[EM] Burlington manifesto

[Jameson Quinn]

(Note: The email subject is mostly a joke; I doubt this email will be
coherent and enduring enough to be considered a manifesto. Also, if you
skip to the bottom, I'll talk a bit about how my recently-proposed 321
voting system is slightly better than I'd thought/said earlier.)

I wish to propose that the best way to evaluate a voting system's results
is by looking at how it would behave in a "chicken dilemma" as illustrated
by the Burlington election results. To review, that election had three
major candidates, who can be considered as a mostly one-dimensional
spectrum. From left to right, these were the Progressive, Kiss; the
Democrat, Montroll; and the Republican, Wright. From now on, I'll refer to
these three candidates as Left, Center, and Right, for clarity. As is
common in one-dimensional situations, Center was somewhere close to the
political median of the town, but slightly off-center in the direction of
Left, the side with the shorter tail. Thus, Center was the Condorcet winner
and Right was the Condorcet loser. But, due to center squeeze, Center was
the plurality loser; and due to a longer tail, Right was the plurality
winner.

I'd say that a good voting system should tend to elect Center in this case.
It should also tend to avoid the Condorcet loser Right. However, if despite
ideology Center is an inherently weak candidate, there should be some
possibility that Left will win.

Why is this a good way to evaluate voting systems results? It has three
primary advantages. It is:

   - *Discriminating*: real voting systems proposals vary widely in their
   potential results in this scenario.
   - *Meaningful*: I believe that this situation is relatively common. In
   fact, I'd argue that almost all real-world elections will either be easy
   (in that all reasonable systems give the same result), or their difficulty
   will hinge on some variant of the chicken dilemma. In particular, Condorcet
   cycles will be quite rare compared to Burlington-like scenarios.
   - *Objective*: (bear with me) A system's quality is determined by the
   answers to three simple questions. In order of importance: Does it elect
   Center with honest votes? Is there no rational strategy feedback loop which
   leads to the Condorcet loser Right winning the election? And finally, if
   Center's overall utility is actually the lowest, is there some plausible
   way the system could elect the pairwise winner of the extremes (Left, in
   this case)?

Calling Burlington analysis "objective" may seem like a strange claim,
especially compared to other possible ways of evaluating systems. Aren't
Bayesian Regret, or rigorously-defined criteria, more objective than some
ad-hoc analysis of a single scenario? And the answer is: yes, but...

Compared to Bayesian Regret: Yes, BR provides a single, objective number
for a system's honest performance. But over 10 years after BR analysis
started, we still haven't managed to agree on how to incorporate strategy.
Simply adding a fixed strategy percentage doesn't account for strategic
incentives. Yet any possible accounting for strategic incentives requires a
model of how voters will respond to those incentives, which, without data,
is an inherently non-objective judgment call. (And actually, real data is
more likely to come from Burlington-based experiments, like the ones I plan
on Mechanical Turk, than from implementing dozens of systems and seeing
their results in public elections, which would take decades if it's even
possible.)

Compared to criteria: Yes, criteria provide objective ways of comparing
voting systems. But the key point is that these are ways, plural. As our
interminable arguments here on the mailing list demonstrate, there's no
single objective way to combine different criteria into a single measure of
which system is better. Also, criteria tend to put too much focus on
implausible scenarios. If a Burlington-like scenario is (to pick a
plausible guess) three or four times as likely as a Condorcet cycle, we
should give it correspondingly more attention.

Note that I'm not saying that this is the only way to compare voting
systems. Simplicity of description, summability, and simplicity of voting
are still separate and worthy considerations. Acceptability to incumbents
may be a consideration in some cases too. All I'm saying is that Burlington
is the best test of result quality.

...

So how do different systems stack up on the Burlington test?

*Plurality: *Elects center with honesty? Fail; elects the Condorcet loser
instead. 0/10
Doesn't elect Condorcet loser, even with strategy? Fail. 0/5
Could elect pairwise winner of extremes if Center is inherently weak? If
the two extremes are seen as the frontrunners, this would be the strategic
result. Success; 5/5
Total quality 5/20

*Approval*: Elects center with honesty? Depends on what you mean by
"honest", but under most definitions, yes. 8/10.
Doesn't elect Condorcet loser, even with strategy? Fail; the archtypical
chicken dilemma. 0/5
Could elect pairwise winner of extremes if Center is inherently weak? Yes,
as long as the chicken dilemma didn't get in the way. 4/5
Total quality: 12/20 (But remember, this analysis doesn't account for
system simplicity, which is Approval's main advantage)

*Range*: Elects center with honesty? Yes; 10/10
Doesn't elect Condorcet loser, even with strategy? Fail; the archtypical
chicken dilemma, with extra-nasty feedback. -1/5 (negative score).
Could elect pairwise winner of extremes if Center is inherently weak? Yes,
as long as the chicken dilemma didn't get in the way. 4/5
Total quality: 13/20
*
Majority Judgment*: Elects center with honesty? Yes; 10/10
Doesn't elect Condorcet loser, even with strategy? Fail; the archtypical
chicken dilemma, though feedback is somewhat mitigated; 1/5
Could elect pairwise winner of extremes if Center is inherently weak? Yes,
as long as the chicken dilemma didn't get in the way. 5/5
Total quality: 16/20
*
Condorcet*: Elects center with honesty? Yes; 10/10
Doesn't elect Condorcet loser, even with strategy? Usually not, though it
is in theory possible for the L voters to shoot themselves in the foot by
strategically provoking a L>R>C>L cycle but end up electing R thereby.
SInce this is pretty implausible, I'll give Condorcet systems 5/5 here.
Could elect pairwise winner of extremes if Center is inherently weak? No
way. 0/5
Total quality: 15/20

*SODA*: Elects center with honesty? Yes; 10/10
Doesn't elect Condorcet loser, even with strategy? Almost certainly. Voters
probably won't explicitly truncate because they're too lazy and because the
risks outweigh the benefits. And candidates won't truncate because to do so
would decreases their negotiating power and their direct vote; and also
possibly because the optional
rule<http://wiki.electorama.com/wiki/SODA#Finish_resolving_the_.22Chicken_Dilemma.22>would
make it pointless to do so. 4/5
Could elect pairwise winner of extremes if Center is inherently weak? Yes;
in this case, either candidates or voters could decide that truncation was
worth it. 3/5
Total quality: 17/20

*IRV*: Elects center with honesty? No, but at least it doesn't elect the
Condorcet loser; 2/10
Doesn't elect Condorcet loser, even with strategy? Correct; LNH defuses the
chicken dilemma and allows C and L to cooperate to elect L. 5/5
Could elect pairwise winner of extremes if Center is inherently weak? Yes;
in fact, it goes too far in this direction. 4/5
Total quality: 11/20 (and remember, this analysis ignores IRV's
disadvantage of non-summability, but also its arguable advantage of better
acceptability to incumbents.)
*
321 voting*: (My recent proposal, inspired by David's IRV3/AV3. 3-level
rated ballots. Of the 3 candidates with the most ratings, take the 2
candidates with the most top-ratings, and then take the 1 pairwise winner
among those.)
Elects center with honesty? No, it's like IRV, but see below*; 5/10
Doesn't elect Condorcet loser, even with strategy? LNH guarantee for top
two ratings, like IRV. 5/5
Could elect pairwise winner of extremes if Center is inherently weak? Like
IRV. 4/5
Total quality: 14/20

*Why did I rank 321 voting as better than IRV for electing the centrist?
Because I realized that there is a plausible strategic way for this to
happen: the Right voters could put both Right and Center in top rank. This
is rational for them, because (just as with IRV, but unlike
Approval/Range/MJ) they have no hope of winning outright. In my previous
message, before realizing this, I had said that there was no rational
strategic  reason for anyone tow put two candidates at equal-top ranking in
321 voting.

So obviously, I could easily have been putting my finger on the scales
there, but I think that this at least gives a pretty reasonable measure of
voting system quality. Even if you don't agree with my precise weights and
scores, I think that looking at just this one Burlington (aka chicken
dilemma, aka Approval Bad Example, aka center squeeze...) scenario gives a
good view of the strengths and weaknesses of the systems.

Jameson
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