[EM] Quick and Dirty Burial Resistant Condorcet

[Forest Simmons]

I apologize for the defiant tone at the end of the previous message ... I
must have gotten carried away with the "Dirty Dozen"' theme.

But isn't it frustrating to you when people use the 2nd law of
thermodynamics (or Arrow and Gibbard-Satterthwaite in the EM context) to
justify their stubborn resistance to any kind of engineering progress?

In the previous message Q&D Burial Resistant Condorcet was formulate in the
typical "stitched together" form ... "Elect the CW if there is one, Else
..."

In this message I would like to formulate a seamless version:

Let X be the Smith candidate who on the fewest ballots is ranked ahead of
any other Smith candidate. On each ballot approve all candidates down to X,
but include X only when no Smith candidate is ranked ahead of X.

Elect the candidate approved on the most ballots.

This method can be described as electing the approval winner when the
approval cutoff is (at the rank of) the weakest of the Smith candidates,
which itself is approved on (and only on) those ballots which do not
approve any other Smith candidate.

In other words, the approval cutoff is inclusive only when necessary to
ensure approval of at least one member of Smith.

Since a Smith member is approved on every ballot, the method satisfies the
Condorcet Criterion, i.e. it elects the only Smith member when Smith is a
singleton.

How does that grab you?

-FWS

El dom., 2 de ene. de 2022 7:30 p. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:

> Is there any burial resistant Condorcet method simpler than this?
>
> The basic pre-requisite is to understand that whenever there is no
> Condorcet Winner there will be a pairwise cycle, called a "top-cycle" of
> candidates whose members are not defeated by any candidates outside of the
> cycle, just as a Condorcet Winner is a candidate undefeated by any other
> candidate.
>
> Here's the Q&D burial resistant method:
>
> Lacking a Condorcet Winner elect the candidate X having the greatest
> pairwise victory over the top-cycle member Y that has the smallest ratio of
> first to last place votes within the top cycle.
>
> Two examples illustrate the method:
>
> Example 1.
>
> 49 C
> 26 A>B
> 25 B (sincere B>A)
>
> The top cycle is ABCA
>
> Candidate A has the smallest ratio 26/74 of first to last place votes.
>
> Candidate C is the only candidate with a pairwise victory over it, so C
> wins.
>
> Notice how our rule does not reward B for insincerely lowering A to
> (equal) last?
>
> Example 2.
>
> 45 A>B (sincere A>C)
> 35 B>C
> 25 C>A
>
> Candidate C has the smallest ratio  25/45 of first to last.
>
> Candidate B wins as the only candidate with a pairwise victory over C. So
> A's burial of C backfires.
>
> Typically, the faction A that buries or truncates a Condorcet Winner C to
> create a top-cycle cannot by so doing become a pairwise victor over the
> buried Condorcet Winner ... but must (in order to create a cycle) help some
> other candidate B defeat C by insincerely voting B>C.
>
> Our Quick and Dirty method insures that if the sincere CW's rightful
> victory is subverted, it goes to B, not to A.
>
> Is this method quick enough and dirty enough for the FairVote IRV
> promoters?
>
> What objections/criticisms might they have?
>
> Do they have any counter proposal that rivals this one in any way?
>
> If so, let them educate us ... we'll gladly join them if they can show us
> a better way!
>
> If not, then they should join us to educate the politicians, public, and
> last but not least, the academics still stuck in the pre-EM era!
>
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