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

[C.Benham]

On 11/19/2016 10:26 AM, Forest Simmons wrote:

> An interesting fact is that MDDA(pt/2) is just another formulation of 
> my version of ICA.

Yes, that had dawned on me.  It's also like symmetrically completing 
ballots only at the bottom, saying
that above-bottom equal-rankings contribute nothing to the pairwise 
scores of the candidates with the
same above-bottom ranking versus each other, and then saying that unless 
all candidates have a majority-
strength defeat any that do are disqualified.

But isn't that a little bit different from the normal version of the 
"Tied-at-the-Top Rule", because that treats
equal-top equal ranking differently from all below-top equal-ranking?

I am a bit concerned about this (sincere) scenario:

40: A>B
10: A=B
35: B
15: C

With all the voters' approval cutoffs left in the default position B 
wins but A is the CW. Of course if the 40 A>B
preferrers vote  A>>B there is no problem, but might there be a case for 
the default placement being just below
the top-voted candidate/s?

For a method with this cute game-theoretic  defence of the 'sincere CW 
who is the smallest faction's favourite' and also
a way of addressing the Chicken Dilemma scenario , this looks very good.

It meets FBC, Mono-add-Plump and Irrelevant Ballots Independence, 
Plurality and Mono-raise.

Chris Benham



On 11/19/2016 10:26 AM, Forest Simmons 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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