[EM] James--Majority rule definition, 29 March, 0632 GMT

[James Green-Armytage]

This is James G-A, replying to Mike Ossipoff, on the topic of possible
majority rule definitions,
>
Mike:
>One way (but only one way :-) of defining a majority pairwise preference
>is 
>as an instance of a majority praeferring one candidate to another. And
>one 
>way of defining the strength of that majoritly pairwise preference has to
>do 
>with how big a majority that is. Completely arbitrary, of course :-)

	Not arbitrary, but also not the only valid way to define it. Another way
to define the strength of a majority preference is the size of the
majority times the strength of the preference on each ballot comprising
the majority. This is the definition given by cardinal weighted pairwise,
and it has an equally valid claim to be a definition of majority
preference strength.

James:
>
>	Lately, I have been defining majority rule violation as the selection of
>an option outside the Smith set.
>
Mike:
>The Smith set has nothing to do with majority.

	It has everything to do with majority. The Smith set is the smallest set
of candidates who are preferred by a majority to every candidate outside
the set. If you pick a non-Smith candidate, you are needlessly ignoring a
majority preference. If you pick one of multiple Smith candidates, you are
ignoring at least one majority preference, but you are in a situation
where it is necessary to do so. Hence it is necessary to chose from the
Smith set in order to guarantee that no majority preference will be
unnecessarily ignored. 
>
James:
>
>I think that the Smith set is the narrowest majority rule
>definition we can make that stands some chance of gaining general
>consensus.
>
Mike:
>...except that the Smith set isn't a majority rule definition.

	Of course it is, in the following sense: If a voting method chooses a
non-member of the Smith set, I say that it has violated majority rule. If
a method chooses a member of the Smith set, I say that it has upheld
majority rule. If a voting method always elects a member of the Smith set,
I call it a strong majority rule method. I argue that this definition is
meaningful and useful.

James:
>
>	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
>
Mike:
>I have never said that wv is the only way to define defeat strength.
>Perhaps 
>you would like me to define defeat strength in all of the possible ways. 
>Forgive me, but it seemed best to only define it in one way, and, if it's
>ok 
>with you, I chose wv.

	My contention is that there is no basis on which to define it in only one
way. You can do so if you want, but you shouldn't expect other people to
accept your definition.

Mike:
>You don't say how you'd rather define the magnitude of a majority
>pairwise 
>vote. Margins? 

	No. When it comes to choosing an actual method, I prefer the defeat
strength definition that CWP gives. When it comes to defining majority
rule for general purposes, I prefer to leave defeat strength out of the
definition, i.e. to define majority rule compliance as choosing from the
Smith set.

Mike:
>But why is that important to you, how many people accept my definition of 
>majority rule.

	If you don't care if anyone accepts it, why bother posting it on a
discussion list? By doing so, you are implicitly asking for others'
feedback. If you don't care if anyone adopts your criteria, you might as
well not mention them to other people.
>
Mike:
>But I'm not saying that CP shoudn't do that. Or, in your terminology, I'm 
>not saying that it's un-normative for CP to do that :-)  It's a good
>thing 
>when CP elects Kerry in that example, a good thing that CP has and uses 
>information other than the pairwise votes, when that can thwart offensive 
>order-reversal, or when it can resolve a natural circular tie in a way
>that 
>is fairer.

	I'm glad that we are agreed on that point.

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

P.S. If you're not satisfied with the dictionary definition of the word
"normative", I suggest that you look it up in the glossary of an
introductory economics textbook. My usage is based on the latter.