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

[C.Benham]

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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