To the person conducting the poll:
Are you going to count the rankings to determine a winner? By what method?
I suggest that you look for a Condorcet winner, an alternative that isn't
pairwise-beaten, in any of its pairwise comparisons. And announce it to this
mailing list.
Also, I hope that you'll post, to this list, all the ballots, so that people
can apply, to them, whatever rank-count method they want to.
I claim that something is missing from the poll: On the ballot, you list
Condorcet as a method. Condorcet isn't a particular method. Condorcet is a
family of methods, in which we elect the CW if there is one; and, if there
isn't one, we elect the candidate whose greatest pairwise defeat is the least.
That's Condorcet's method. Of course it leaves open the question of how we
measure the magnitude of a pairwise defeat.
It's widely-agreed now that pairwise opposition, in a pairwise comparison, is
the best way to measure a pairwise defeat.
In other words, if X pairwise-beats Y, measure that defeat by the number of
people who ranked X over Y. I've called that winning-votes, and I and some
others have been abbreviating it wv.
The wv method that does Condorcet's method most literally is Plain Condorcet.
It's also the briefly and simply defined Condorcet version, and therefore is
the one suitable for a public proposal.
I defined PCin my previous post to this mailing list. But its definition is so
brief that I'll state the definition here:
Definition of Plain Condorcet (PC):
If there is a candidate who doesn't have a pairwise defeat, s/he wins. If more
than one candidate are without pairwise defeat, then they win.
Otherwise, the winner is the candidate whose greatest pairwise defeat is the
least (as measured by wv).
[end of PC definition]
So, I suggest that, instead of just listing Condorcet, it would be better to
ask for some nominations of Condorcet versions. I claim that PC is the publicly
proposable one, though Ranked-Pairs might be briefly-worded anough to be
proposable too.
So then, allow me to nominate two Condorcet versions, to replace Condorcet on
the ballot:
Plain Condorcet
Ranked-Pairs
I'd also like to nominate a pairwise-count method that isn't a Condorcet
version, but is just as good as PC. It may have been proposed by Forest, some
years ago:
MinMaxPairwise-Opposition (MMPO)
Definition of MMPO:
The first line is the same as for PC.
Otherwise, the winner is the candidate whose greatest pairwise opposition is
the least.
A pairwise opposition, of X, is the number of people ranking some one
particular candidate over X. So, X has a pairwise opposition with respect to
each candidate. So we elect the candidate whose greatest pairwise opposition is
the least.
[end of MMPO definition]
I'd previously thought that MMPO is briefer to define clearly than is PC, but
now I'm not so sure.
Anyway, so I nominate the following methods:
PC
MMPO
Ranked-Pairs.
If those methods were on the ballot (People should be invited to nominate
methods, and all nominated methods should be on the ballot), I would rank as
follows:
1. PC
2. MMPO
3. Approval
4. Ranked-Pairs
5. Range-Voting (RV)
I like the triangular shape of that ranking, which is entirely accidental.
It could be argued that Approval is more winnable than the rank methods,
because there are so many contentiously-divergent proposals for counting
rankings. True. But sometimes peope object to Approval, perceiving it as a
spoiled Plurality ballot. Though it can be explained that Approval is the 0,1
points system, and amounts to each person casting _one_ vote between some two
sets of candidates, I feel that people might be more enthusiastic about the
greater ambitiousness of a rank method. So maybe it's better to offer them a
really good, but briefly-defined rank method, such as those that I've nominated.
That's why I've ranked PC and MMPO over Approval. I've ranked Ranked-Pairs
below Approval, because its definition might not be as clear to voters asked to
sign an initiative petition or vote for enactment of a voting system.
I've ranked Range-Voting last, among the candidate I rank, because, though it's
better than the methods I didn't rank, it has a strategy problem that Approval
doesn't have (when some people vote sincerely and other people strategize).
Also, it's more difficult to implement than Approval.
Now, the question is, to get a winner in the poll, which method do we use, for
counting the ballots?
I suggest Voter's-Choice:
In addition to voting a ranking, invite each voter to designate a method for
counting this election. For that purpose, of course it would be necessary for
the ballot to allow for Approval balloting and RV balloting.
Count the ballots by all of the methods that have been designated by someone.
Give each method's winner a point-score equal to the number of people who have
designated that method.
The winner is the
