[EM] majorities and ordinal-only pairwise methods

[Russ Paielli]

Kevin Venzke stepjak-at-yahoo.fr |EMlist| wrote:
> Russ,
> 
> --- Russ Paielli <6049awj02 at sneakemail.com> wrote:
> 
>>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 defeats can be cyclic. You need a means of deciding which defeats to
> keep while hopefully satisfying some criteria.

Yes, I agree. The problem is that those means are arbitrary and are not 
based on the directly expressed will of the voters. They can't be, 
because ordinal-only methods simply neglect to collect critical 
information on voter preferences.

> 
>>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.
> 
> 
> I think you can view it as the ability to argue against a defeat sustained
> directly. For instance, suppose X beats Y pairwise. We'd want to say that 
> Y can't win now. But if we do that then every candidate could become
> disqualified. Instead we can check to see whether Y has a path of wins 
> back to X. We could use a (hopefully monotonic) means of identifying the
> weakest part of this cycle, and break it there.
> 
> Of course RAV just substitutes an approval measure for WV or Margins.
> It's unchanged, that increasing the strength of one candidate's wins can
> cancel another candidate's wins.

The key point is that DMC/RAV bases its elimination of candidate X on 
how the voters actually rated X in direct competition with all the other 
candidates -- not on how candidate Z fared in a pairwise race with 
candidate W.

Ordinal-only methods simply do not collect enough information from the 
voters, so the cyclic ambiguity resolution procedure must necessarily 
resort to arbitrary rules that have little relation to actual voter 
preferences.

> 
>>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?
> 
> 
> Why do you think it's not as fair? I don't remember you arguing that it
> isn't as fair.

Suppose your favorite candidate was eliminated due to a 51-50 defeat, 
but your last choice won despite a 50-3 defeat. Would you consider that 
fair?

We could argue all day about the definition of "fair," but my point is 
that the wv measure of defeat "strength" is arbitrary. One person here 
on EM argues incessantly that it is a better measure because it thwarts 
strategy, but that is a piss-poor rationale. Appointment by a dictator 
also thwarts voting strategy, but does that make it a preferable method? 
Of course not.

Common sense also informs me that wv is not a reasonable measure of 
defeat "strength." By that measure, Bush's victory over Gore in Florida 
2000 was "stronger" than Reagan's victory over Mondale in 1984 because 
Bush got more votes. (That argument is bogus even if we normalize for 
population growth.)

If your football team squeaks by with a 42-40 win, is that a "stronger" 
win than a 37-0 rout? I don't think so, and I doubt many other football 
fans do either.

Now, you-know-who will probably reply that I once advocated wv and have 
now switched over to margins just because I don't like him. The truth is 
that I really don't care which is better because they both stink, and 
they are also both too complicated for public acceptance. As far as I am 
concerned, those debating about wv vs. margins might as well be debating 
about how many angels can dance on the head of a pin.

> RAV is more likely to agree with WV here than Margins. That's why I don't
> mind it much.
> 
> 
>>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?
> 
> 
> I would also like to hear again the benefit *inherent* to combining ordinal 
> and cardinal information. It seems to me that you, Jobst, and James all have
> different purposes in doing this.

I tried to explain this a few weeks ago. See 
http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2005-March/015216.html

A key point is that cardinal methods are not subject to cyclic 
ambiguities. Thus, they can be used to "break" cycles based on the 
*directly* expressed preferences of the voters. But you know that.

--Russ