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

[Michael Ossipoff]

On Sat, Nov 19, 2016 at 6:37 PM, Forest Simmons <fsimmons at pcc.edu> wrote:

> No hurry.  Let's give it some time, and if it survives scrutiny
>

Sure, and it seems to be surviving scrutiny better than anything else so
far.


> , we can call it by a descriptive title or the VOBS (Venzke Ossipoff
> Benham Simmons) method, like they do in physics.
>

It's true that progress is ultimately collaborative, but of course
eventually one individual notices, finds, puts together the as-yet
un-noticed possibility that is hiding in the discussion, and people
particularly take note of that final arrival at a goal.


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

In a debate between Brams (or Fishburn) and the Saari, main Borda advocate,
the Approval advocate called Borda "the Borda System (BS)", and referred to
it as BS throughout the discussion
.
Michael Ossipoff




>
> 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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