[EM] (3) Kristofer and Steve on MJ &IRVa vs. MAM

[Kristofer Munsterhjelm]

On 06/11/2016 06:04 PM, steve bosworth wrote:
> To Kristofer,
> 
> Thank you for your earlier than expected response and especially for
> putting me onto Majority Judgment (MJ).
> 
> MJ seems to be even a better system for electing a single-winner than my
> IRVa.  In different ways, each allows each citizen to express the
> intensity with which she supports or opposes each candidate and
> guarantees the election of a winner who is supported by an absolute
> majority.  However, in contrast to IRVa, MJ enables each citizen within
> the MJ winner’s majority to be a part of that majority purely as a
> result of her own judgments.  She would never have to rely on her IRVa
> first choice but eliminated candidate sequentially to transfer her
> ‘default vote’ to the remaining candidate he currently sees as the one
> mostly likely to represent him and her most faithfully, i.e. until a
> majority candidate is discovered.  Also, while both IRVa and MJ would
> seems to offer no practical opportunity for anyone to manipulate an
> election with many voters and candidates, theoretically MJ would seems
> to be even more resistant to strategic voting.
> 
> Do you agree?  Is MJ currently your own preferred method for electing a
> single-winner?
> 
> Your answers to these questions may help further to clarify any later
> discussion we may have both about IRVa and MAM.

Before I answer that point, let me pose a question to you. Do you agree
that MAM elects F given the ballot set you presented in your previous post?

With that done, let's continue.

There are different scenarios and my best methods depend on the scenario.

Scenario 1 is pure utilitarian voting, which I consider to be a very
unlikely setting for practical political elections. Here a voter knows
how much more benefit candidate A will give than candidate B, and
everybody has a common numerical (ratio) scale for evaluating the
candidates. An example of such a scenario would be a computer AI using
many different subprograms to determine which strategy is the best based
on what it currently knows; or, in a voting situation, all the voters
being perfect capitalists for whom log(dollars earned) is a good measure
of utility. Here Range is best, although if strategy is involved, I
would prefer something closer to DSV like SARVO-range to take that into
account. There may be even better ones that depend on making assumptions
about the statistical distribution the voters' votes come from, but I
haven't investigated that yet.

In scenario 2, the voters grade the candidates, but not on a curve. When
the voters grade the candidates (rank them, but are able to skip ranks),
and their grading of the candidates that do stand is independent of
which candidates stand, then we have this scenario, and MJ is best.
Most noticeably, it circumvents Arrow's impossibility theorem in this
situation. "Grading is independent of which candidates stand" means that
voter X will rank candidates A and B at Excellent and Good whether or
not candidate C is in the running. That is, even if candidate C is
completely awful, it won't affect X's decision of what grade to give A
and B. This property may hold or not hold - it depends on the voters'
behavior. Based on their exit poll data in France, Balinski and Laraki
argue that this property is preserved for real elections.
However, it's not hard to imagine a setting where pretty much every
candidate is good, so the voters spread out their ranks to make it
easier to distinguish them. Thus, if someone awful were to join, the
voters would compress their rankings of the good candidates so as to
make the scale large enough to show the system just how awful the awful
candidate is. E.g.
without the awful candidate:
	- Agreeable Capitalist is Excellent
	- Agreeable Socialist is Good
And with:
	- Agreeable Capitalist and Socialist are both Excellent
	- Horrible Authoritarian is Poor

Scenario 3 involves grading on a curve or ranking without skipping. I
think that Condorcet is best in that situation. Since introducing a new
candidate will affect all ranks, every method is subject to Arrow's
impossibility theorem and no method can pass IIA. However, we might get
close.I prefer a method that is:
	- Condorcet (a candidate who wins every hypothetical runoff wins outright)
	- Smith/Schwartz and similar extensions (Condorcet for sets)
	- Independence from clones
	- Monotonicity and reversal symmetry (to limit how bizarrely the method
acts given honest votes).
	- Tougher independence criteria if possible (IPDA, ISDA).

Note that if there is a Condorcet winner, then the method obeys IIA. You
can remove any candidate (except the winner, obviously) and the outcome
will stay the same.

As long as the Condorcet method is "advanced" (pretty much cloneproof,
Smith and monotone), I don't have a problem switching from one to the
other. Different methods pick winners according to different objectives,
but they don't matter as much in my opinion. For instance, Schulze
passes a minimax objection property and I think Schulze argued that it
would make fewer voters unhappy on average than would not passing that
criterion. On the other hand, MAM is simple, passes another resistance
to complaints criterion, and passes local IIA.
Perhaps River would be my "ultimate" Condorcet method (though it doesn't
provide a full ranking) but I'm not sure. It is simpler than MAM, even
more Smith-like, and passes independence from Pareto-dominated
alternatives, which makes it very hard to dump loser candidates into the
system and have them affect the outcome.

---

If I recall correctly, Range advocates say that either we're close
enough to scenario 1 that Range is still the best, or that Range
degrades gracefully when ew move into scenarios 2 and 3, so we can still
use it. They would point at the simplicity and the real world use of
Range (e.g. star ratings on web sites). On the other hand, a problem
with Range is that there's an incentive to rate either maximum or
minimum, and again IIRC, so many users ended up doing so that YouTube
switched from star ratings to thumbs up/down rating.

If we are in scenario 2 or close to it, then MJ is a good choice. We
might also be between scenarios 2 and 3. If we are, we could possibly
still argue for MJ in this way: since it's so resistant to strategy and
to noise in general, if a few voters alter their grade scale based on
the candidates, that's no problem as long as most voters act like in
scenario 2. So if that argument is correct, we have to go pretty far
towards scenario 3 before MJ is no longer a good method.

However, questions of which scenario we're in would ultimately have to
be answered by actual data about real elections. Dynamics also
complicate the picture: if a system provides relatively good results
under honesty and doesn't reward strategy too much, the voters might
become more honest over time simply because they don't get the payoff
for strategy. But it'd have to be found out by trying the method;
mathematics can't answer that. If voters were completely Homo Economicus
rational, they wouldn't bother voting in the first place, after all.

I see IRV to pretty clearly be a scenario 3 method. No surprise then
that I value Condorcet methods above it. For scenario 2, I value MJ over
it. For one, IRV fails IIA even where MJ passes it. I would also rather
have MJ than IRV in a scenario 3 setting, because I consider Bucklin
better than IRV, and scenario-3 MJ is basically Bucklin.

Finally, you can hedge your bets by using two methods and then holding a
runoff between the two. E.g. Range and MJ, or MJ and Condorcet. The
voters would use the most expressive ballot: rating candidates in the
former case, or assigning grades/valuations in the latter. But Balinski
and Laraki also suggest that the context of the ballot alters the
voters' behavior: a rating ballot may encourage the voters to normalize
whereas a grade ballot might not. If so, you'd have to give half the
population rating ballots and half grade ballots (at random), and that's
a little too complex.

---

I hope the above explains my thoughts about MJ and Condorcet well
enough, and that it'll help you reply to the rest of my previous post.

It does seem I didn't explain the problem with inferring preference
strength well enough, however. What I meant was, suppose voters have
internal preference intensities or utilities so that 100% is a saint and
0% is the devil. Then a ranked ballot can't distinguish between:

A (99%) > B (98%) > C (97%) > D (3%)
and
A (99%) > B (50%) > C (48%) > D (3%)

(Suppose for the sake of the argument that the voter wants to make all
his preferences clear, so he doesn't equal rank. After all, 99% *is*
better than 98%, and the voter might want to make that clear to the method.)

My argument is that trying to say anything about the utilities of the
candidates (the preference strength or intensity) based only on the
preference is flawed, because it tries to extract more information from
a ballot than that ballot actually does contain. The only thing that
ranking A ahead of B tells you is that the voter prefers A to B. That
holds whether A is in 99th place and B is in 100th, or A is in first
place and B is in second. Thus, the only thing the method can infer from
a candidate being ranked first is that the voter prefers that candidate
to everybody else, but there's not a substantial difference between
voter X ranking A first and B second, and voter X ranking A second and B
third, except that in the latter case, whoever he put first is someone
he prefers to both A and B.

Applying that argument to IRV: IRV focuses excessively on the first
preference by only taking first preferences into account when deciding
who to eliminate, and that doing so tries to extract more information
than the ballot supports. It is similar to assuming that A>B>B>C>D is
much more likely to be a

A (99%) > B (50%) > C(48%) > D(3%)

ballot than a

A (99%) > B (98%) > C(48%) > D(3%)

one. But we can't say that from rankings alone.

Actually, it's stronger than that. Because IRV uses the same logic after
eliminating each candidate, it's liable to misinterpret a

A (99%) > B (50%) > C(48%) > D(3%)

ballot as well, because if A gets eliminated, then B and C are very
close in utility even though there's no way IRV can know that. To be
even more simple about it, IRV's logic assumes that there are a few good
candidates and a whole lot of fringe ones. When the number of good
candidates increases, IRV runs into trouble, and the Burlington election
is a very good example of just that happening.

You might argue that the same applies to Condorcet, but in reverse.
Because there's no utility (scenario-1) information in a ranked ballot,
Condorcet can't distinguish a 99-98-48-3 ballot from a 99-50-48-3 ballot
either. That's true, but Condorcet doesn't try to infer anything about
the ranked ballot beyond what I said it can tell the method: if voter X
ranks A ahead of B, all that means is that he prefers A to B. All you
can tell from a ranking is relative preference, and that's all that the
Condorcet criterion needs.