[EM] "Beatpath GMC" compliance a mistaken standard?
Kristofer Munsterhjelm
km-elmet at broadpark.no
Sun Jan 11 11:11:47 PST 2009
Juho Laatu wrote:
> --- On Sun, 11/1/09, Kristofer Munsterhjelm <km-elmet at broadpark.no> wrote:
>
>> Let's consider the first election first, with
>> truncation extended to full preference:
>>
>> 26: A > B > C
>> 25: B > A > C
>> 49: C > A = B
>
>> A B C: 100 prefer {A B C} to the empty set
>
> This case is interesting (not that it
> would have any impact on the ongoing
> mutual majority discussion but just
> for theoretical interest).
>
> The number of candidates was not exactly
> stated in the example. If there are e.g.
> four candidates then the votes would be:
>
> 26: A > B > C = D
> 25: B > A > C = D
> 49: C > A = B = D
>
> Set {A, B, C} has in this case no support.
>
> Let's assume that there are also other
> citizens (=potential candidates who
> are however not candidates) than the
> named candidates. The opinions of the
> first 26 voters could be as follows.
>
> 26: X1 > A > B > X2 > C = D = X3 > X4
>
> The point here is that the voters have
> not said that they would prefer A, B, C
> and D to the other citizens / potential
> candidates (X1, X2,...).
>
> It is ok to say that if there are no
> "mutual majorities" the winner can be
> elected from the whole set of candidates
> {A, B, C} or {A, B, C, D} or whatever set.
> One can not say that the voters would
> prefer the all the candidates (or those
> that are named on the ballots) to other
> citizens. What is the meaning of saying
> that they prefer these candidates to an
> empty set?
There is no real meaning - it's just an artifact of taking the process
to its conclusion. The only thing it means is that all voters who voted,
voted for the candidates they voted for, which is a tautology.
Smaller unanimity sets can only exist if there's a candidate or a
candidate set that everybody ranks last.
Also note that changing a vote from A > B to X1 > A > B can dissolve
what would otherwise be a majority for {A B}. Mutual majority isn't
complete - it only says that in certain cases (majority support for a
set), certain things should happen (the method should elect from the
set). In that respect, it's kind of like independence of clones. You can
make a method that technically passes mutual majority yet wouldn't be
any good, just like you can prefix a method with "remove clones" yet it
would be a bad method if a single voter didn't vote clones in strict
clone order.
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