[EM] SMA vs ACC (Reply to James' posting will be along in about a day or 2)

[MIKE OSSIPOFF]

SMA does better than ACC, because SMA deletes candidates who have majority 
defeats that aren't in a cycle of majority defeats.

For instance, in the 49,12,12,27 example. Let me replace Bush, Gore, & Nader 
with A, B, & C.

If the A voters truncate, they make a strategic circular tie in which 
B>A>C>B.

Sure, if the B voters know that it will be between A & B, then they will put 
their Approval cutoff above A, or maybe not rank A, even if they prefer A to 
C.

But that means they have to do strategy based on information that they have.

With SMA they don't need to know anything of the kind. With SMA the B voters 
can rank A, and can even have A above their Approval cutoff, and A still 
can't win. That remains true even if all the B voters prefer A to C, and 
even if they all rank A and have A above their Approval cutoff.

That's because, with SMA, the mere fact that A has a majority defeat, and 
someone (B) doesn't, is enough to ensure that A can't win. SMA deletes A 
from the rankings because A has a majority defeat that isn't in a cycle of 
majority defeats.

Of course that advantage is also true with wv. It's true likewise with NES, 
which share's wv's defensive strategy properties.

After A is deleted, SMA chooses the Approval winner. It could be written to 
first start over, deleting everyone who _now_ isn't in the Smith set, and 
that would now elect C, since only B & C remain, and C pairwise-beats B. But 
it's probably better as-is.

SMA doesn't bring the maximum possible improvement that NES does. With SMA, 
if someone considers the candidates to be in 2 sets such that the merit 
differences within the 2 sets are negligible compared to the merit 
difference between the sets, that person still has strategic incentive to 
equal-rank all the better-set candidates in 1st place together. That 
incentive isn't as strong, but it's still his best strategy.

The rule to repeatedly eliminate the candidate with fewest Approval votes, 
checking the Smiths set each time, and deleting anyone who isn't in the 
Smith set, means that there's an additional thing that the A voters would 
have to know in order to be sure that they could succeed at offensive 
truncation or order-reversal. But that offensive strategy could still work. 
If B has fewest Approval votes and gets deleted from the rankings, then A 
wins--only A & C then remain. Since A beats C, the Smith set then is {A}.

Again, with SMA, A can't win, by truncation, because he has a majority 
defeat and someone (B).
doesn't.

With offensive order-reversal by A, with SMA,  or ACC,  or the 
successive-eliminations ACC, A could win under some conditions, if the B 
voters rank A and have A above their Approval cutoff.

That's true of wv & NES too. Offensive order-reversal, if it occurs, might 
succeed unless it's countered, with any good method, any method that doesn't 
have worse problems.

Mike Ossipoff

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