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

[James Green-Armytage]

James G-A replying to Kevin Venzke...

Kevin:
>You don't need to suppose that ballots are cast sincerely, since there is
>no way to fill out ballots such that they couldn't possibly be sincere. If
>a method fails Smith for any set of ballots, it must fail your criterion.

	I just wanted to make sure that the criterion was failed by plurality,
approval, and other methods that don't allow full rankings. Maybe there is
a better way to do this.

Kevin:
>
>So this criterion isn't different from the "Smith criterion."

	That's okay; it's not trying to be different from the Smith criterion.

Kevin:
>
>I doubt it is useful to identify the Smith set with "majority rule,"
>unless
>"majority" as in ">50% of all the votes" is not a useful idea.
>
	Okay then, how do you define majority rule? The question I'm interested
in is not whether we can invent an interesting new concept; the question
is what is the most appropriate criterion to be identified as "majority
rule". When we say that a given method is a majority rule method, what
should we mean by this?
	I suggest that, essentially, we should mean that it is
Smith-efficient.Why the Smith criterion? Because choosing from the Smith
set is the way to ensure that no expressed majority preference (pairwise
defeat) is unnecessarily overruled.
	In some ways, this question has more political significance than
mathematical significance. Many of those who consider IRV to be the best
single-winner method claim that it ensures majority rule. Is this true? If
not, what criterion does IRV fail that makes it not a majority rule
method. I suggest that it is the Smith criterion. 
	I suggest that narrower definitions, such as the one that Mike has
formulated, are too narrow, in that it is necessary to choose one of
several viable defeat strength definitions. I suggest that broader
definitions, such as the mutual majority criterion and Condorcet
criterion, are unnecessarily broad. I suggest that the Smith criterion is
the majority rule definition that is broad enough to be generally
acceptable, but narrow enough to be exclude methods that unnecessarily
ignore the will of a majority, e.g. IRV, minimax, etc.

my best,
James