[EM] Quick & Clean Election Methods

[Forest Simmons]

What's the simplest one pass method that isn't a pushover for manipulators?

Here are two possibilities that seem promising to me:

Method1:

Lacking an undefeated candidate ...elect the candidate with the strongest
pairwise victory over the candidate with the greatest Bottom count.

[The candidate with the greatest bottom count may have gotten there by the
sincere CW's truncation of him ... or by Chicken defection of the candidate
that put her there.]
candidate.

Method 2 ...Lacking an undefeated candidate ...elect the candidate with the
strongest defeat over the minMaxPS candidate.

First scenario:

48 C
28 A>B
24 B

Candidate A is both the Max Bottom and the minMaxPS candidate ... and A's
only enemy is C ... who is therefore the winner according to both methods.

Now our second scenario:

a A>B(Sincere A>C)
b B>C
c C

Method1:
Candidate A, which has the greatest Bottom count, is defeated only by C,
the sincere CW.

Method2:
MaxPS(C) is b+c=n-a.
MaxPS(B) = a+b=n-c
MaxPS(A)=a<min(b+c, a+b)
So A is the minMaxPS candidate, as in the previous method, so the same
candidate C is elected.

Both methods give the same "correct" outcome, but (by my taste) the second
method is cleaner, and more portable (e.g. for use in tournaments).

On the other hand, method1 will be easier for voters to grok.

One way to make both methods Landau efficient is to take the winner W and
back it up 3k more steps ( giving covering-wv defeats priority over plain
old wv defeat strength) ... which in this example would just confirm C, but
in another case with many candidates, this "after burner" might require k>1
in order to "converge".

Don't mention Method2 or anything about Smith, Landau, Chicken, burial, etc
to anybody not already interested in that stuff ... unless you want to
destroy our prospects for success.

Keep to the simple procedure with simple examples ... when someone is ready
for more, they will start to ask questions.

Thanks!

-Forest
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