[EM] Peak Approval Sorted Margins

[Forest Simmons]

El mar., 10 de may. de 2022 11:09 a. m., Ted Stern <dodecatheon at gmail.com>
escribió:

> Comments below:
>
> On Tue, May 10, 2022 at 10:41 AM Forest Simmons <
> forest.simmons21 at gmail.com> wrote:
>
>> This is an aggregate method that can be taken apart and reassembled to
>> fit the circumstances.
>>
>> The longest path from start to finish begins with ranked choice ballots.
>>
>> Step 1 converts the ballots to 3-slot ballots. This step can be
>> accomplished in two main ways (detailed presently) or bypassed entirely by
>> getting direct 3-slot approval input as in Ted Stern's Approval Sorted
>> Margins, for example.
>>
>
> I would credit you as the originator of Approval Sorted Margins. My
> modification was Preference Approval Sorted Margins, with 3 approval slots
> of Preferred, Approved, Rejected.
>

Definite improvement over my version.

>
>
>>
>> The first main way is to distinguish Top, Bottom, and Middle positions on
>> the ranked ballots.
>>
>> The second main way is to give Top slot status to every candidate X on
>> ballot B for which there is some candidate Y outranked by X, that defeats
>> every candidate that outranks X.
>>
>> Bottom slot status goes to X if it is outranked by some Y that defeats
>> every candidate that X outranks.
>>
>> Middle slot status goes to ranked candidates not assigned Top or Bottom
>> status by the above rules.
>>
>
> I'm not quite clear on the TMB slots. Could you give an example of this in
> a simple election, then apply the positions on an example ballot?
>

Think of Range or Score based on ballots where you rate/grade candidates on
a scale of zero to two.

>
> The unclear thing to me is whether the 3 slot approval is per-ballot or
> based on the overall pairwise array.
>

In this example each candidate's Top score is the percentage of ballots on
which it was rated 2 or graded Top. Its bottom score is the percentage of
ballots on which it was rated zero or not rated (i.e. truncated, abstained,
left blank). The middle score is the percentage of ballots on which the
candidate received a rating of one or a grade of Middle..

>
>
>>
>> Step 2 is converting 3-slot Top, Middle, and Bottom tallies into Robert
>> Bristow-Johnson's  "peak approval" scores.
>>
>> Let t, m, & b be the respective slot values. Then the peak approval score
>> is ...
>> (t-b)/(2-t-b) or (t-b)/(1+m)
>>
>
> To clarify, are t, b, and m the totals of individual ballot t/b/m scores
> from each ballot?
>

Yes, but I should have said fraction or percentage of the ballots ... so
the formula would make sense.  In that context 1=100percent.

>
>
>>
>> with the David Gale value t-b as the tie breaker.
>>
>> Step 3. Do peak approval sorted margins, as in any other Sorted margins
>> method.
>>
>
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