MSDSV

Here's the email which introduced the idea of majority score declared strategy voting (MSDSV):

Motivation

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.

Rules

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 voting (majority threshold for eliminations) and of IRV (eliminate and then re-tally votes that lost their top-voted candidates).

Properties

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 Condorcet 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 (i.e., 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.

General discussion, comparison to other voting systems

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

FBC
Handles center squeeze (i.e., some form of weakened Condorcet guarantee that's compatible with FBC)
Relatively simple to explain
Minimal strategic burden
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).)
Handles CD, or at least, CD offensive strategies don't in practice mess up the center squeeze properties.
Some arguable track record

Comparison:

SODA does well on 1, 2, 4, 5, and 6, and horribly on 3 and 7.
MSV does well on 1, 2, 5, and 6, is OK on 3 and 4, and bad on 7.
Approval does well on 1, 3, 5, and 7, is OK on 2, and bad on 4 and 6.
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.