Kevin--
You quoted me:
So, a method would satisfy WDSC if the C>A>D>E>B>F>G voters, comprising a majority, could deny B the win by voting C=A>D=E>B=F>G. It isn't necessary that there be any other way for them to deny B the win.
I replied:
You got it. One is all it takes.
You'd continued:
I think that's kind of a silly way to satisfy WDSC
I reply:
It was you who talked about a method in which it had to be done in that particular way. You must distinguish between silliness of WDSC and silliness of your hypothetical methods. A good way to make that distinction would be to find a silly way that needs to be voted in order to make an actual proposed method meet WDSC. Can you do that?
You replied:
That would be missing the point. If WDSC makes a meaningful guarantee, there shouldn't be a silly, meaningless way of satisfying it.
I reply:
WDSC doesn't make a guarantee, meaningful or otherwise. Methods that comply with WDSC make a meaningful guarantee.
It's conceivably possible to devise some unproposable method for which you can write an example in which a meaningful guarantee made by that method isn't violated, and some people are voting in a way that you might call sillly.
That doesn't mean that the guarantee isn't meaningful. It only means that a silly method is being discussed.
Kevin continues:
FBC:
>By voting a less-liked candidate over his/her favorite, a voter should >never gain an outcome that he/she likes better than every outcome that >he/she could get without voting a less-liked candidate over his/her >favorite.
I think this is clear, but hard to use. Suppose if I vote B>A>C>D>E, when A is my
sincere favorite (that is, I like candidates who come earlier alphabetically), then
B is elected. Suppose we try 20 other ways of voting, all with A at the top or
equal top, and these all elect E. I want to conclude that this is an FBC failure.
I can't, though, because it might be the case that e.g. A=E>B=D>C will elect A.
I replied:
The way to demonstrate that a method fails a criterion is to find a situation in which, with that method, the criterion�s premise conditions are met, and the criterion�s requirement is not met.
I continue the reply:
So far, then, you haven't shown that your hypothetical method fails FBC. Find an example in which the FBC's premise is complied with and FBC's requirement is not met.
You seem to be complaining that sometimes it might be difficult to find a failure example. Yes it might, but that has no bearing on the value of the guarantee that a complying method has. I don't have an FBC failure example for Condorcet(wv). There isn't one with 3 candidates, unless I've made an error, but maybe there's one with more candidates.
FBC isn't the only criterion for which it can sometimes be difficult to find a failurle example or prove that there isn't one. You're using a double standard if you only speak of that in regards to one or more of my criteria.
Kevin had said:
So I think a criterion like WDSC could afford to be more precise.
I replied:
But you forgot to say in what way WDSC, or a criterion like it, is imprecise. A criterion is imprecise if you can show that its wording could mean more than one thing, or that it isn�t possible to say what its wording means.
I meant that a criterion like WDSC should guarantee more. As it is, not only is it abnormally difficult to verify compliance, but there are silly ways of satisfying it. Compare my rendition:
I reply:
Different criteria guarantee different things. If you want a criterion that guarantees more than WDSC does, then I direct your attention to SDSC, SFC, and GSFC.
Yes, WDSC is really a minimum requirement for a barely adequate method. What's wrong with defining a modest bare minimum requirement?
Kevin continued:
As a first guess, I suggest: "If a majority of all the voters vote A in first or equal first, and B in last or equal last, then B mustn't win." If that doesn't resemble Mike's intention
I reply:
...and it doesn�t resemble WDSC.
But it implies WDSC, is easier to check, and doesn't allow silly methods of compliance.
I reply:
When you say that your criterion implies WDSC, you mean that compliance with it implies compliance witih WDSC. That doesn't mean that your criterion is valuable, or should be considsered as a substitute for WDSC.
For instance, Plurality meets your criterion. In fact, can you name any proposed method that fails your criterion? A criterion that is met by all proposed methods isn't very useful for comparing proposed methods. As a separate question, is there any proposable method, even if it isn't actually proposed, that fails your criterion?
Mike Ossipoff
_________________________________________________________________
FREE pop-up blocking with the new MSN Toolbar � get it now! http://toolbar.msn.click-url.com/go/onm00200415ave/direct/01/
---- Election-methods mailing list - see http://electorama.com/em for list info
