[EM] Poll for favorite single winner voting system with OpaVote

Thu Oct 13 17:45:50 PDT 2011

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 alternative that has the hightest point total.

[end of definition of Voter's-Choice]

I have to say that, if we're using RV to help find the winning method, then I will, of course, vote strategically in RV, giving maximum points to to all of the alternatives to which I've given an Approval vote.

I don't know what points-range RV's nominator would like to specify. I kinow that RV advocates like fine resolution, and so let's say it's 0-100.

So, then, here is there rest of my ballot (My ranking is written above in this posting):

Approval:

I give Approval votes to all of the candidates that I ranked, because I consider all of them adequate

RV: I give maximum points to all of the candidates I've given Approval votes to.

My method designation: I designate PC.

I request that, after the results are posted here, we be allowed to add defensive truncation if we feel it's appopriate.

Mike Ossipoff

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