[EM] What are some simple methods that accomplish the following conditions?

[Ted Stern]

Forest,

I like the idea of an Approval-Sorted-Margins based method.  I think it is
simple enough to explain and handles cycles in an transparent fashion.
You, Chris and I had some private conversations about this some years back.

I would prefer an explicit approval cutoff.  I think the following version
is easy to understand:

   - Equal rating allowed, rating from 0 to 9 (10 slots)
   - Bottom 5 slots (0-4) are disapproved, top 5 slots (5-9) are approved.
   - Rank inferred from rating.

What is Strong FBC, and why doesn't Approval meet it?

Chris's "tweaked IRV" seems to be a version of DMC/ASM with elimination.
Does that elimination change approval cutoffs and other pairwise counts?
If not, it could be summable.  If it does, and is not summable and doesn't
satisfy either FBC or CC, why do you like it?

Ted

On Thu, Jun 27, 2019 at 2:55 PM Forest Simmons <fsimmons at pcc.edu> wrote:

> A simple, easy to understand solution!
>
> On Wed, Jun 26, 2019 at 10:10 PM C.Benham <cbenham at adam.com.au> wrote:
>
>> Earlier in response to this I suggested some Condorcet methods. Here is a
>> non-Condorcet method
>> that also fills the bill: a tweaked IRV:
>>
>> *Voters strictly rank  candidates from the top and also give an approval
>> cutoff, default placement
>> of which is just below top.
>> Candidates that are pairwise beaten by a more approved candidate are
>> disqualified.
>> If more than one candidate is undisqalified then eliminate the candidate
>> highest-ranked on the fewest
>> ballots. Repeat until only one undisqualified candidate remains. Elect
>> that candidate.*
>>
>> As compensation for failing Condorcet, this should keep most of IRV's
>> resistance to Burial strategy and
>> be more-or-less immune to the "DH3" pathology.  The normal IRV winner can
>> only lose to a candidate
>> that both pairwise beats it and is explicitly more approved.
>>
>> https://rangevoting.org/DH3.html
>>
>> In all 3 of Forest's scenarios all but one candidate is disqualified.
>>
>> Chris Benham
>>
>> On 31/05/2019 8:03 am, Forest Simmons wrote:
>>
>> In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.
>> I am interested in simple methods that always ...
>>
>> (1) elect candidate A given the following profile:
>>
>> P: A
>> Q: B>>C
>> R: C,
>> and
>>
>> (2) elect candidate C given
>> P: A
>> Q: B>C>>
>> R: C,
>> and
>>
>> (3) elect candidate B given
>> P: A
>> Q: B>>C  (or B>C)
>> R: C>>B. (or C>B)
>>
>> I have two such methods in mind, and I'll tell you one of them below, but
>> I don't want to prejudice your creative efforts with too many ideas.
>>
>> Here's the rationale for the requirements:
>>
>> Condition (1) is needed so that when the sincere preferences are
>> P: A
>> Q: B>C
>> R: C>B,
>> the B faction (by merely disapproving C without truncation) can defend
>> itself against a "chicken" attack (truncation of B) from the C faction.
>>
>> Condition (3) is needed so that when the C faction realizes that the game
>> of Chicken is not going to work for them, the sincere CW is elected.
>>
>> Condition (2) is needed so that when  sincere preferences are
>> P: A>C
>> Q: B>C
>> R: C>A,
>> then the C faction (by proactively truncating A) can defend the CW
>> against the A faction's potential truncation attack.
>>
>> Like I said, I have a couple of fairly simple methods in mind. The most
>> obvious one is Smith\\Approval where the voters have control over their own
>> approval cutoffs (as opposed to implicit approval) with default approval as
>> top rank only.The other method I have in mind is not quite as simple, but
>> it has the added advantage of satisfying the FBC, while almost always
>> electing from Smith.
>>
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