Condorcet.org40 ABC, 12 BCA, 13 BAC, 35 CBA
| A | B | C | |
| A | X | 40 | 53 |
| B | 60 | X | 65 |
| C | 47 | 35 | X |
The plurality (first preference) scores are as follows:
A 40
B 25
C 35
By plurality, A wins. With IRV, B is eliminated and A wins against C. In any Condorcet method, including Ranked Pairs, B will win. But why should B win? Do I just like the letter "B"? Am I saying that a "middle" candidate should win no matter how unpopular? And who decides who is the middle candidate?
To understand why B should win, it is first necessary to question the idea of popularity implied by my rhetorical questions above. It is implied that support in first preferences is the sole measure of popularity. Someone who feels this way can only choose plurality as an election method. I, however, question whether popularity is even a definable concept. Remember that originally it seemed like the "majority will" would be a definable concept, and essentially, it turned out this wasn't the case (see Arrow's theorem). But even if we decided that popularity was definable, first choice preference would seem to be an odd choice, considering all the strange results that plurality gives (see the Introduction).
I don't think, therefore, that it is true that B is less popular than A or C. Notice that in the example, all A-1st and C-1st voters vote B second. If they disliked B, they had the opportunity to defeat B by ranking it lower.
As for who decides what the middle candidate is, the answer is the voters. The middle candidate is not the middle candidate because it is middle among the candidates. However, if you arrange all the voters along the A B C spectrum along which they voted, then the middle ground is occupied by B voters. If you imagine that A B C represents a spectrum with A at the left, and B on the right, then a majority of people are to the right of A and to the left of C. B is in the middle in the sense that its supporters having a minority on either side.
Normally, opinions will be arranged in a bell curve. That is, most people will have opinions in the middle of the political spectrum, and decreasingly many will be found at the extremes. As a result, even under plurality, the middle candidate will win. If the middle candidate is not a plurality winner, there must be something else wrong with it, and it shouldn't win anyway.To understand why this is untrue, you have to visualize a bell curve. Now, I am going to assume that people vote purely on the basis of position on the political spectrum. This is obviously a simplification, but it will prove an important point. That is, that the winning candidate can lose even if people vote purely on the political spectrum. No one votes the middle candidate lower because they see "something else wrong" with the candidate.
Now assume there are three candidates A, B, and C. They are arranged along some kind of spectrum that I will call left vs. right. In fact this spectrum could refer to many different policy continuums, not just the left-wing vs. right-wing political debate. Now, I will place B in the very middle of a bell-curve population, with A and C to the left and right respectively. So, assuming that people vote based on electing someone nearest to them in political views, everyone who is to the left of A will vote for A. Similarly, everyone to the right of C will vote for C. The ground between A and C will go three ways. The voters who are closer to A then B will vote for A. The voters who are closer to B than either A or C will vote for B. The voters who are closer to C then B will vote for C.
What we see in this example is that the portion of the political spectrum staked out by either A or C is much greater than that of B, but B's area is more densely populated. The further A and C are from the middle, the more of the spectrum, and the more voters B gets. If they are far enough out, B is sure to win. If they are close enough in, B will have fewer plurality votes than either of them. There is little that B can do to prevent being squeezed out, if A and C are willing to compromise their policies enough to win.
So, plurality and IRV may very well result in the centre being squeezed out, with the election being decided on the basis of which of the left or right parties is willing to compromise enough to gain power. Since my explanation of why a middle candidate can be lowest in plurality votes does not have anyone voting except on the basis of position on a political spectrum, it is fair to conclude that the statement that their must be something wrong with the middle candidate if they don't win, is false.