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....
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