Though some consider Approval to be the best voting system, and I claim that Approval & Condorcet's method are the best two methods, I'm describing Approval first because of its great simplicity; listing it first isn't intended to imply that I consider it better than Condorcet's method.
What are some of Approval's advantages over Plurality, and over nearly all rank methods? In Approval, no one ever has any strategic incentive to vote a less-liked candidate over one's favorite. Strictly speaking, that can't be said for any other single-winner voting system. For example, with the popular elimination rank-counting system known in England as the Alternative Vote, and currently being promoted in the U.S. as Instant Runoff, it's claimed that a voter who votes a needed compromise over less-liked candidates is free to vote his favorite in 1st place. But often the compromise will be eliminated before the voter's traveling vote can reach it--unless the voter insincerely ranks the compromise in 1st place, over his favorite. As I said in the introduction, the need for that kind of voting is what we want to get rid of with a better voting system.
Instant Runoff advocates complain that Approval doesn't let voters express all their preferences, but at least it counts all the preferences that a voter has expressed, something that can't be said for Instant Runoff.
When Approval lets people vote for more than 1 candidate, some claim that that's a violation of "1-person-1-vote". No. Not unless that rule is narrowly construed to mean that a voter should only be able to vote for 1 candidate, in which case that rule should be violated, because it's the cause of our lesser-of-2-evils problem. But if 1-person-1-vote means that each voter should have equal opportunity to vote his/her preferences and to have them counted, then Approval doesn't violate that rule, though Instant Runoff arguably does, when it erratically chooses which people's preferences it will count or not count.
Approval is a point system in which a voter can give either 1 or zero points to any candidate. Plurality is a similar point system with the peculiar rule that a voter may only give a point to 1 candidate. Approval is Plurality done right. Plurality with the voter freedom that it should have had all along.
Maybe in principle, voters in Plurality all vote for their favorite. Realistically, we all know that isn't what happens. Many people vote for a compromise instead. Why shouldn't they be able to give their favorite at least what they give their compromise? Why should they have to vote their compromise over their favorite when they compromise?
If I vote for my favorite, and my 2nd best, B, and B beats C because of my vote for B, the C voters have nothing to complain about. If they object that I had too much power because I voted for 2 candidates, they can be reminded that Approval only lets me give 1 vote to any candidate. The people who voted for B over C were saying that they like B better than C, and want to help B beat C. I'm one of those voters. What's wrong with counting my preference for B over C. Why should A's entry into the election affect the count of how many people prefer B to C?
How much has to be changed in order to change from Plurality to Approval? Where the ballot now says "Vote for 1", it would instead say "Vote for 1 or more". That's it. That's the only needed change. No new balloting equipment or software needed. Expense? Zero.
Though a rank method like Instant Runoff amounts to a completely new voting system, Approval is nothing but rectified Plurality, making it easier to propose than a completely new system would be.
When proposing any rank method, one can encounter a fierce and seemingly hopelessly deadlocked debate on how ranked ballots should be counted, as there are innumerable ways to count them. Approval neatly avoids such debates, because there's only one way to count Approval votes: Add them up.
Earlier I said that Approval is the only method that never gives anyone strategic incentive to vote a less-liked candidate over their favorite. That's what the following criterion is about.
Merely a more self-contained way (no external definitions needed) of saying that there are no strategic incentives to vote someone else over one's favorite. In particular one never feels forced to do so in order to defeat an especially disliked candidate.
This criterion is met only by Approval. No other method meets it.
Approval is the only method that meets that criterion. Remarkably FBC & SARC are met by no method except for Approval.
WDSC differs from FBC in that, for a majority to accomplish what it wants to, its members have no need to reverse any preference. FBC was only about downvoting a favorite, but it stipulated no conditions.
A number of good methods meet WDSC. Approval is the simplest of them. Instant Runoff isn't one of them.
WDSC is one of several defensive strategy criteria. A majority has the power to accomplish anything that they all want. If they want to elect someone, they can, with almost any method. Likewise if they want to defeat someone. But the problem is what they have to do in order to accomplish that goal. WDSC says that, with a complying voting system, they at least don't have to reverse any of their preferences to accomplish that. The term "defensive strategy" refers to what a majority has to do in order to accomplish something that they all agree on. The better a method is, the less drastic is the defensive strategy that it requires.
With Plurality, there could be a longtime corrupt incumbant, Xc,who has, over the years, established good quid-pro-quo relationswith his backers. Maybe Xc is the traditional coming-together-point for the progressives--because the other party has worsepolicy positions, and is considered just as corrupt as Xc andhis party.
Now, say eventually a new candidate, X, enters the election.He has the same policy positions as Xc, but he isn't corrupt.Everyone knows that he's better than Xc. But his votegetting powerisn't proven. Because he might not have the support of the peoplewho give big money to political campaigns, X might not be winnable.
And say you decide to be principled, and you're one of the fewpeople who change their vote from Xc to X. You & the other peopledoing that won't make X win, because there aren't that many ofyou daring to do that. But you might make Xc lose to that otherparty with the worse policy positions. So you'd better keep votingfor Xc, right? Sadly that's right, with Plurality. So here's acriterion about that:
Unanimously Unpreferred Candidate Critrerion (UUCC):
If everyone prefers X to Xc, then there shouldn't be a situationwhere Xc wins, and where if one voter changes his vote in sucha way as to no longer vote Xc over X, that could cause theelection of someone whom that voter likes less than Xc.
Approval meets UUCC. Plurality & IRV fail UUCC.Condorcet (defined in a separate article) meets UUCC. ***