2	3	2	4
1st choice	A	A	H	H
2nd choice	H	H	A	A

Using this method, we see that Hawaii would win with a majority, 6 out of 11 votes (~55%).