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For my definition of 3PD, I should define "discriminate":<br>
<br>
A voter discriminates among a set of candidates iff s/he votes some of
them over others in any order she wants to.<br>
<br>
I referred to a method that I call "DP". That stands for
Defection-Proof. It was proposed by Chris Benham. It doesn't meet CD,<br>
and I guess that only pairwise-count methods can, but it doesn't fail in
the Approval bad-example, something that can be said for<br>
only very few methods.<br>
<br>
Definition of DP:<br>
<br>
Voting is 3-slot: Preferred, Middle, and Bottom.<br>
<br>
Bottom is the default for a candidate not ranked on a ballot.<br>
<br>
To rank a candidate other than at bottom is to "approve" that candidate.<br>
<br>
If the number of voters approving X but not Y is greater than the number
of voters approving Y, then disqualify Y.<br>
<br>
Among the undisqualified candidates, elect the one preferred on the most
ballots.<br>
<br>
[end of DP definition]<br>
<br>
DP meets FBC and 3P, and doesn't fail in the Approval bad-example.<br>
<br>
CD is probably too demanding, referring, as it does, to a Condorcet
candidate.<br>
<br>
Maybe a criterion an be written that better reflects the Approval bad
example (the ABE).<br>
<br>
Maybe something like:<br>
<br>
If a majority prefer A and B to all the other candidates, and if, A
would win if the 1st choice supporters of both candidates <br>
voted both over all the others, then A should win even if A's 1st choice
voters vote B over the others, but the B<br>
voters don't vote A over the others.<br>
<br>
[end of tentative CD definition]<br>
<br>
When I have a good definition to reflect the ABE, I'll call it CD. <br>
<br>
As for the criterion that I've previously called CD, I'll call it CCD
(Condorcet Co-operation/Defection Criterion).<br>
<br>
Maybe someone has already posted about this, but Bucklin gives the voter
a lot more than 3 protection-levels, as I've<br>
defined that term. It gives the voter as many protection levels as there
are rank positions in the voter's ballot.<br>
<br>
So I'll modify the 3P criterion to say "..at least three...", instead of
"...three..."<br>
<br>
And, if a method, like Bucklin, gives an unlimited number of protection
levels, then it meets the<br>
Unlimited-Protection-Levels Criterion, which I abbreviate "UP".<br>
<br>
MDDA meets 3P and 3PD, but fails UP. Bucklin meets 3P, 3PD and UP.<br>
<br>
But, regrettably, Bucklin fails in the ABE.<br>
<br>
Can a method meet UP and not fail in the ABE? <br>
<br>
Yes. IRV (= whole) meets FBC and UP, and doesn't fail in the ABE.<br>
<br>
I now consider IRV (= whole) to be the best method. Certainly the best
for public political elections.<br>
<br>
Between MDDA and DP, I prefer DP, because I consider the ABE to be more
important than<br>
discrimination among candidates protected at a protection-level.<br>
<br>
(Below "ABE" means "doesn't fail in the ABE")<br>
<br>
<br>
A criterion compliance chart:<br>
<br>
-----------------FBC--------3P-----3PD--------UP----ABE<br>
<br>
Bucklin---------Yes--------Yes-----Yes--------Yes----No<br>
MDDA----------Yes---------Yes----Yes---------No----No<br>
DP--------------Yes---------Yes-----No---------No----Yes<br>
MCA------------Yes---------Yes-----No---------No----No<br>
MAMPO---------Yes---------No-----No----------No---No<br>
IRV(= whole)---Yes-------Yes-----Yes--------Yes---Yes<br>
<br>
Mike Ossipoff </div></body>
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