[EM] Classifying 3-cand scenarios. LNHarm methods again.

[Abd ul-Rahman Lomax]

A comment on Later-No-Harm.

The discussion of voting systems largely ignores what may be the most 
widely-used voting system! Certainly, outside of governmental usage, 
it's the most widely-used, and that is repeated ballot. As described 
in Robert's Rules of Order, voters vote for one candidate. If it is 
secret ballot, the typical ballot is just a blank piece of paper, on 
which the voter writes the name of the candidate. But this isn't 
"Plurality," because, if no candidate gains a majority, the election 
fails and is repeated.

Repeated. No eliminations. Yet, without a great deal of explicit 
consideration, this is considered impossible for public elections, so 
the closest we get to it, in practice, is Top-Two Runoff, which isn't 
a close simulation at all, though it's better than Instant-Runoff 
voting, particularly if write-in votes are allowed in the runoff.

What happens in a series of vote-for-one elections? First of all, 
usually, unless there are lots of candidates, one wins with a 
majority, and I don't think anyone considers this a poor outcome! 
(Theoretically, it can be less than optimal, under unusual 
conditions, but how about we consider how to get to voting systems 
that at least respect the will of a majority, to start, before we 
look for further tweaks that might detect the presence of something 
better and then ask the majority if they, now that they know this, prefer it?)

But, obviously, especially if there are more than two candidates, 
there can be majority failure. If all the candidates are stubborn and 
they all are nominated again, it would seem to be a simple and 
useless repeat. Except that the voters may now vote differently. In 
practice, some candidates withdraw, sometimes recommending that their 
supporters vote a certain way, i.e., endorsing another candidate. And 
voters shift their votes until there is a majority.

Now, it's possible to speed this process up. I've seen Approval 
Voting used that way; in this case, there was an approval poll, with 
a series of options, and the poll was taken by asking the members 
present to raise their hands if an option, when it was named, was 
acceptable to them. From the results of the approval poll, it was 
apparent that there was one and only one alternative that was 
acceptable to everyone (except for one person.) The motion was then 
presented to adopt that alternative, and voting was immediate with no 
further discussion, and the result was unanimous. Yes, the single 
holdout changed her vote.

The problem with basic Approval voting, though, is that it asks 
voters to relax their approval standard too quickly, right from the 
start. There is an improved form, Bucklin, I call it "Instant Runoff 
Approval." In the first rank, one only lists one's favorite, or (in 
Bucklin-ER, which I highly recommend) any candidate reasonably equal 
in approval.

In the last rank, with Duluth Bucklin, one was able, before 1920, in 
the U.S., to vote for as many candidates as one chose. So it was a 
preferential ballot, but it was also Approval Voting, the claim that 
approval has never been done in U.S. political elections is false.

There was a middle rank. For those who don't know how Bucklin was 
counted, if there was no majority in first rank votes, the second 
rank votes were added in. And if still no majority, the third rank 
votes were then added in. In original Bucklin, at that point the 
candidate with the most votes won. This is very much the same as 
Approval voting, which is, after all, as usually proposed, a 
plurality method, i.e., majority is not required.

However, something has been overlooked. Going back to repeated 
ballot, repeated *Bucklin* ballot would simulate three rounds of 
Approval voting with no eliminations. If it's a two-round system, 
three-rank each time, it is somewhat equivalent to six rounds of 
repeated ballot. It is much more similar to repeated ballot than is 
instant runoff voting, because there are, at least within a single 
ballot, no eliminations.

If, however, there is to be elimination for the second ballot, 
Bucklin provides means to make a better determination of who is to be 
eliminated than does IRV (and much better than plurality). I won't go 
into the details, but a good Bucklin ballot would almost always make 
it possible to detect a Condorcet winner and make sure that this 
candidate was in the runoff. (The ballot would do this reasonably 
well with it being standard 3-rank ER Bucklin, but it could be made 
4-rank, which really means, with the default lowest rank, 5 total 
ranks, so that there are two unapproved ranks. This is really a Range 
ballot, and if it gets a Range winner into the runoff, lots of 
interesting possibilities would result.)

And a runoff with Bucklin should work quite well with only three 
candidates: the two best (by some standard) and a write-in! Why a 
write-in? Because things go wrong sometimes! If the voters actually 
prefer a write-in candidate more than two on the ballot, it is silly 
to insist on two; and with Bucklin, one could vote for a write-in and 
not spoil the election.....

Bucklin has been very inadequately studied, partly because 
assumptions were made about it that weren't accurate. For example, 
Warren Smith seems to have been unaware that voters could leave the 
second rank blank, reserving the second choice for the third rank. It 
really was a Range ballot! (Range 4). And if equal ranking had been 
allowed in all ranks, in a runoff system, in the primary, it would 
have been that, fully, with Range rating 2 having a very clear 
meaning: I prefer this candidate to a runoff.

Ah, Later No Harm. When it was introduced as a voting system 
criterion, by What's-His-Face, a referee for the paper expressed 
disgust. Why? Well, for a voter to not reveal a lower preference 
because it might "harm" a greater one is antisocial! It's like saying 
"I won't support this choice unless it becomes completely impossible, 
I'm dead-set against the other options, no use even asking me about 
it unless you take my candidate out back and shoot him, he's 
'eliminated.' Then, maybe, I'll let you know what else I would 
support." This is not what people to, face-to-face, when they are 
trying to work out a good compromise! Rather, they might well start 
with everyone saying what their favorite is, that's a quite good 
first step. But then it gets more complicated, and people start 
deciding what compromises don't represent too much loss of value.

Approval voting theorists realized this, and proposed that Approval 
would work well as a series of polls in which voters gradually 
lowered their approval cutoff. Bucklin. It was done almost a century ago....

And it works fine with truncation. Truncation just means more 
likelihood of needing a runoff.

The only system that works with maximum efficiency, though, with 
truncation, is Asset Voting, which was invented even further back, 
about 120 years ago....