[EM] Benefit of a doubt runoff challenge

[Forest Simmons]

Are the beatcycles that sometimes arise from expressed ballot preferences
... are these cycles more likely to arise from occasional inevitable
inconsistencies inherent in sincerely voted ballots? ... or from ballots
that reflect exaggerated preferences from attempts to improve the election
outcome over the one likely to result from honest, unexagerated ballots (?)

Should Condorcet methods be designed on the assumption that most ballot
cycles are sincere? .... or on the assumption that most are the result of
insincere ballots (?)

Some people think that the question is irrelevant ... that no matter the
answer, the  best result will be obtained by assuming the sincerity of the
voted ballots. Others think healthy skepticism is necessary for optimal
results. What do you think?

[Healthy! Who could be against healthy?]

Here's a compromise method intended to test these assumptions:

Suppose the benefit of a doubt camp agrees on a Condorcet Criterion
compliant method that we might call BOAD for benefit of a doubt.

All parties agree on the Condorcet Criterion.

So the following runoff proposal is only for use in absence of a ballot CW:

Let W be the winner of the BOAD method.
Let X be the uncovered candidate with the most winning votes against W, and
let Y be the candidate with the most winning votes against X.

[It is easy to show that ubverted CW's are never covered. In fact a buried
CW has a two step beatpath back to the "bus" under which the buriers buried
it ... via the burier faction favorite.]

I propose a sincere two stage runoff of the form (W v X) v (W v Y).

To be more specific, the first stage choice is between (W v X) and (W v Y).

The second stage will either be a choice between W and X, or a choice
between W and Y, depending on the outcome of the first stage.

Notice that W will be in the final stage no matter what. The first stage is
just to determine who will go up against W in the second stage.

This can be thought of as a way of giving a benefit of a doubt to the BOAD
supporters ... a gesture of good faith on the part of the voters that are
more skeptical about the innocence of the cycle that elections like this
are trying to resolve.

Is this an unfair handicap against the skeptical voters?

Suppose one of them claims that it gives an unfair advantage to the BOAD
supporters. Here's a possible line of questioning to the complainer:

Q. Do you believe in general that these preference ballot cycles are
insincere?
A. Yes.
Q. So do you believe that this one was caused by insincere voting, as
opposed to the lack of a Sincere CW?
A. Yes.
Q. Do you believe that the subverted Sincere CW must be an uncovered
candidate?
A.Yes
Q. So most certainly X or Y if not W itself is the subverted sincere CW?
A. Yes.
Q. Would the sincere Condorcet winner among X,Y, and W be the best possible
outcome of this X,Y,W runoff?
A. Yes.
Q. Suppose that X turned out to be the sincere CW among the three.  Who
would be the winner of the (W v X) matchup?
A. x
Q. Then who would win the second stage?
A. X
Q.  By the same reasoning wouldn't Y win if Y was the CW?
A. Yes.
Q. And if W turned out to be the CW?
A. Then I suppose W would win by the same logic..
Q. So the sincere CW wins no matter it be X, Y, or W. Can you imagine a
better outcome?
A. No
Q. Then where's your complaint?

So neither side of the controversy has a legitimate complaint of
disadvantage.

It might be a bit tedious, but that's the price you pay for perfection!

fws
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