Folks,
The other day I had a little dispute here on EM with a "prolific" EM participant regarding the definition of a majority. I said that he apparently has no regard for majorities. I was only half kidding. Let me explain.
A fundamental problem with ordinal-only pairwise methods is that, if no Condorcet winner exists, a majority must be arbitrarily overruled to determine a single winner. I refer, of course, to the majority of voters who participated in a particular pairwise race and who have their votes overruled.
The "defeat dropping" schemes used in these methods involve comparing the "magintude" of a pairwise defeat by comparing it to other pairwise defeats. But why should the status of a defeat of X by Y depend in any way on a race between W by Z -- two completely different candidates? The voters would no doubt be surprised to know they were making a statement on the X-Y race in the process of voting on the W-Z race.
The aforementioned EM participant replied that, of course, one must ultimately drop defeats or candidates to determine a single winner. He then predictably regurgitated his standard lecture about how and why defeats should be dropped. But he never explained why the status of a defeat of X by Y should depend in any way on the race between W and Z.
The aforementioned EM participant also routinely makes a big deal about the fact that "winning votes" is a more strategy-resistant method of measuring defeats than margins. However, the fact that it is not as fair doesn't seem to bother him the least. I have an even more strategy-resistant method: appoint the tallest candidate. No, it isn't very fair, but it's very strategy resistant! And saying that a 51-49 defeat is "stronger" than a 50-0 defeat isn't very fair either -- but it is more resistant to strategy! Does anyone else see a pattern here?
The aforementioned EM participant recently suggested that the best public proposal would be to drop ordinal methods altogether and go with cardinal ratings. Is he the only participant here who hasn't figured out the benefit of combining ordinal and cardinal information? Will someone please give the poor guy a clue?
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