Approval Voting

Learning Outcomes

  • Conduct internet searches and write statements using Boolean logic
  • Construct a truth table
  • Use DeMorgan’s laws to write and negate logical statements

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.


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, we find:

Titanic received 5 approvals

Scream received 6 approvals

The Matrix received 7 approvals.

In this vote, The Matrix would be the winner.

In the following video you will see the example from above.

Try It

Our mathematicians deciding on a conference location from earlier decide to use Approval voting. Their votes are tallied below. Find the winner using Approval voting.

30 10 15 20 15 5 5
Seattle X X X X
Tacoma X X X X X
Puyallup X X X X
Olympia X X X

What’s Wrong with Approval Voting?

Approval voting can very easily violate the Majority Criterion.


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.

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.