Comparison of VoteFair Ranking with plurality, majority, instant-runoff, Condorcet, and Borda-count methods

The following table compares VoteFair ranking with other voting methods — and reveals VoteFair ranking to produce much fairer results than the other methods.

Notice that both VoteFair ranking and instant-runoff voting (IRV) produce fairer results than plurality and majority voting, but instant-runoff voting does not always produce fair results, and it cannot handle a ballot on which a voter indicates an equal preference between two choices.

Keep in mind that the interest in the Condorcet and Borda-count methods arises because these methods allow voters to indicate a second choice, third choice, and so on, not because they are useful and fair in real-life situations. (They aren't.)

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Comparison of VoteFair Ranking with other voting methods

Voting method	Fair results?	Second, third, etc. preferences considered?	Voter can indicate equal preference among two or more choices?	A sincere voter has the same influence as a strategic voter?
VoteFair	Yes, always	Yes, all the alternate preferences of all the voters are considered.	Yes	Yes, strategic voting attempts are not effective.
Runoff (and instant runoff)	Usually, but unfair results easily occur if there are more than two or three main choices.	Some alternate preferences of some voters are considered (and others are ignored).	No, if an equal preference is encountered the ballot must be ignored.	Usually, but in some cases strategic voting can slightly increase a voter's influence.
Majority (used in a few U.S. general elections)	Yes if a majority is achieved, but this seldom happens if there are more than two main choices.	No, only one mark is allowed.	No, only one mark is allowed.	No, voting for a preferred but unpopular choice weakens the most similar popular choice.
Plurality (used in most U.S. primary and general elections)	No, a "splitting" of votes can easily cause a less-popular choice to win.	No, only one mark is allowed.	No, only one mark is allowed.	No, a sincere voter has less influence than a strategic voter.
Condorcet	If a winner is identified, the result is fair (and matches the VoteFair result), but this method often fails to identify any winner.	Yes	No, if an equal preference is encountered the ballot must be ignored.	No, in some situations strategic voting can slightly increase a voter's influence.
Borda count	No	Yes	No, if an equal preference is encountered the ballot must be ignored.	No, strategic voting easily increases a voter's influence.

To better appreciate the fairness of VoteFair Ranking over other voting methods, consider an election between three candidates named Clifford, Farah, and Gordon in which 100 voters have the following preferences:

40 voters prefer Clifford (as their) first (preference), Farah second, and Gordon last
35 voters prefer Gordon first, Farah second, and Clifford last
25 voters prefer Farah first, Gordon second, and Clifford last

Based on these preferences, the various voting methods would produce the following results:

Voting method	Winner
VoteFair	Farah
Instant runoff	Gordon
Majority	None of the choices has won a majority (more than half) the votes.
Plurality	Clifford
Condorcet	Farah
Borda count	Farah

Notice that VoteFair ranking reveals the most popular candidate to be Farah. This makes sense because a majority of voters (60 out of 100) prefer Farah over Clifford, and a majority of voters (65 out of 100) prefer Farah over Gordon.

In contrast, plurality voting — which is used in almost all U.S. elections — declares Clifford to be the winner (because he receives the most first-preference votes). Majority voting — which is used in U.S. Presidential elections — would not produce any winner because none of the candidates receives a majority (more than half the votes). Instant runoff voting (IRV) is commonly claimed as a fair alternative, yet IRV would designate either Clifford or Gordon as the winner. (Variations of IRV can resolve the tie one way or the other, but the outcome still isn't fair.) The Condorcet and Borda-count methods would declare Farah as the winner, but these two methods are well-known to produce unfair results in other situations

To better appreciate the differences in voting methods, here is a tally table that summarizes the pairwise preferences of all the voters.

All possible pairs of item names	Number of votes with indicated preference
All possible pairs of item names	Prefer X over Y	Equal preference	Prefer Y over X
X = Farah Y = Gordon	65	0	35
X = Farah Y = Clifford	60	0	40
X = Gordon Y = Clifford	60	0	40

Hopefully you now recognize that plurality and majority voting — and even instant runoff voting — can easily fail to produce fair results. In contrast, VoteFair ranking always correctly identifies the most popular candidate.

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