[EM] Quick and Dirty Burial Resistant Condorcet

[Ted Stern]

Hi Forest,

This sounds like an interesting method to me!

However, I would change the winning criteria to "Elect the most approved
member of the Smith Set".

On Mon, Jan 3, 2022 at 11:06 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> 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!
>>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220103/f0408d21/attachment.html>