[EM] majorities and ordinal-only pairwise methods

[Russ Paielli]

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?