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
<[email protected]> 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.
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?
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.
A greater Approval system using DSV or official strategizing under
influence of a poll would still meet Majority in terms of approval
ballots submitted to the final stage, but perhaps not in terms of rank
or rate ballots originally intended - some might, others might not.
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