Forest wrote:
"..MinMax is the only commonly known Condorcet method that satisfies the
following weak form of Participation:
If A wins and then another ballot with A ranked unique first is added to the
count, A still wins."
That is Mono-add-Top, I think coined by Douglas Woodall. It is met by IRV.
"Beatpath, River, Ranked Pairs, etc. fail this weak participation criterion,
but they do
satisfy this even weaker version:
If A wins and then another ballot with only A ranked is added to the count,
then A still wins."
That is Mono-add-Plump.
Forest,
Is there some method that you like or take seriously that actually fails this
criterion?
Chris Benham
Forest Simmons wrote (21 April 2010):
________________________________
I don't know if Juho is still cheering for MinMax as a public proposal. I used
to be against it because of its clone dependence,
but now that I realize that measuring defeat strength by AWP (Approval Weighted
Pairwise) solves that problem, I'm starting to
warm up more to the idea.
MinMax elects the candidate that suffers no defeats if there is one, else it
elects the one whose maximum strength defeat is
minimal.
There are various ways of measuring defeat strength. James Green Armytage has
advocated one called AWP as making Condorcet
methods less vulnerable to strategic manipulation.
If all ranked candidates on a ballot are considered approved, then the AWP
strength of a defeat of B by A is the number of ballots
on which A is ranked but B is not.
Then more recently I was reading a paper by Joaquin Pérez in which he shows
that MinMax is the only commonly known Condorcet method
that satisfies the following weak form of Participation:
If A wins and then another ballot with A ranked unique first is added to the
count, A still wins.
Beatpath, River, Ranked Pairs, etc. fail this weak participation criterion, but
they do satisfy this even weaker version:
If A wins and then another ballot with only A ranked is added to the count,
then A still wins.
Proof: First add a ballot in which no candidate is ranked. The above
mentioned methods allow this, and it doesn't affect their
outcome since no mention of absolute majority is made in any of them. Then
raise A while leaving the other candidates unranked.
This cannot hurt A since all of the above mentioned methods are monotone.
Knowing that Beatpath satisfies the weaker version but not the weak version may
be an inducement for voters to bullet vote candidate
A to make sure that they avoid the no show paradox. But MinMax is free of this
temptation; they wouldn't have to truncate the other
candidates.
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