[EM] Mike: majority rule definition

[James Green-Armytage]

Hi Mike,
	Here's the third and last part of tonight's reply. The topic is defining
majority rule.

>I told Markus that I was going to define majority rule soon. My
>definition 
>of
>majority wishes is similar, and I guess that I'd better state that 
>definition
>now, instead of being vague about what I mean by majority wishes and 
>majority
>rule.
>
>If a majority prefer X to Y, that's a majority pairwise preference (MPP).
>The strength of that MPP is measured by the number of voters who prefer X
>to 
>Y.

	Well, obviously that's one way to define the strength of a pairwise
defeat. Margins provides another way, and cardinal pairwise yet another.
>
>An MPP for X over Y is outdone if there is a sequence of MPPs from Y to X,
>consisting of MPPs that are all at least as strong as the MPP of X over Y.
>
>To violate majority wishes means to elect someone who has an MPP against
>him
>that isn't outdone.

	Lately, I have been defining majority rule violation as the selection of
an option outside the Smith set. This is close to your definition, except
that you get more specific by assuming that there is a single normative
definition for "defeat strength", and then proceeding to define majority
rule along the lines of what Jobst calls the "uncovered set". (I think
that's basically it, right?)
	I have to object to the defeat strength part of your definition, in part
on the behalf of cardinal pairwise. Winning votes is surely one way to
define defeat strength, and it is not a bad one, but I do not accept it as
the one and only definition, and I doubt that very many other people will
either. I think that the Smith set is the narrowest majority rule
definition we can make that stands some chance of gaining general
consensus.
	Do you really think that it would be a majority rule violation to choose
Kerry rather than Bush in the example above (in part I, that is)? I don't
think so at all. But I think it would be if we accepted your recent
definition.

(These last bits aren't part of the "majority rule" thread, but they're
too small for a separate post):
>Of course there's no point pursuing the issue of who has better made
>their 
>case. I merely was asking if there were any additional arguments.

	I think that there will be soon, but I don't have the time to get into it
just yet. First of all, I'd appreciate your reading my recent (3/14/04)
post on strategic vulnerability in "margins" methods, and noting your
points of agreement and disagreement. Perhaps we can proceed from there.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015125.html

>I defined AERLO and ATLO as separate options for flexibility, but you
>have a 
>point: Flexibility isn't necessarily something that the public want to
>deal 
>with. Maybe AERLO and ATLO should be combined as one option, effectively 
>AERLO + ATLO, for simplicity.
>
	This would be similar to approval-weighted pairwise.

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