[EM] Focus of runoffs?

Abd ul-Rahman Lomax abd at lomaxdesign.com
Thu Jun 13 11:20:19 PDT 2013

At 03:15 AM 6/13/2013, Kristofer Munsterhjelm wrote:
>Say we have an organization or government that wants to use a better 
>type of two-round runoff than top-two Plurality. What kind of 
>distribution should the candidates for the second round have?
>To be a little more specific, and to make the concept a bit easier 
>to think about, consider a top-n runoff with Approval ballots in 
>both rounds. Furthermore, to not have to deal with differences in 
>cloning problems, say that each group has at least n candidates, so 
>you have at least n centrists, n left-wing candidates, n right-wing 
>candidates and so on.

This analysis is highly restricted to partisan elections. I 
understand why this analysis is done. However, real *nonpartisan* 
elections with real voters don't work that way, apparently. The signs 
are strong that voters vote based on positive affect, and that the 
supporters of one candidate are, in general, a fairly accurate sample 
of the preferences of all the other votes as to any different 
candidate. That explains why IRV would not change preference order, 
the shifts tend to be small.

Partisan elections are very different, because, to a large extent, it 
is the party that matters to voters, not the candidates. So I might 
have an opinion about a Republican candidate, say, *even though I 
really don't know anything about the person.*

>Then what candidates should the runoff method pick for the second 
>round? It could pick according to ordinary Approval. If we consider 
>the electorate to be centrist, that would lead to n centrists being 
>elected to the second round. The lack of variety might keep the 
>voters from bothering to turn up in the second round. On the other 
>hand, because they're all similar, it might lead to a more detailed 
>discussion of different shades of centrist policy, thus informing 
>the voters more and letting them make better choices in the second round.

It would be top-two or top-three approval. Approval has some obvious problems.

>On the other extreme, the method could pick the candidates for 
>second round using minmax Approval. This would produce a great 
>variety of candidates, so the second round decision would probably 
>seem more meaningful to the voters. On the other hand, because the 
>ideological positions are so clearly defined and the n candidates 
>would be spread across the spectrum, it would be easier for say, a 
>right-wing candidate to say "that guy over there is a leftist; vote 
>for me if you like capitalism" (or whatnot) instead of discussing 
>the more subtle aspects of politics.

In pure repeated elections, there are no eliminations, but candidates 
might voluntarily withdraw.

Basically, as a baseline, I suggest considering repeated elections 
seeking majority approval, no eliminations. I would have thought that 
the only way to practically do this would be Asset Voting, because 
Asset could effectively run continuous elections, among the electors, 
the public voters.

However, there is another example from U.S. history. Reading the 
compilation done of the history of voting in Vermont, prepared by the 
state-established commission on IRV, which essentially turned the 
matter over to the League of Women Voters and Common Cause, i.e., to 
FairVote, I found that Vermont, until some time into the 20th 
century, *required a majority* for some elections, including 
Congressional elections. They simply kept voting until they found a 
majority. This was either with Town Meeting, or with actual repeated 
balloting at some interval. It was said, there, that sometimes they 
took a year to settle. I'm sure that was repeated balloting with 
vote-for-one, because this is something that could take a few polls 
with Approval, and some fewer with Bucklin, which simulates a series 
of approval elections with declining approval cutoff.

My sense -- unproven -- is that Bucklin with proper design, used in a 
2-round system would *almost always* not only find a majority, but 
would find a Condorcet winner to boot.

The trick is in how the runoff candidates are chosen. First of all, 
something needs to be specified. Many runoff systems allow write-in 
candidates in the runoff. That provides a way for the electorate to 
fix problems with the system, and this has actually happened, I've 
cited Long Beach, California. The first poll in a runoff system can 
show the problem, and the electorate can then fix it.

However, advanced voting systems can handle three candidates, 
generally. Where they might fail to find a majority, in the final 
round, the likelihood is high that the regret will be small from the 
choice they will then make, as a plurality result.

So what three candidates? Or two? Basically, my sense is that two 
candidates will usually be enough.

But we need a more complex ballot than Approval. I suggest 
Bucklin-ER, because it simulates a series of approval runoffs. If 
there is a majority failure, it is because voters, in effect and 
often with knowledge, preferred a runoff being held to voting for a 
deeper compromise. And so they get what they want.

Bucklin-ER, a basic version close to historical usage, uses a Range 4 
ballot with ratings of 0 and 1 collapsed into a single unapproved 
rating. For a fuller and more ideal vote analysis, this method can 
simply use a Range 4 ballot. The Bucklin analysis might stop with 
midrange. This could create, on the face, two possible winners: A 
"most approved" winner and a "range winner," i.e, sum of all votes, 
considering them as Range ratings. But there is another possibility: 
pairwise analysis. If pairwise analysis shows a candidate who beats 
both of the other two winners, that candidate may be included in the 
runoff. And if this preference is persistent, this candiate will win 
the runoff, and thus the method satisfies the Condorcet criterion. 
(As I've noted many times, when a Condorcet and Range winner differ, 
this indicates low preference strength in the votes for the Condorcet 
winner, and *therefore* various effects are likely to push runoff 
results toward the Range winner.)

There is another possiblity, that the primary and runoff are Range. 
So it would be top-two range into the runoff, and with an additional 
pairwise winner included if needed.

>Between these extremes, we have selection by proportional 
>representation. For Approval, that would be PAV or one of the 
>combinatorial methods (biweight, etc). This approach is not as 
>focused on the candidates everybody agrees are good (as in ordinary 
>Approval) not on the candidates at least someone thinks is very good 
>(as in minmax Approval), and thus, basically, is a combination of both.

This is a place where STV might work, actually. But I'm not sure it's 
worth the complications. If it's STV, I'd run it three-winner, then 
use Bucklin in the runoff. Same ballot! Different amalgamation.

>Which do you think would be best? What kind of discussion would give 
>the best candidates in the long run -- one of subtleties in centrist 
>policy, of breadth among a very wide variety of positions, or 
>proportional representation?
>I suppose TTR lies somewhere around the PR choice, selecting 
>candidates by SNTV. But SNTV is not a good proportional 
>representation method, n=2 doesn't give a great variety of 
>candidates anyway, and TTR may be set up the way it is to fix 
>problems in Plurality, not just to let the voters get a second look 
>at the most suited candidates.

plurality for the runoff makes some sense if there are only two 
candidates on the ballot, but is a big problem if there is a write-in 
campaign. It should be possible to vote for a sincere favorite as a 
write-in and to also participate in the realistic election. Approval 
*begins* to handle this, but has an obvious problem with the 
inability to indicate preference among the approved set. Bucklin handles that. 

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