Score Voting with Condorcet-triggered top-two runoff

[Ted Stern]

Consider an election with score ballots.  Voters would be instructed to give a non-zero score to any candidate they approve of, with score describing the strength of their preference.  Majority Judgment style qualitative descriptions could also be used.  Scores would be normalized so that there is at least one maximum score on a ballot.  Overall candidate score would be Total Score (not average).

With a ratings ballot, rankings can be inferred.  So besides tabulating total scores, also accumulate the instant round robin array to enable determination of a Condorcet winner, if one exists.

Find Total score winner (TS) and Condorcet winner (CW), if one exists.

If a CW exists and the CW and TS are the same, there is one winner, CW = TS.

If there is a CW but CW does not equal TS, have a runoff between CW and TS.  

If there is no CW, have a top two runoff between the Total Score winner and the Total Score runner up.

Basically, this is a Score voting election, but with a modified top-two runoff triggered in the event of a difference with the Condorcet result.

My motivation is that a Condorcet confirmation would add confidence to, and increase satisfaction with, a single-round score result, while the top-two runoff would enable voter re-evaluation in the event of an unclear result.

Thoughts?

Ted

[Toby Pereira]

This is quite interesting. I know people have discussed before that you can work out the winners under several different methods (rated and ranked) using a single score ballot, but what you do with that information is arguably the important part.

Normalising scores - there have been arguments put for and against this, but I would argue that this is a separate matter rather than an intrinsic part of the system. A bit like if you designed a new Condorcet method and then declared that it is to be a winning votes (or margins) method, when really it could actually be either. And there is always the question of exactly how to normalise. You mentioned having at least one maximum score, but do you extend that to having at least one zero? Also, do you allow the normalisation to give fractional scores or do you round to the nearest integer? With fractions, I might decide that I want to give a candidate 8.5 out of 10. So I might sit there for a while and work out that if I give a maximum of 7, then by giving this candidate a 6, it would work out at about 8.57, which wouldn't be available to me if I just used the full maximum of 10. But anyway, this is a bit of an aside.

If there is no Condorcet winner, you have suggested a run-off between the candidates with the top two scores. Another possibility would be to pick the score winner and also the winner under a specific Condorcet method. It might be that the runner up isn't in the Smith Set, so wouldn't necessarily be the candidate you'd want in the run-off against the score winner.

Also if you pick the score winner and runner up for the run-off, they might be effective clones, so you could instead pick the two candidates who would be elected in a two-seat sequential proportional election. Having said that, if the top two are near clones then they probably are the genuine top two, because they would also have survived a potential Burr dilemma situation. And having a run-off between these two would encourage people not to defect (i.e. give a top score to one but not the other) in the original vote.

[Ted Stern]

I'm fine with not normalizing scores.  If it makes the method simpler, it would be a reasonable option.

The gist of the idea here is to have some kind of fall-back if the score winner is not definitive.  Having a Condorcet winner is fairly strong confirmation of overall sentiment, but without that consensus, there would remain some doubt.

I think having a runoff between clones would actually be a good thing, since the basic approach I suggested does not really consider votes against.  If there is no clear consensus on the winner, a top-two runoff would actually give an opportunity to prevent the most strongly disliked clone from winning.

Ted

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[Warren D Smith]

By definition, the CW would win a runoff versus TS.
(At least if the first round votes ordered them honestly,
and the electorate did not change.)

So this method is kind of silly in that respect.

But if you took that attitude I suppose you'd want to skip the
time-waste and just
use a Condorcet voting method. Or if you took my attitude, then
skip the other time-waste and just use score voting, and if you wanted a runoff,
then make it between the top 2 scorers. Which is simpler and in practice
largely equivalent.


--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

[Toby Pereira]

Your figures provide evidence that a top two run-off could be desirable - http://rangevoting.org/StratHonMix.html

[Warren D Smith]

A top-2 runoff 2nd round definitely could be desirable with range voting.

It tends to compensate for strategy-caused distortions in the result from
plain range, because in the 2nd round A-vs-B runoff, all votes
(even by strategists) will be honest. And in computer simulations,
one indeed finds
that range+runoff is superior in terms of Bayesian Regret measurements,
to plain range, provided there are enough strategic voters in the voter-mix.
If, however, the voter-mix is mainly honest, then plain range is superior
to range+runoff.

Returning to the Condorcet issue, see
http://rangevoting.org/AppCW.html
http://rangevoting.org/CondAppConflict.html
which had made the point that with range or approval, PROVIDED the voters
employ a certain simple and fairly realistic strategy, a Condorcet winner
automatically will be elected.

That differs from using a Condorcet voting method as follows:
if a Condorcet winner (CW) [based on honest votes] exists, then:

VOTING METHOD.............Honest Voters............Strategic voters
Range............................can elect non-CW...............elects CW
Condorcet............................elects CW...............can elect non-CW

!!