[EM] majorities and ordinal-only pairwise methods

[Kevin Venzke]

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.

> 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 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.

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.

Kevin Venzke



	

	
		
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