[EM] Direct Democratic Defeat Elimination

[Forest Simmons]

In this method no candidate X can be eliminated without a direct democratic
defeat from some competing candidate Y.

Candidate X suffers a Direct Democratic Defeat from candidate Y iff a
majority of the voters expressing a preference between them prefers Y over
X.

The best known eimination method being proposed today fails to respect this
principle ... reserving Direct Democratic Defeat Elimination exclusively
for the last candidate to be eliminated.

Beyond the basic Direct Democratic Defeat Elimination (DDDE) requirement we
need to invoken other criteria to establish the priority of elimination.

Naturally we should eliminate the democratically weaker candidates before
the democratically stronger candidates.

One measure of democratic weakness is lack of democratic support in direct
democratic comparison with other candidates.

The democratic support for Y over X is the number of ballots that rank Y
over X.

We need a measure of the nominal over-all support of Y over the other
competing candidates ... not just one of them.

A natural candidate for such a measure is the Max democratic support for Y
against the competing candidates.

If that max support is small, then Y is generally democratically weak
compared to candidates with larger max support.

Beyond that this particular measure of weakness is uniqely helpful in
preventing unscrupulous "sophisticated" voters from gaming the system ...
and our method uses it in a way that makes the most insidious of those
manipulations backfire on the manipulators.

With that introduction, here's my most succinct formulation of Direct
Democratic Defeat Elimination:

If there is a candidate that suffers no direct democratic defeat from any
competing candidate, elect that candidate.

Otherwise ...

Every remaining candidate suffers a direct democratic defeat ... so ...

While every remaining candidate suffers a direct democratic defeat ...
peatedly eliminate the democratically weakest remaining candidates (one by
one, weakest first) along with any candidates that are too weak to defeat
them.
EndWhile

You may wonder how there could be any candidate too weak to democratically
defeat the nominally weakest candidate.

It is possible because the general weakness of the nominally weakest
candidate is just that ... a general weakness that may not correctly
predict which candidate will prevail in every single Direct Democratic
comparison.

[But is much more reliable than IRV's general weakness measure (number of
top votes) ... and unlike IRV ... we only eliminate with direct democratic
corroboration.]

For example, it can happen that the candidate Y whose max support is
minimal, defeats some other candidate X that is democratically defeated by
every other candidate, yet has a max support against Z larger than Y's max
support against Z.

So this "along with ..." clause serves to keep weak or "dark horse"
candidates from escaping elimination... but more importantly to back-fire
on the manipulators if there are any.

The lay reader may want to skip over the next quite technical paragraph
that shows precisely how the democratic structure of the elimination of
"weakest along with those drmocratically defeated by wwakest" precipitates
the back-fire against unscrupulous manipulators.

[For example, if manipulating supporters of X down-ranked (what would have
been) a sincere ballot set wiinner Y to create a rock-scissor-paper cycle
in which the weakest democratic support was Y's against X ...that would
backfire on the insincere down rankers... because Y would be the weakest
support candidate in the cycle ... and would bring down X with it when
eliminated.]

That's all for now ...

Any takers?

If not, what part needs beefing up ... perhaps from being unclear or
unconvincing?

-Forest
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