In favor of fair elections

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The outcome of an election ought to reflect voters’ preferences - that’s only fair.

Designing a fair election is easy when there are only two candidates on the ballot. The candidate with the most votes wins the election. But what if there are three candidates, or thirteen?

As the number of candidates increase, so do the difficulties in administering a fair voting system.

Voting theory addresses problems inherent in polling an electorate in a representative fashion. Mathematicians have devised and studied voting theory and voting systems since the mid-1700.

This entry compares the advantages and disadvantages of five common voting systems.

Select One

The traditional but problematic method of voting is to choose one candidate from a ballot of more than two. The more good candidates on the ballot, the more likely a bad candidate will win the election. Consider these election results:

18Candidate Awesome
19Candidate Brilliant
19Candidate Brilliant
20Candidate Fantastic
21Candidate Marvelous
22Candidate Terrible

Candidate Terrible can win the election with 22 votes under the Select One voting system. But 78% of voters preferred a good candidate to a bad one.

Runoff Election

How can we address the inherent unfairness of the Select One voting system? A common practice is to conduct a second election among the top two vote-getters. In the example above, Candidate Marvelous and Candidate Terrible would be on the ballot for a runoff election.

Runoff elections neither look good in theory nor deliver in practice. Mathematics predicts a runoff election will select a candidate who appeals to a small percentage of voters. In practice runoff elections do just that plus they also lead to extreme partisan divisiveness.

Runoff elections encourage lying. In the context of elections, you tell the truth when your vote expresses your preferences. Voting against your preferred candidate is lying. Would you lie, that is, cast your vote for a candidate you don’t prefer to prevent a worse one from winning?

Voters dislike the runoff election system because they are often forced to lie. If Candidate Fantastic supporters back their favorite, Candidate Terrible wins. Candidate Fantastic supporters can abandon Fantastic and support Candidate Marvelous.

Ranked Voting

Under the Ranked Voting system, a voter ranks preferred candidates ordinally, that is, 1st, 2nd, 3rd, and so on. One voter may mark a ballot this way:

Candidate Awesome
1stCandidate Brilliant
3rdCandidate Fantastic
2ndCandidate Marvelous
Candidate Terrible

Another voter might vote like this:

1stCandidate Awesome
3rdCandidate Brilliant
2ndCandidate Fantastic
Candidate Marvelous
Candidate Terrible

Someone's bound to vote like this:

Candidate Awesome
Candidate Brilliant
Candidate Fantastic
Candidate Marvelous
1stCandidate Terrible

It's easy for voters to grasp how to mark their ballots to express their preferences. What is harder to explain is ballot scoring.

Voting theory offers several competing methods of scoring ranked voting ballots. Each method of scoring ballots has its fans and foes. In practice, debates over ballot scoring algorithms can drown out important policy discussions.

Approval Voting

Approval voting lets a voter express approval for all acceptable candidates, no matter how many or few.

You can vote for your top pick for the office:

XCandidate Awesome
Candidate Brilliant
Candidate Fantastic
Candidate Marvelous
Candidate Okay
Candidate Mediocre
Candidate Terrible
Candidate Awful

You can express your approval for several candidates for the office:

XCandidate Awesome
Candidate Brilliant
XCandidate Fantastic
XCandidate Marvelous
Candidate Okay
Candidate Mediocre
Candidate Terrible
Candidate Awful

You can vote for any candidate you wouldn’t mind seeing in office:

XCandidate Awesome
XCandidate Brilliant
XCandidate Fantastic
XCandidate Marvelous
XCandidate Okay
Candidate Mediocre
Candidate Terrible
Candidate Awful

You can embrace your inner contrarian:

Candidate Awesome
Candidate Brilliant
Candidate Fantastic
Candidate Marvelous
Candidate Okay
XCandidate Mediocre
XCandidate Terrible
XCandidate Awful

Approval voting lets you vote for your preferred candidates. Do you prefer Fantastic to Marvelous? Vote for Fantastic. Do you prefer either of them to Terrible? Vote for both.

Approval voting shares a drawback with ranked voting. Ballot scoring algorithm debates can distract voters from important issues and candidate qualifications.

Approval Voting does not permit voters to express how much they approve of candidates. A voter can express either complete approval for a candidate or none at all, that is, 100% or 0% approval.

Ranged Voting

Ranged voting allows for expressions of approval between 0% and 100%. Voters can express how much they approve of each candidate in the race.

Voters begin with a ballot such as the one below:

NO OPINIONCandidate Awesome
NO OPINIONCandidate Brilliant
NO OPINIONCandidate Fantastic
NO OPINIONCandidate Marvelous
NO OPINIONCandidate Okay
NO OPINIONCandidate Mediocre
NO OPINIONCandidate Terrible
NO OPINIONCandidate Awful

Voters may vote for as many or as few candidates as they wish. The application of a ranged voting system can vary. Voters can express a preference for each candidate by assigning:

  • a percentage, where 100% indicates complete approval,
  • a number between 0 and 10, where 10 indicates complete approval, or
  • a number between 0 and 100, where 100 indicates complete approval.

Voters can register disapproval, that is a 0, for as many candidates as they wish. Voters can even leave “No Opinion” for one or more candidates.

100%Candidate Awesome
90%Candidate Brilliant
NO OPINIONCandidate Fantastic
70%Candidate Marvelous
20%Candidate Okay
NO OPINIONCandidate Mediocre
0%Candidate Terrible
0%Candidate Awful

To score the ballots, find the arithmetic average of the ranged votes for each candidate. First add the ranged votes for each candidate, and divide by the number of voters who voted for that candidate.

Example: Ten voters cast their ballots. Candidate Awesome received the following votes:

100%, 100%, 100%, 90%, 80%, 80%, 80%, 70%, 40%, No Opinion.

Add together the value of the votes and divide by the number of voters who expressed an opinion. A vote of “No Opinion” doesn’t count for or against a candidate. In the example above, Candidate Awesome got 82.2%.

(100% + 100% + 100% + 90% + 80% + 80% + 80% + 70% + 40%)/9= 82.2%

If 82.2% is the highest score, then Candidate Awesome wins the election.

Ranged Voting and the Hard Grader

Ranged voting allows a voter the flexibility to give their favorite candidate less than 100%. Suppose a hard-grading voter casts a ballot like this:

70%Candidate Awesome
60%Candidate Brilliant
30%Candidate Fantastic
40%Candidate Marvelous
20%Candidate Okay
_NO OPINION_Candidate Mediocre
0%Candidate Terrible
0%Candidate Awful

The hard-grading voter’s favorite candidate is Awesome. Another Candidate Awesome Supporter expressed 100% approval. Ranged Voting critics say that the system is invalid because one voter’s vote counts for less than another’s.

Proponents of ranged voting agree that the hard-grading voter is at a self-determined disadvantage. Ranged Voting proponents say the trade-off is acceptable. Some votes may count less than others but a candidate with limited appeal is extremely unlikely to win.

Summary and Conclusion

Under a good voting system, voters can express their true preferences. A candidate with limited appeal should not be able to prevail in a good voting system.

Select One and Runoff Election are not good voting systems. Candidates with limited appeal routinely prevail under Select One and Runoff Election. Voters cast their ballots for candidates they don't prefer to prevent a worse outcome.

Ranked Voting, Approval Voting, and Ranged Voting are three good voting systems. They let voters express their true preferences. Ranked Voting and Approval Voting should prevent candidates with limited appeal from gaining office. But ballot scoring methods tend to draw attention from important issues and candidate qualifications. If we focus on ballot scoring, it’s possible for an unqualified candidate or unwise proposal to prevail.

Ranged Voting lets voters cap their approval for their preferred candidate below 100%. Critics say it's unfair if some votes count more than others. Fans say Ranged voting’s advantages outweigh its disadvantages. One advantage Ranged Voting offers is an easy ballot scoring method.


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