Approval Voting

V. Vitols, Anaheim Hills, Calif. posed a question to Scientific American Magazine:

Approval Voting is a voting procedure in which voters can vote for as many candidates as they wish. Each candidate approved of receives one vote and the candidate with the most votes wins. It was independently proposed by several people in the 1970s. In the United States, the case for Approval Voting seems particularly strong in primary and nonpartisan elections which often draw large fields of candidates.

Unlike more complicated ranking systems, Approval Voting is simple for voters to understand and use. Approval Voting is used today by various governments and organizations around the world (including its use by the United Nations to elect the secretary-general). And, lest you get lost in the details, keep in mind that almost everyone agrees that the traditional single-vote plurality system does the worst job of picking the best candidate.


Approval Voting has several compelling advantages over other voting procedures:

First period high school physical education class has decided to take a vote to determine which activity they will take up next in PE. Their choices are aerobics (A), badminton (B), football (F), or softball (S).

The winning activity will be determined using Approval Voting.

Suppose the following summarizes the responses of the class:

12 students vote for Aerobics and Badminton

5 students vote for Badminton, Football, and Softball

10 students vote for Football and Badminton

13 students vote for Softball and Badminton

To determine the winning activity, we must calculate the number of votes received by each. The activity with the most votes wins.

How many total votes did AEROBICS receive? answer

How many total votes did BADMINTON receive? answer

How many total votes did FOOTBALL receive? answer

How many total votes did SOFTBALL recieve? answer

Which activity is selected by first period using Approval Voting? answer

 

Second period class votes to choose from among the same 4 activities (AEROBICS, BADMINTON, FOOTBALL, SOFTBALL) but decides to use the Borda Count method rather than Approval Voting to select their next activity. Suppose the preference schedule below summarizes the preferences of the second period PE class.

10

16

14

S

S

F

B

B

B

F

A

S

A

F

A

To determine the winning activity, we must find the Borda Count total for each activity. The activity with the largest Borda Count total is the winner.

What is the Borda Count total for Aerobics? answer

What is the Borda Count total for Badminton? answer

What is the Borda Count total for Football? answer

What is the Borda Count total for Softball? answer

Which activity is selected by second period using the Borda Count Method? answer

 

What might have happened if Approval Voting had been used?
(Suppose the class was surveyed and all students indicated that they would approve their first two choices and disapprove their last two choices.)

 

10

16

14

1st (APPROVED)

S

S

F

2nd (APPROVED)

B

B

B

3rd (NOT APPROVED)

F

A

S

4th (NOT APPROVED)

A

F

A

To determine the winning activity, we must calculate the number of votes received by each. The activity with the most votes wins. Notice that each activity in bold above receives an approval vote (and it does not matter whether it was first place or second place).

How many total votes did AEROBICS receive? answer

How many total votes did BADMINTON receive? answer

How many total votes did FOOTBALL receive? answer

How many total votes did SOFTBALL recieve? answer

Which activity is selected by second period using Approval Voting (when everyone approves of their first two choices from the previous preference schedule)? answer

 

What might have happened with Approval Voting for the second period class if each student approved their first two choices (as above) EXCEPT the students that made Softball their first choice (who only approve Softball)?

 

10

16

14

1st
(ALL APPROVED)

S

S

F

2nd
(ONLY 14 VOTES IN LAST
COLUMN APPROVED)

B

B

B

3rd (NOT APPROVED)

F

A

S

4th (NOT APPROVED)

A

F

A

Looking at the preference schedule above, this means that 26 (10 + 16) students who chose Badminton as their second choice would no longer vote for it under this Approval Voting scheme. So...

How many total votes did AEROBICS receive? answer

How many total votes did BADMINTON receive? answer

How many total votes did FOOTBALL receive? answer

How many total votes did SOFTBALL recieve? answer

Which activity is selected by second period using Approval Voting (when everyone approves of their first two choices from the previous preference schedule)? answer


As you can see from the above examples, Approval Voting is similar in some respects to the Borda Count method. Both methods involve computing a total and the winner is the candidate or choice with the largest total. However, the entire process is much simpler with Approval Voting. In addition, Approval Voting is perfectly suited to situations where candidates or choices are added or removed after a vote has already been taken. example

A Nice Property of Approval Voting

In an election using Approval Voting, adding or removing candidates or alternatives does not change the point totals of the other candidates or alternatives.
(If candidates/alternatives drop out, simply remove then from the list. If candidates/alternatives are added, vote totals for the original candidates/alternatives stay the same and voters only have to give their approval or disapproval of the candidates/alternatives that were added.)

 


Try these Approval Voting Exercises


Back to A Nonpreferential Voting Method