[EM] Method For Electing the Sincere CW

[Forest Simmons]

I believe that far more often than not, in public elections there is a
sincere CW ... including almost all cases where the ballot Smith set has
three or more members. Elsewhere I have explained in detail why I believe
that, as well as why I believe  Impartial Culture ballot distribution
models are largely to blame for misleading experts to believe otherwise
despite complete lack of evidence supporting their assumptions ... evidence
that would require (nonexistent) support from sincere data from actual
elections in order to be taken seriously.

If election methods were adopted that included a final pairwise choice with
a fresh ballot option, for example, we could actually generate some sincere
data where none currently exists.

In the mean time I continue to believe the results of realistic low
dimensional models ... namely that unless you bend over backwards to
cleverly contrive counterexamples, spatial models will almost never yield
voter distributions that result in Smith sets with more than one member:
but with hardly any ingenuity a sincere CW can be buried by insincere
voting.

Fortunately, when that kind of subversion is done unilaterally, the
resulting Smith set will have only three members, one of which is the
sincere CW.

In this case, the only one with any appreciable statistical probability,
there is a way to recover the sincere CW.

Suppose the ballot cycle is XYZX, and the weakest link in the cycle is the
defeat of X by Z.  Then all classical Condorcet methods, whether MinMax,
Ranked Pairs, Beatpath CSSD, or River ... all of these break the cycle at
this weakest link and rectify the Smith set finish order as X>Y>Z, without
looping back to X.  In essence the Z>X defeat is considered an innocent
error in voter judgment that must be overridden (by reversal) to increase
the likelihood of a "true" ordering of the 3  Smith candidates, from best
to worst.

Our approach is less dogmatic: we simply offer a type of runoff that will
naturally result in a win by the Sincere CW when there is one, and
otherwise seamlessly make the same choice as Classical Condorcet (that is
in the highly unlikely case that the ballot cycle is sincere).

The runoff ballots look like
X vs (Y vsZ)
where X is the Classical Condorcet winner, and Y and Z are the other two
members of Smith.

If it turns out that the Classical Condorcet Winner X is also the Sincere
CW, then a majority of the runoff voters will prefer X to the projected
winner of a Y vs Z match ... so more ballots than not will be marked in
favor of X as opposed to going on to address the decision (Y vs Z).

What if the Sincere CW is Y?

Then the projected winner (in the XYZX cycle for example, or from accurate
polls)) of the Y vs Z match is Y, and since Y is also the Sincere CW, most
voters (by definition of SIncereCW)) prefer the projected winner (Y) of the
Y vs Z match to any other candidate including X. Therefore most voters will
vote to eliminate X. which makes the final match between Y and Z ... which
Y will win since it is the Sincere CW, and no voter can benefit from
insincere voting in a final binary choice.

What if the Sincere CW is Z?

Does Z then become the projected winner of the Y vs Z matchup?

That depends on whether or not the voters know that Z is the Sincere CW.

The X faction voters know this because that knowledge was the knowledge
that empowered them to bury Z under Y in order to create the YZXY ballot
cycle.

By the time they get these runoff ballots, the Z faction voters will
realize that their candidate got thrown under the bus by the X voters.

And also by this time the Y faction will know that insincere support they
got from the X faction will not carry over to a final match between Y and
Z, because most X voters sincerely prefer Z over Y ... and at this late
stage of a final contest between Y and Z, the X faction gets zero benefit
from voting Y over Z.

Therefore, the rational projection is that Z would win a final contest
between Y and Z.

But voters sincerely prefer Z over X, so most voter prefer X to be
eliminated, in favor of the projected winner (Z) of the choice between Y
and Z.

In summary, if there is a Sincere CW, it will win in this kind of runoff.

What about the one in a million chance that there is no Sincere CW or (what
is more likely) deliberate media obfuscation successfully convinces the
voters that Sanders is not the Sincere CW even when all of the most
accurate opinion polls show that he is ... and by a substantial margin!

In that case the voters are apt to take as the most reliable projected
winner of the Y vs Z contest the (insincere) ballot result of Y>Z in the
XYZX ballot cycle.

So the question becomes whether or not the voters prefer X to Y.

According to the ballot cycle they do. If so, X will be elected. ... which
is why we gave the Classical Condorcet winner X, pride of place in the
three candidate runoff ballot.

In summary, if a cycle is sincere or so shrouded in lies the voters are
laboring under more misinformation than information, then the Classical
Condorcet method winner will win.

Otherwise, the Sincere CW does exist and will win!

-fws
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