[EM] Re: Plurality is not a "yes/no voting system"

[MIKE OSSIPOFF]

Tom Ruen said:

Adam Tarr says Approval voting can fit under "Yes/No voting" or "Ratings 
voting", however I deny that plurality can be classified as a "yes/no" 
voting method.

I reply:

That's a strong statement, Tom, saying that something _can't_ be classified 
a certain way.

As was already pointed out, a Plurality voter is giving one candidate a 
"favored" classification and the others "nonfavored" classification. 
Plurality is a 2-level ratiing system, one that gives a rating to each 
candidate. Plurailty is 0,1 CR. But with a peculair requirement that the 
voter give "nonfavored" status to all the candidates except for one.

Sure, you could call Plurality a rank system too, if you want to. But 
Plurailty is counted in the simple way that all CR versions are counted. CR 
is by far the more straightforward interpretation of Plurality, as opposed 
to a rank method.

What you've written below consists of your own personal definitions, and 
that's fine for you. But you mustn't expect to define those things for 
everyone. Of course the fact that your definitions are completely new 
doesn't mean that they aren't any good. But it's for you to show why we 
should adopt them and abandon the existing meanings of those terms.

You continued:

Labeling a class of methods as "yes/no" to me implies a series of 
independent questions where a valid respond can consider independent 
responses on each question.

A method that allows independent answers is a categorical "ratings method".

I reply:

Independent of what?

You continued:

A method that has a limitations on answers can only be a "rank" system.

I reply:

Not at all. CR 0-10 limits point ratings to a specified range of integer 
values, but that does not make it a rank method.

As for the definition of a rating method vs a rank method, the defined 
difference needn't just be about the balloting itself. The most natural 
definition of the difference between rank methods and rating methods 
involves the count. Rating methods have a count rule based on the actual 
values of ratings, while rank methods have a count rule  based on the order 
of ratings (which are called "rank positions", and are usually integers 
whose value is greater for lower-rated candidates). CR, or course is the 
usual ratings method, and it counts by just adding up each candidate's 
ratings from the voters.

So, if a rank method's balloting allowed you to give  whatever rank position 
numbers you wanted, it wouldn't make any difference what values you gave 
them. All that matters is the order of the rank position numbers.

That suggests a balloting-based definition similar to or the same as one 
that someone has already suggested: Rank balloting means that the the 
candidates receive integer ratings called "rank positions", with a larger 
number indicating a lower rating, and that a candidate rated next-lower than 
X must have a rank number that is one greater than that given to X.

I define "X is rated lower than Y" in a ballot as "Y is voted over X" in 
that ballot.

The previous paragraph is a suggested definition of rank balloting. The 2 
paragraphs before that is a definition of a rank count. A rank method must 
use a rank count, and they all use rank balloting, thugh they needn't. For 
instance, one could count CR ballots by Condorcet if one wanted to. Counting 
rating ballots by a rank count.

A rating method likewise must use a rating count. By the way, Borda is a 
rank method and a rank-count, even though it assigns points that are added 
up. The voter doesn't assign the points. The count rule assigns the points 
based on the order in the ranking. If we changed Borda' s balloting to allow 
the voter to assign arbitrary ratings, and just added them up, that would be 
CR, not Borda. To meaningfully apply Borda to such ballots, we'd look only 
at a ballot's order of ratings, and let Borda's count rule assign the 
ratings that are added up.

A rating balloting could be defined as a ballot that allows numbers to be 
assigned to candidates according to some rule that's broader than the 
balloting rule for rank balloting.

Plurality and Approval, with only two ratings values available, could, in 
principle, be called ratings methods or rank methods, based on that 
definition. But, because their count rule is identical to that of other CR 
versions, it's much more natural to call Plurality & Approval rating 
methods, CR versions in particular.

Mike Ossipoff

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