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

[Michael Ossipoff]

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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