[EM] Trying to have CD, protect strong top-set, and protect middle candidates too

[Forest Simmons]

No hurry.  Let's give it some time, and if it survives scrutiny, we can
call it by a descriptive title or the VOBS (Venzke Ossipoff Benham Simmons)
method, like they do in physics.

We might have to change the order of the initials to avoid tempting people
to call it the "Very Old BS method."

On Sat, Nov 19, 2016 at 2:08 PM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

> It seems to me that _this_ is the method that you'd rather have named
> after you, if it meets FBC, CD, Mono-Add-Plump, and resists truncation &
> burial.
>
> Michael Ossipoff
>
>
> On Sat, Nov 19, 2016 at 4:49 PM, Michael Ossipoff <email9648742 at gmail.com>
> wrote:
>
>> Well, this looks like the sought-after method that meets FBC & CD, and
>> has wv strategy.   ...and without a major criticism.
>>
>> My first impression is that MDDA(pt/2) would be easier to explain &
>> propose.
>>
>> Thanks for what seems to be the method with the sought-after
>> properties-combination!
>>
>> Michael Ossipoff
>>
>> On Fri, Nov 18, 2016 at 6:56 PM, Forest Simmons <fsimmons at pcc.edu> wrote:
>>
>>> Does optional approval cutoff wreck burial protection?
>>>
>>> Suppose we have a sincere scenario
>>>
>>> 40 C>B
>>> 35 A>B
>>> 25 B>C
>>>
>>> and the C faction decides to bury the CWs B.  The B faction anticipates
>>> this and responds by truncating C.  It is in the interest of the A faction
>>> to leave the default implicit approval cutoff in place.  The C faction
>>> doesn't want to give A too much support so they use the explicit cutoff
>>> option:
>>>
>>> 40 C>>A
>>> 35 A>B
>>> 25 B
>>>
>>> The approval winner is B the CWs.
>>>
>>> If they left the implicit cutoff in place it would be worse for them;
>>> their last choice would be elected.
>>>
>>> So I think MDDA with optional explicit cutoff is fine with respect to
>>> truncation and burial.
>>>
>>> How about the CD?
>>>
>>> In this case the sincere profile is
>>>
>>> 40 C
>>> 35 A>B
>>> 25 B>A
>>>
>>> The B>A faction threatens to defect from the AB coalition.
>>> The A faction responds by using the explicit cutoff:
>>>
>>> 40 C
>>> 35 A>>B
>>> 25 B
>>>
>>> The approval winner is C, so the threatened defection back-fires.
>>>
>>> It seems to me like that is plenty of chicken defection insurance.
>>>
>>> The obvious equilibrium position (for the chicken scenario) is
>>>
>>> 40 C
>>> 35 A>>B
>>> 25 B>>A
>>>
>>> Under MDDA(pt/2) the only uneliminated candidate is A.
>>>
>>> But if the B faction defects, all candidates are eliminated, and the
>>> approval winner C is elected.
>>>
>>> This is why I like MDDA(pt/2).
>>>
>>> An interesting fact is that MDDA(pt/2) is just another formulation of my
>>> version of ICA.  They are precisely equivalent.  Here's why:
>>>
>>> In my version of ICA, X beats Y iff
>>>
>>> [X>Y] > [Y>X] + [X=Y=T] + [X=Y=between] , in other words,
>>>
>>> [X>Y] > [Y:>=X] - [X=Y=Bottom],
>>>
>>> which in turn equals
>>>
>>> 100% - [X>Y] - [X=Y=Bottom], since  100%= [X>Y] + [Y>=X].
>>>
>>> So X beats Y iff
>>>
>>> [X>Y] > 100% - [X>Y] - [X=Y=Bottom].
>>>
>>> If you add [X.Y] to both sides and divide by 2, you get
>>>
>>> [X>Y] +[X=Y=Bottom]/2 > 50%,
>>>
>>> precisely the "majority-with- half-power-truncation" rule.
>>>
>>> So (my version of) ICA is precisely equivalent to MDDA(pt/2).
>>>
>>> I believe it to be completely adequate for defending against burial,
>>> truncation, and Chicken Defection.
>>>
>>>
>>> Now suppose that p<q<r, and p+q+r=100%, and we have three factions of
>>> respective sizes p, q, and r:, with r + q > 50%.
>>>
>>> p: C
>>> q: A>>B
>>> r: B>>A
>>>
>>> Then under the pt/2 rule both C and B are eliminated, but not A, so A is
>>> elected.
>>>
>>> Suppose that the B factions defects.
>>>
>>> Then A is also eliminated, and the approval winner C is elected.
>>>
>>> Etc.
>>>
>>> So which of the two equivalent formulations is easier to sell?  ICA or
>>> MDDA(pt/2) ?
>>>
>>> Forest
>>>
>>
>>
>
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