Chris--
The subject line of your message says that Plurality is a ranking method in theory and in effect.
Well, that would of course depend on what your theory is, and what effect(s) you're talking about.
Plurality is a rank method? Ok, now I'm going to define a new method, which I call Ranked Ossipoff Choice (ROC). Here are its rules:
Voters vote rankings. The rankings are collected from the voters. Then I make the choice, disregarding the rankings.
By your reasoning, that's a rank method too.
You'll protest that at least Ranked Plurality gets some information from the rankings. But the important thing is that Ranked Pluralitly receives rankings, and then does Plurality. Ranked Ossipoff Choice receives rankings and then Ossipoff chooses.
Both of those "rank" methods receive rankings and then do what the method's name, after "ranked..." says. Therefore if Ranked Plurality is a rank method, then Ranked Ossipoff Choice is a rank method.
But if it would make you happy, I could look through the rankings and find one that lists, somewhere in the ranking, something that I like, and choose that alternative. Then I too am using information from the rankings in making my choice.
Here I quote your definition of "admissible":
(BTW,"admissable" means "capable of being allowed;permissible", in other words eligible to be counted according to the rules of the method.)
I reply:
"eligible to be counted according to the rules of the method". A method is defined by its rules.
By your own admission, a method's rules specify what kind of a vote is eligible to be counted.
So if 2 methods differ only in what kind of voting is admissible, then they are not the same method. That isn't complicated. That doesn't involve adavnced theory, or require your theorists to tell us if it's so.
You can say that ranked Plurality is "like Plurality". You can say that it's "equivalent to Plurality" in some specified regard. But if you say that ranked Plurality is Plurality, then you're mistaken. Even by your own definition of admissibililty.
You said:
This is the full text of Steve Eppley's discussion/definition of his "Minimal Defense" criterion from which Marcus Schulze copied:
minimal defense <http://www.alumni.caltech.edu/%7Eseppley/Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm>: If more than half of the voters prefer alternative y over alternative x, then that majority must have some way of voting that ensures x will not be elected and does not require any of them to rank y equal to or over any alternatives preferred over y.
I reply:
Preferred by whom?
That isn't how I say it. Here's how I define SDSC:
If more than half of the voters prefer X to Y, then they should have a way of voting that ensures that Y won't win, without any member of that majority voting a candidate equal to or over a candidate that s/he likes more.
A voter votes X and Y equal if s/he votes X over someone, and s/he votes Y over someone, but s/he doesn't vote X over Y, and s/he doesn't vote Y over X.
[end of SDSC definition]
Do me a favor, and don't post someone else's definition to say what my criteria are.
You continued:
(Another
wording is nearly equivalent: Any ordering of the alternatives
must be
an admissible vote, and if more than half of the voters rank y
over x
and x no higher than tied for bottom, then x must not be elected.CB: I must say I greatly prefer the "nearly equivalent" wording as being much more concise, simple and reasonable-sounding.
I reply:
Concise:
Sometimes brevity can take away too much meaning. The first sentence can have more than 1 meaning. "Any ordering of the alternatives must be an admissible vote" could be taken to be a reqirement that everyone votes admissibly, rather than as a requirement about the method's rules.
Simple:
Maybe. But maybe simplicity can sometimes conflict with the goal of completely defining something.
Reasonable-sounding:
What's reasonable-sounding to you is a subjective perception on your part. You forgot to tell us what you think is unreasonable about my definition of SDSC. Use the definition I wrote above. It doesn't matter what you think is unreasonable about someone else's wording of a criterion of mine.
Maybe you think it's reasonable to write a criterion so that Plurality fails the criterion by decree. That just shows that what's reasonable to you isn't reasonable to me. I dislike rules criteria. My own wording of SDSC, the one that I wrote above, doesn't make any requirements specifically about particular rules that a method should have--only about its results. But maybe you like rule criteria, and that's fine.
I'd said:
"Equivalent to [in some particular specified regard]" most definitely does not mean "is"."
You replied:
"First Preference Plurality" (as Woodall calls it, a name I prefer to "ranked Plurality") is not just
equivalent to Plurality "in some particular specified regard". It is equivalent in EVERY regard that
is of interest to voting theorists.
I reply:
You're invoking authority, a form of argument that relies on other opinions which, you allege, back you up, and which we shouldn't question. I'm not saying that authorities or theorists are never right, only that depending on invoking someone else's opinion is a weak argument.
Apparently you're saying that balloting rules aren't of interest to voting theorists, though, as you yourself admit, rules about voting-admissibility are part of a method's rules. Do voting theorists say that a method isn't defined by its rules?
You continued:
It transmits voted preferences into a result identically
I reply:
No it doesn't. Plurality doesn't "transmit" voted preferences identically to Ranked Plurality, because Plurality doesn't even receive the preferences that Ranked Plurality receives. And a Plurality ballot doesn't say "List your 1st choice". It says "Vote for 1".
You continued:
, and is therefore of course strategically equivalent.
I reply:
0-10 CR is strategically equivalent to 0,1 CR (Approval). But 0-10 CR is not 0,1 CR.
You continued:
This (Tue.Jul.15,03) quote from Alex Small in the "Arrow's Theorem" thread is of some relavence (sic) /interest:
"In the formal derivations of Arrow's Theorem that I've seen, an election method is defined as a mapping from the set of voter preferences to the set of candidates.
I reply:
That isn't correct. Voting systems have, as their input, votes, not preferences.
But, even aside from that, even if we change "preferences" to "voted pairwise comparisons", the statement still isn't correct. The method isn't a mapping from the set of voted pairwise comparisons to the set of candidates. It's a mapping from the set of all of the configurations of voted pairwise comparisons that would be admissible for a given set of voters, to the set of candidates. A particular configuration of voted pairwise comparisons gives us a particular set of candidates as the winners.
But, again, by your own definition of admissibility, a method's rules consist of more than its count rule. They include its balloting.
You said:
For the purpose of rationally analysing voting methods, the fact that "different voting is admissable"
is only relavent (sic) if it gives a different result.
I reply:
For the purpose of determining whether 2 methods are the same, differences in their rules are relevant.
You continued:
In FPP, the only restriction on vote admissabilty that is relavent (sic) is that the voter can mark as
favourite one candidate only. Obviously it makes no difference whether voters are not allowed to enter
lower rankings or are compelled to enter lower rankings or anything in between.
I reply:
It makes a difference when the ballot is thrown out because it ranks candidates. That can change the outcome of the election.
This isn't complicated: Different rules, different method.
Mike Ossipoff
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