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

[Forest Simmons]

I'm sure it was intentionally subtle, but not too subtle, by Brams or
Fishburn, either one or both.

On Sat, Nov 19, 2016 at 4:08 PM, Michael Ossipoff <email9648742 at gmail.com>
wrote:

>
>
> 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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