Voting Theory: Learn It 5

Approval Voting

Up until now, we’ve been considering voting methods that require ranking of candidates on a preference ballot. There is another method of voting that can be more appropriate in some decision making scenarios.

approval voting

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.

Let’s take a look at an example.

A group of mathematicians are getting together for a conference. The members are coming from four cities: Seattle, Tacoma, Puyallup, and Olympia. Their votes are tallied below. Find the winner using Approval voting.

  [latex]30[/latex] [latex]10[/latex] [latex]15[/latex] [latex]20[/latex] [latex]15[/latex] [latex]5[/latex] [latex]5[/latex]
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. Let’s explore this through an example.

Consider the voting schedule:

  [latex]80[/latex] [latex]15[/latex] [latex]5[/latex]
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 [latex]80[/latex] voters B would receive approval from [latex]100[/latex] voters C would receive approval from [latex]20[/latex] 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.