[EM] Mike: majority rule

[James Green-Armytage]

James G-A replying to Mike, on the topic of majority rule definitions...
>
James:
>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.
>
Mike:
>That's my Smith Criterion definition. For a long time it was at a (now 
>defunct)
>website. That criterion, there, was listed under the name "Generalized 
>Condorcet
>Criterion".
>It's the obvious generalization of my Condorcet Criterion to the Smith
>set. 
>And
>it was posted at a website for a long time.

	Okay. I'm glad that we can agree on a definition of the Smith set. I'm
not really attached to any of the definitions in the post that you were
replying to... I just wrote them on the spot in an attempt to clarify what
I was saying for your benefit.
>
Mike:
>Again: Your Strong Majority Rule Criterion isn't new, because it's my
>long-posted version of the Smith Criterion.

	As I said to Kevin, I'm not trying to make up something new. I'm trying
to argue that the Smith criterion (which is not new) is the most sensible
criterion to look at when someone asks whether a given method "ensures
majority rule".

James:
>	Another accepted use is "more than half of the voters who express a
>preference between two options/candidates".
Mike:
>That accepted use only applies as a sometime replacement  for "a pairwise 
>defeat". No one ever says, "Candidate Smith has a majority defeat,
>because 
>more people vote Jones over Smith than Smith over Jones." No one would
>call 
>that a majority defeat for that reason. No one would call it a majority 
>defeat unless more than half of the voters vote Jones over Smith.
>You can say that, to you, majority never means anything but a pairwise 
>defeat, but the fact remains that majority means a set of voters
>consisting 
>of more than half of the voters. Whether you recognize that meaning or
>not, 
>it's the main use of "majority".

	This probably won't impress you into thinking that it's a good
definition, but I note it as a response to your comments on common usage:
The IRV people use "majority defeat" in much the way that I have been
using it. Take the following ballots:
45: A
45: B
4: C>A
6: C
	They will tell you that A wins over B by a majority, because after C is
eliminated, the 6 C ballots are considered to be spoiled ballots. They
will say that in the A-B simulated runoff, A wins by a majority of
non-spoiled ballots (49 out of 94 = 52.13%). The same logic can be applied
to pairwise comparisons.

Mike:
>thanks for telling us, but you've merely substituted one word for 
>another.

	Yes. Giving a new name (majority rule) to an existing criterion (Smith)
is exactly what I am trying to do. I explain my reasons for wanting to do
this in my recent reply to Kevin. Trust me, it's short. 
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-April/015460.html
	If you don't think that what I'm trying to do is useful, that's fine. We
can just drop the issue at that point, I think. I understand what you are
trying to do with your majority rule definition: you want to use it as
part of your definition of defensive strategy, right? I was interested in
a majority rule definition with a different purpose. Specifically, I was
interested in a definition that we Condorcet-appreciating people could use
to show IRV supporters that IRV only "ensures majority rule" in a very
weak sense. We had different purposes, which explains why we came up with
different definitions. I'm guessing that there is no further need to argue
about it.

Sincerely,
James
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