[EM] The worst about each system; Approval Preferential Voting (new name for an MCA-like system)

[Jameson Quinn]

What are the worst aspects of each major voting system?

-Plurality: Everything. It routinely requires dishonest strategy from a
large minority, or even a majority, of voters. Enough said.

-IRV: Voting can hurt you (nonmonotonicity). That means that small third
parties can survive, but once they threaten to pass 25%, you're back to the
problems of plurality. A great learning tool to understand this is
http://zesty.ca/voting/voteline/ , which lets you play with one-dimensional
scenarios and see how common nonmonotonicity is.

-Condorcet: complexity. While the basic idea of one-on-one matches is
simple, the details of tiebreakers are enough to make most voters' eyes
glaze over. Moreover, the need to individually rank numerous candidates is
more work than many are ready for, and the inevitable shortcuts they'll take
could harm results.

-Approval: divisiveness. By forcing all votes into an all-or-nothing mold,
it does not allow partial alliances between candidates. Consider the
probable results in the recent Hawaii election, where the majority democrats
split their votes between two candidates, leading to a Republican win. Lets
assume for a second that, because the two democrats were distinguished
mainly by individual not ideological factors, cross-party approvals are
insignificant; and that Democrats are pretty evenly split between the two
choices. Then, there are two possible results: either the less-cooperative
Democratic faction wins, or, if the "uncooperative arms race" gets
out-of-hand, the condorcet-loser Republican wins. In other words, the system
has incentives not to cooperate between two frontrunners running
approximately even in the polls, no matter how close they are, and these
incentives are unhealthy whether or not they get out-of-hand.

-Range: Strategy is too powerful. If one faction is more inclined to
honestly rank, seeing themselves as neutral judges, while another faction
has selfish reasons to strategically vote approval-style, the strategic
faction will dominate, even if they are a minority. Range is very robust
under strategy, if it's not factionally biased; but too vulnerable to
factionally biased strategy. You can rationalize until you're blue in the
face about how minority Range winners reflect a true societal preference;
but imagine how you'd feel if Bush/Gore/Nader had been decided for your
least-favorite against the will of the majority, due partly to a certain
complicity of some people who should should SHOULD have been on your side,
and partly to the obvious and dishonest machinations of the winning side,
and you'll see that this is still a real problem. (OK, I know that doesn't
take a lot of imagination for some people.)

-Bucklin: Bucklin (with equal rankings, of course) doesn't really have a
single biggest weakness. It is still technically just as vulnerable to
divisiveness as approval; but the trappings tend to hide this fact, and so
it shouldn't be as much of a problem in practice. Still, it doesn't have any
really strong points either. It's not the best honest system like Range; it
doesn't give a Condorcet guarantee; and it's more complex than Approval,
without really fixing Approval's greatest flaw.

So, allow me to restate my favored single-winner system, which, I think,
avoids all of the major pitfalls above. I call it Approval Preferential
Voting (the acronym, APV, is I believe only taken by American Preferential
Voting, an old name for Bucklin; and since this system could be considered a
Bucklin variant, I think that's just fine.)

Voters rank each candidate as preferred, approved, or unapproved. If any
candidates have a majority ranking them at-least-approved, then the one of
those which is most preferred wins outright. If not, then the two candidates
which are most preferred against all others (ie, the two Condorcet winners
based on these simple ballots, or the two most-preferred in case of a
Condorcet tie) proceed to a runoff.

(As a ballot mechanic, parties as well as candidates could be ranked, and
any candidate not specifically ranked would default to her party's ranking.)

This method is very simple. I think that the description above, without the
parentheses, is simple and intuitive; it uses only concrete terms. It is
also very easy for a voter to sort candidates into three rankings; I'd argue
that this is the easiest possible ballot task, easier in general than either
two or four ranking categories. (Two means too many compromises, and four
means too many fine distinctions.)

It's not quite the same as MCA or any other Bucklin system, since if there
are two approval majorities, the preferences, not the approvals, break the
tie. This makes APV more lesser-no-harm-like than Bucklin, encouraging
voters not to truncate.

Note that APV is still not a lesser-no-harm method. But it is in some sense
a lesser-minimum-harm method; extra approvals cannot hurt your candidates
chances for an outright win OR for a win if there's a runoff, the only way
they can hurt is the unlikely situation where they are pivotal in preventing
a runoff. I think that this minimizes the divisiveness I discussed with
Range above; for instance, in Hawaii, I'm sure the two democratic factions
would have had little trouble giving each other sufficient honest approval
for the strongest one to win outright.

Also, if there is no runoff, this method "violates Arrow's theorem". That
is, because it does not use a preferential ballot (and thus doesn't have
"unlimited domain" by Arrow's terms), it satisfies some Arrow-compatible
definitions of the Majority Criterion and Independence of Irrelevant
Alternatives Criterion (including clones). (APV as a whole does violates
both those criteria, but I'd argue that this would be unlikely in practice.)

This system as a whole is monotonic (unlike most two-round systems). Raising
a candidate X can only help X win if there are already one or more
candidates with majority first-round approval; it can only avoid a runoff if
thereby X wins; it cannot knock X out of the runoff; it cannot knock a
weaker opponent out of the runoff (this is the step where many two-round
systems fail); and it obviously helps in the runoff itself against any given
opponent.

It does technically fail the participation criterion; your vote could knock
your second-favorite candidate out of the runoff, thus causing your favorite
to lose to a worse candidate in the runoff. However, this is pretty
implausible, since, in order to knock out your second-favorite, your
favorite must demonstrate that he's stronger than her in a Condorcet sense,
which would strongly suggest that he's more likely to win a runoff than her.
(Even in the extremely-rare cases where this wasn't true, it would be almost
impossible to know that was so based on polling; so this failure is a very
implausible basis for any strategy in any event.)

The worst downside of this method that I can see is that, unlike the voters,
the leading candidates have little motivation (except reciprocation) to
express approval for other candidates. Negative ads could still be the order
of the day. But you can't solve everything.

I've advocated for the different aspects of APV before, but I haven't
presented (or named) it as a whole. I'd appreciate any comments. Honestly, I
think this should be the simple, practical reform we're all pushing for,
even as we argue and develop more-complex systems with better theoretical
properties.

JQ
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