[EM] Median systems, branding, and activism strategy

[Jameson Quinn]

As voting reform activists, we must work together as much as possible. In
general, that means that raising awareness should start with teaching
people about approval. Still, if someone is unsatisfied with the
expressivity of approval, we should have a backup offering.

Personally, I think that median systems offer the best backup offering in
that sense. That doesn't mean I intend to undercut people promoting Score
or Condorcet; just that I think median systems offer a good compromise
between expressivity and low rewards to strategy. From my perspective,
Score is great for honest voters, but for strategic voters it has exactly
the same expressivity problems that approval does. And Condorcet is too
complex — not just to describe in the abstract, but to present the results
of even a single election in a clear, intuitive form.

But median systems have a problem. There are too many of them, and even
more names.

Off the top of my head, I can think of the following names:

   - Bucklin: A general class of median systems which are implemented via a
   descending threshold. Also used to describe various specific ranked or
   hybrid ranked/rated systems used during the progressive era. For instance,
   some use "Bucklin" to mean "median using full or truncated rankings, using
   the highest majority as a tiebreaker"; others mean the Grand Junction
   system of "median using 3+1 numbered rank/grades with skipping allowed and
   ties allowed at the third grade only; highest majority tiebreaker".
   - Majority Choice Approval (MCA): I've seen this applied to various
   3-rank median systems, but I think the canonical one is: "if there is a
   majority top-rank, then the highest such; otherwise, the candidate with the
   most non-bottom rankings."
   - Majority Judgment (MJ): as defined by Balinski and Laraki
   - Graduated Majority Judgment (GMJ): as defined by me.

There are also a number of possible descriptive "branding" terms for a
median / Bucklin system:

   - Instant Runoff Approval
   - Graded Instant Runoff
   - Descending Threshold Approval
   - Majority Threshold
   - Grade Voting
   - Majority-Based Grade Assignment

It seems to me that Median and Bucklin advocates should come to a consensus
on what specific system to promote, and what to call it. That doesn't mean
we should cease discussing the different systems in fora like these; just
that when promoting systems to the public, we should be on the same page.

Which system is best? I think the clear choices are MCA or GMJ, and I'd
personally favor GMJ. MCA is the simplest well-defined median system. GMJ
is good because:

   - Unlike the specific systems called "Bucklin", it has no vestige of
   ranked thinking, and thus requires no dishonest strategy.
   - It's more expressive than MCA.
   - Unlike MJ, GMJ can easily be expressed in terms of a Bucklin-like
   descending threshold, a single algebraic formula, or a graphing procedure.
   (As far as I know, MJ can only be expressed in one way). GMJ is also easier
   to "program" into a spreadsheet in my experience.
   - Unlike MJ, GMJ results can be succinctly and unambiguously expressed
   as a single number for each candidate.
   - Unlike MJ, the GMJ winner for a given honestly-voted utility profile
   tend to be stable as the number of evenly-spaced grading categories varies,
   even in moderately "pathological" examples (such as a single-peaked versus
   a two-peaked candidate).
   - However, the actual results will agree with other median systems in
   almost all realistic cases.

What should we call it? GMJ isn't a horrible name, but if people prefer to
use one of the above "branding" terms or something similar, I'd be open to
discussing it.

But I think it's important for us to join our voices in better harmony on
this. Abd, in particular: why do you continue to talk about "Bucklin" (ie,
the grand junction system) when there are better-designed,
more-clearly-defined Bucklin systems available today?

Jameson
ps. None of this message should be read as an attempt to abandon the common
effort to promote approval voting as a first step.
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