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Study Guides > Mathematics for the Liberal Arts Corequisite

Approval Voting

Learning Outcomes

  • Determine the winner of an election using the Approval Voting method
  • Evaluate the fairness of an election determined by the Approval Voting method
  With Approval Voting, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.

Example

Example 1: A group of friends is trying to decide upon a movie to watch. Three choices are provided, and each person is asked to mark with an “X” which movies they are willing to watch. The results are:
Bob Ann Marv Alice Eve Omar Lupe Dave Tish Jim
Titanic X X X X X
Scream X X X X X X
The Matrix X X X X X X X
Totaling the results using approval voting, we find:
  • Titanic received 5 approvals
  • Scream received 6 approvals
  • The Matrix received 7 approvals.
In this vote, The Matrix would be the winner.   This seems like a great voting method--what could go wrong? Example 2: Consider the voting schedule:
80 15 5
1st choice A B C
2nd choice B C B
3rd choice C A A
Clearly A is the majority winner. Now suppose that this election was held using Approval Voting, and every voter marked approval of their top two candidates.
  • A would receive approval from 80 voters
  • B would receive approval from 100 voters
  • C would receive approval from 20 voters
B would be the winner. Some argue that Approval Voting tends to vote the least disliked choice, rather than the most liked candidate.   The following video works through these two examples.
https://youtu.be/-8put6XKw20?list=PL1F887D3B8BF7C297
 
What’s Wrong with Approval Voting?
As we saw in the last example, approval voting can very easily violate the Majority Criterion.
Additionally, Approval Voting is susceptible to strategic insincere voting, in which a voter does not vote their true preference to try to increase the chances of their choice winning. For example, in the movie example above, suppose Bob and Alice would much rather watch Scream. They remove The Matrix from their approval list, resulting in a different result.
Bob Ann Marv Alice Eve Omar Lupe Dave Tish Jim
Titanic X X X X X
Scream X X X X X X
The Matrix X X X X X
Totaling the results, we find Titanic received 5 approvals, Scream received 6 approvals, and The Matrix received 5 approvals. By voting insincerely, Bob and Alice were able to sway the result in favor of their preference.  

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