[EM] Quick and Dirty Burial Resistant Condorcet

[Forest Simmons]

Good idea!

Although it seems to me that the highest approval candidate would have to
pairwise beat or tie the approval cutoff candidate X pairwise (which would
be impossible for a non-Smith candidate to do) ...I could be wrong ... and
in any case redundancy reinforces communication and understanding.

El lun., 3 de ene. de 2022 3:04 p. m., Ted Stern <dodecatheon at gmail.com>
escribió:

> 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!
>>>
>> ----
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>> info
>>
>
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