[EM] Bucklin/IRV hybrid? Motivated by MSV strategy

[Jameson Quinn]

I've been thinking about strategic rules of thumb in majority score.
Basically, the rule I've come up with is:

-Support (top-rate) candidates who are best or comparable to the best; say,
above 0.9 on an honest normalized score ballot.
-Reject (bottom-grade) candidates if they're "worse than the average
serious candidate". One way to make this precise might be: if you'd prefer
a random lottery where first a number n is picked uniformly among {2,3,5},
then a random lottery is performed among the top n candidates by honest
plurality. Obviously, for an actual rule of thumb, the imprecise wording is
better, but I'm just including the precision to help clarify what I mean.
-Assist candidates if they are the best or comparable to the best among
serious candidates you are relatively sure will not be eliminated by
majority rejection. So, first discount any candidates you think have over
1/3 chance of scoring under 50 or of having over 50% rejection; then
re-normalize your honest score ballot for the rest; then assist any
candidates who are above 0.9 and whom you're not already supporting.
-Accept the rest.

So, basically, simplified further, this rule suggests assisting anyone who
you'd otherwise accept, if you think that the candidates you support will
all be eliminated. When you put it like that, it looks like a job for a DSV
method.

So, here's the voting system that results; essentially, majority score
declared strategy voting (MS DSV):


   - Voters rate candidates support, accept, or reject. Default is accept.
   - Eliminate any candidates with over 50% reject, or with support at or
   below 25%, unless this would eliminate all candidates.
   - For all ballots which support no non-eliminated candidates, change
   "accept" to "support".
   - Winner is remaining candidate with most support.

This is a system that has aspects of Bucklin (majority threshold for
eliminations) and of IRV (eliminate and then retally votes that lost their
top-voted candidates).

Is this the best of both worlds between Bucklin and IRV? Not exactly.

   - Note that this system, unlike majority score, is not easily summable.
   - Unlike IRV, this is not later-no-harm, although I suspect you could
   handcraft a "later-no-harm unless..." weakened criterion it would pass.
   (Moving X from reject to accept on a ballot which supports Y cannot cause Y
   to lose unless Y was majority-rejected???)

However, this does have some good properties.

   - FBC
   - Majority, mutual majority (note that MSV does not have MM, IRV does)
   - Voted majority Condorcet winner? (Neither MSV nor IRV have this
   property! I am not 100% sure this system has this property, but I'm pretty
   sure it does at least for 3-candidate elections, and I suspect that it
   extends to n candidates.)
   - Voted majority Condercet loser??? (same qualifications, but I'm less
   sure)
   - Voted Condorcet loser (without qualifying by "majority"!) for
   3-candidate elections in which all voters use full ballot range (ie, at
   least one candidate each in top and bottom)
   - Handles CD as well as MSV
   - Handles center squeeze better than either MSV or IRV; this is pretty
   well encapsulated by the VMCW property above.

So, I'm not (yet) proposing this as a replacement for MSV. It's simpler and
better from a voter-facing (ballot) perspective, but more complicated from
an explanation and counting perspective. In particular, I think the lack of
summability is a problem.

But still, it's a top-shelf system from a theoretical angle, IMO. It
doesn't have SODA's "strong delegated equilibrium for a delegatable weakly
semi-honest majority Condorcet winner" property, which helps with the
chicken dilemma; but really all that property is saying is that SODA
removes the possibility for CD offensive strategy by forcing the CD threat
candidate (what we've conventionally called candidate C) to declare a
strict preference between the subfactions (conventionally, A and B), and if
lazy voters will then delegate to C then offensive strategy won't work.
Aside from that, which is, now that I put it that way, somewhat of a cheap
trick, I think MSDSV is the best system I know of for dealing with both
center squeeze and CD well.

....

Here's my "ideal characteristics" for a political single-winner election
system, more or less in descending order of importance:

   1. FBC
   2. Handles center squeeze (ie, some form of weakened Condorcet guarantee
   that's compatible with FBC)
   3. Relatively simple to explain
   4. Minimal strategic burden
   5. Summable (ideally O(N), no worse than O(N²) in practice, though I
   might accept some special pleading for the use of prior polling to reduce
   to O(N²).)
   6. Handles CD, or at least, CD offensive strategies don't in practice
   mess up the center squeeze properties.
   7. Some arguable track record

SODA does well on 1,2,4, 5, and 6, and horribly on 3 and 7. MSV does well
on 1,2,4, and 5, is OK on 3 and 4, and bad on 6. Approval does well on
1,3,4, and 6, is OK on 2, and bad on 4 and 5. MSDSV does well on 1,2,4,5,
and 6, and is bad on 3 and 7. Various Condorcet-like methods (MAM, ICT,
sorted approval methods) are good on 2, 4, and 6, but none as good as the
aforementioned on 1, and all fail 3 and 7. MJ and other Bucklin methods
are, as far as I can tell, dominated by MSV on all but 7. And other methods
just don't compete. So, MSDSV is on the pareto frontier of the above
criteria, which makes it a top-shelf method.
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