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

[Forest Simmons]

Chris,

I'm convinced; the default approval should be top set only.  How much
control the voters have over adjusting that cutoff on their ballots is
still up for grabs.  I like keeping it simple, but Michael nade some good
points about allowing voters to specify individual disapprovals.

Good point about presenting half-power-truncation as symmetric completion
for truncated candidates.  It's easier to motivate it from that perspective.

The more I think about it the more I like symmetric completion for all
equal rankings below the approval cutoff, not just for truncation.

Then not only do we have mono-add-plump, but also this more detailed
property:

If a new ballot is added that doesn't rank any (previously) disqualified
candidate above all of her disqualifiers or equal to any approved
disqualifier, then the new winner will be from the candidates that are
approved on the new ballot.

What more could we ask for by way of participation incentive?

Forest

On Sun, Nov 20, 2016 at 3:59 PM, C.Benham <cbenham at adam.com.au> wrote:

> 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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