[EM] A four bit (sixteen slot) range style ballot

[Kevin Venzke]

Hi,

--- En date de : Lun 14.6.10, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
> Abd ul-Rahman Lomax wrote:
> > At 10:09 AM 6/13/2010, Kevin Venzke wrote:
> > 
> >> --- En date de : Sam 12.6.10, Abd ul-Rahman Lomax
> <abd at lomaxdesign.com>
> a écrit :
> >> 
> >> > Plurality allows voters to place a candidate
> at the "top of
> >> > their preference listings."
> >> 
> >> That is inadequate to satisfy the criterion, which
> refers to candidates
> >> plural. Woodall's Majority is equal to what has
> been called "Mutual
> >> Majority" on this list.
> > 
> > Sure. It's more general in application than the simple
> restatements of the Majority Criterion. However, the plural
> includes the singular.
>
> > What I see with Plurality is that if a majority of
> voters put the same set of candidates at the top of their
> preference listings, on the ballot, that candidate will win.
> That they only put one candidate doesn't violate or negate
> that statement.

If you owe the bank $100 and you pay it $50, that $50 is included in the
total, yes. The first $50 is required. But also the other $50 is required.

> > Below, Mr. Venzke provides a definition of preference
> listing, which considers it a ballot.
> > 
> > My point, though, is not to insist upon one particular
> interpretation, but to show that interpreting and applying a
> preferential voting criterion, as Woodall's Majority
> Criterion was intended to be, to a voting system that isn't
> constructed as expected, is not a way to objectively judge
> the system, because one then has to make a series of
> possibly biased judgments.
> > 
> > This really comes out when we start to examine
> Approval voting. If a majority of voters prefer a candidate
> over all others, showing that on the ballot, with Approval
> voting, that candidate must win. If they conceal this
> preference by also approving someone else, that candidate
> might lose. So ... does aproval voting satisfy this Majority
> Criterion?

If we either aren't using Woodall's framework or aren't using his 
interpretation of Approval, then it is ambiguous.

> Approval passes mutual majority if you alter it in such a
> way that Plurality, Minmax, etc., also pass it: "If
> everybody equal-ranks a certain set at first place, then
> someone from that set should win". However, that is not what
> Woodall intended, and it reduces mutual majority to simple
> Majority - in which case, why care about mutual majority?
> 
> Approval passes ordinary Majority. If a certain candidate
> (or set) is approved by a majority of the voters, any
> candidate that has a hope of beating it must also be
> approved by a majority.

But note that the way Woodall translates Approval into his framework,
it wouldn't satisfy ordinary Majority. That is arbitrary, but is consistent
with the fact that he doesn't consider equal rankings, and is also
consistent with the way some of our methods treat all explicitly ranked
candidates as "approved" for some purpose.

I personally don't view Approval as satisfying any kind of Majority. But 
I don't consider the argument winnable.

Kevin