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

[Michael Ossipoff]

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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