[EM] Hay guys, look at this...

[Forest Simmons]

I agree with Kristofer about the cliff analogy  and take it a little
further ... are we going to say that because it will be needed only rarely
we can settle for any old simple alternative?

Even if there were no significantly better equally simple solution ... it
would still be shameful engineering practice:

"Boss I cannot give the green light to the Challenger until we fix that
O-Ring problem."

"But we have a deadline to keep ... and there is only a 0.4 percent chance
the thing will cause a problem ... so far, so good ... just cross your
fingers and sign here."

Here's a simple, acceptable method that beats many elaborate Condorcet
proposals including Copeland,Baldwin, Black, Nanson, MinMax, and many
others. If it turned out that twenty percent of Condorcrt election had
cycles in a certain odd ball electorate, it would still be a credible,
upstanding choice.

It has a natural segue from the simplest definition of a Condorcet Winner
into what to do if there is no CW:

A Condorcet Winner C is a candidate that is unbeaten pairwise. This means
that for any other candidate X, the number of ballots on which C outranks X
is greater than the number of ballots on which X outranks C.

In other words, C has a positive margin of support compared to any other
candidate X.

If there is no candidate with a positive margin of support compared to
every other candidate, then elect the candidate with the single greatest
margin of support relative to any other candidate.

Example:

48 C
28 A>B
24 B

A's margin of support relative to B is
28-24=4

B's margin over C is 28+24 vs 48 or 52-48 which equals 4, the same as A's
margin over B.

C's margin over A is 48-28=20, which is greater than either of the other
positive margins, so the Plurality winner C wins in this example.

Example2.

40 A>B
35 B>C
25 C

A's margin over B is 40-35=5
B's margin over C is 40+35-25=50
C's margin over A is 25+35-40=20

Candidate B is the max defeat margin winner with a max margin of 50.

So this time it would have been an embarrassment to elect  the Plurality
winner A ... whose max support margin was a mere 5 votes, the least of all.

So can we agree to elect the candidate with the max fefest margin when
there is no candidate with all positive margins?

-Forest

On Sat, Feb 18, 2023, 3:47 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> On 2/18/23 10:42, Colin Champion wrote:
>
> >     But then I don't favour Kristofer's proposal either. My evaluation
> > suggests that burial is a particular threat for Condorcet methods, and
> > that in its presence their accuracies are: minimax 64%, condorcet+fptp
> > 59%, copeland,fptp 48%. [Usual disclaimers apply.]
>
> That's fair; I was simply trying to find a minimal change to the method
> that would at least grant Smith or something like it.
>
> Really, what I'm concerned about is that there's such a, for lack of a
> better term, steep cliff from the Condorcet domain down to the Plurality
> domain. So everything's nice as long as you play on top of the mountain,
> but if you misstep (i.e. produce a cycle), then you don't gradually
> degrade, you fall directly into plain old Plurality, with all of its
> vote splitting problems. The discontinuity seems like something that's
> just asking to be exploited.
>
> Do you know of any alternate "bang for the buck" methods that would be
> simple enough to be accepted?
>
> -km
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> info
>
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