[EM]Definite Majority Choice, AWP, AM

[Jobst Heitzig]

Dear Chris!

You wrote:

> I like this table. 
Thanks.

> Doesn't AM look like the most "natural" and  "balanced"?
Yes, but that's only an aesthetical judgement...

> I was wondering if it is possible in AM for a
> candidate who is both the sincere CW and sincere AW to
> successfully Buried, and I've come up with an example
> that shows that unfortunately it is, but AWP and DMC
> likewise fail in the same example.
But not DFC (Democratic Fair Choice aka Random Ballot from Forest's P),
as I will show below!

> Sincere preferences:
> 48: A>B>>C
> 01: A>>C>B
> 03: B>>A>C
> 48: C>>B>A
> B is the CW and AW.
Also DFC elects B here.

> Then 45 of the 48 A>B voters Bury B "strongly", i.e.
> with both rankings and approval, while the other 3 of
> the 48 only Bury with their rankings (not approving
> C).
[...]
> All three methods elect the Burier's candidate, A.
But DFC elects A only with 52% probability, and C with 48% probability.
This means the Buriers would get their least prefered candidate with a
large probability, which should deter them from strategizing.

> When there are three candidates in the top cycle, AM
> has the property that the candidate with the lowest
> voted approval score can't win.
But that's also true for DMC and DFC since that candidate is always
strongly defeated.

> Jobst wrote:
> "Here you state the obvious problem when looking at
> both approval and defeat information. Forest's
> ingenious argument was that we should at least not
> elect a candidate where both kinds of information
> agree that the candidate is defeated, leaving us with
> his set P of candidates which are not strongly
> defeated.
> 
> But when we take both kinds of information serious, it
> does not seem appropriate to me to always elect a
> candidate from the two extremes of P like Approval and
> DMC do. Still, DMC has the obvious advantage of
> extreme simplicity.
> 
> I would find it much more natural if the winner was
> somewhere in the "middle" of P!"
> 
> Doesn't  Approval Margins fill the bill?  Welcome to
> the AM fan club!

I don't know... Which cycle resolution technique does AM use? The claim
that the winner belongs to P seems to hold at least when you use an
immune cycle resolution technique like that of Beatpath, RP, or River...

Yours, Jobst