[EM] a majority rule definition based on the Smith set

[James Green-Armytage]

	This is James Green-Armytage, replying to Mike Ossipoff, on the subject
of majority rule definitions, specifically on the possibility of a
majority rule definition based on the Smith set.
	Mike, here is my proposed definition of strong majority rule. Your
feedback is welcome, as is all other feedback.

Definition of strong majority rule criterion: If voters cast ballots
sincerely, and the voting method in question always chooses a member of
the sincere Smith set, the method passes the strong majority rule
criterion. Otherwise, the method fails the strong majority rule criterion.

Definition of casting ballots sincerely: (1) Not voting a more-preferred
candidate below a less-preferred candidate. (2) Not voting candidates
equally when I prefer one over the other, and when the number of available
preference levels on the ballot does not prevent me from indicating my
preference. (Note: if I leave more than one candidate off a ranked ballot,
I consider this to be equivalent to ranking those candidates equally in
last place.)

Definition of Smith set, aka minimal dominant set or GeTChA set: The
smallest set of candidates such that every candidate within the set
pairwise beats every candidate outside the set.
>
>Maybe you want "majority" to mean a majority of those voting a preference 
>between X and Y. But then "majority defeat" justs becomes another word
>for 
>"pairwise defeat". 

	Yes, exactly; that's what I intend. 

>In other words, majority loses its meaning, the "more 
>than half of the voters" meaning that it has in its accepted use. 

	Another accepted use is "more than half of the voters who express a
preference between two options/candidates". That's the definition I
choose. I realize that you don't agree with it, but at least my reasoning
is made clear to you. One benefit of this kind of definition is that it
assures that a batch of spoiled ballots cannot rob a defeat of "majority"
status.
http://wiki.electorama.com/wiki/Neutrality_of_Spoiled_Ballots
>
>James:
>If you pick a non-Smith candidate, you are needlessly ignoring a
>majority preference.
>
Mike:
>Not at all. Maybe, due to truncation, someone is out of the Smith set 
>because of a sub-majority defeat.

	Okay. I meant that you are needlessly ignoring an expressed majority
preference. That is, "expressed" meaning in terms of cast ballots, and
"majority" meaning more than half of those who expressed a preference
between the candidates in question. Again, you don't have to agree, but
you need to know that what I'm saying makes sense within the context of my
own definitions.
>
Mike:
>James, I don't criticize you because you're new to this subject. 

	I've been studying voting methods for approximately 5 years, and I've
been studying them seriously for over 4 years. Not as long as you, but
long enough to develop opinions that are as valid as yours. Your
condescension is out of place.

Mike:
>CP is a 
>perfectly good idea, a good Condorcet enhancement, and probably meets the 
>criteria that I judge methods by. But, for some reason, in voting system 
>discussion, some people new to the subject arrive with some degree of 
>arrogance--the notion that they have it right, and that someone else has 
>been wrong all this time.

	Of course, you're never guilty of arrogance, or of the above notion... 
	Anyway, I suppose that discussion of the attitudes that we take in our
discussions can quickly move off-topic and become offensive, so I intend
to keep such discussion at a minimum.
>
Mike:
>Do you see that your definition of the Smith set suggests that you're a 
>little premature with your statements about who is wrong?

	My wording may have been imprecise, but that doesn't mean that my general
idea was wrong, and I stand by my general idea. Some people are more
capable than others of appreciating ideas independently from the way that
they are expressed; perhaps this is just a matter of personality type.
Anyway, I am willing to work towards more precise wording to express my
ideas, when necessary.

Sincerely,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm

>
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