[EM] Better NEO & MMPO rules. Smith//NEO & Smith//MMPO properties.

[Michael Ossipoff]

Henceforth, when I say "NEO" I refer to Smith//NEO.

To refer to NEO by itself, I'll say "Plain NEO".

MMPO tie rule:

When 2 or more candidates have the same max pairwise opposition, then
compare their next-largest pairwise opposition.

If there's still a tie, then keep applying the above rule until there isn't.

(end of MMPO tie rule)

Complete Plain NEO rules:

The winner is the candidate who wins at the most Approval Nash equilibria.

If there's a tie, then re-apply the above rule with only the tied
candidates in the election.

If, at any stage, the tie can't be reduced, of there are no Aporoval Nash
equilibria, then the winner is the candidate with highest top-count.

(end of Plain NEO rules )

Smith//MMPO:

Apply MMPO to the Smith-set, having eliminated the other candidates.

Smith//NEO:

Apply Plain NEO to the Smith-set, having eliminated the other candidates.

(end of 2 definitions)

As I said, " NEO" means Smith//NEO.

NEO and Smith//MMPO both have no chicken-dilemma, and they both have
MAM-like strategy.

MAM-like strategy:

Truncation can't defeat a CWs (sincere CW).

Defensive truncation (plumping) by the CWs's voters thwarts & penalizes
burial.

(end of dfn)

A difference between the properties of NEO and Smith//MMPO:

In the Chicken-Dilemma example, Smith//MMPO elects A, and NEO elects C.

I'd previously said that NEO elects A, but that was incorrect.

In the Chicken-Dilemma example each of the 3 candidates has an Approval
Nash equilibrium that elects hir.

So the highest top-count wins. C wins.

People at EM prefer to not elect A, though I find nothing unqualified about
the most top-ranked candidate who doesn't have a majority defeat.

Smith//MMPO elects A. NEO elects C.

About burial, it won't often be a problem to you, even if the CWs's voters
don't plump, unless hir voters rank the buriers' candidate over someone you
prefer to the buriers' candidate.

Michael Ossipoff
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