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

Sun Nov 20 15:57:37 PST 2016

Hi Mike,
IC-Smith//MMPO shouldn't work for FBC, but "IC,MMPO" should work (i.e. find the Condorcet winners as under the ICA method, but instead of picking the winner with approval, use the original max defeats, without eliminating anyone).
I'm currently working on a new method DNA scheme, where a code is generated to represent a method, based on who it elects in a specific selection of 3-candidate, 3-faction scenarios. Then certain properties can be defined on the DNA and checked exhaustively. It has limits. But this one supports tying at the top, and an explicit approval cutoff to place on either side of a middle preference.
Related to this, one issue I'd like your thoughts on is how CD is defined on the wiki: Chicken Dilemma Criterion - Electowiki

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Premise item 4 used to say "B voters refuse to vote A over anyone."
But now it says "The A voters vote B over C. The B voters refuse to vote A over anyone."
So now it appears that CD might apply even when the B faction votes B>C:5 C4 A>B3 B>C
That creates an issue, because MMPO elects B in this scenario. So I'm thinking the wiki needs an edit.
I also wonder about creating a stronger version of CD, whose penalty can be invoked not just by the B faction, but also by the A faction. I think there are probably a few reasonable methods that would satisfy this.
Kevin

      De : Michael Ossipoff <email9648742 at gmail.com>
 À : Forest Simmons <fsimmons at pcc.edu> 
Cc : EM <election-methods at lists.electorama.com>
 Envoyé le : Dimanche 20 novembre 2016 16h10
 Objet : Re: [EM] Trying to have CD, protect strong top-set, and protect middle candidates too

I've unsuccessfully looked for an exception to this statement of mine:

"It's probably impossible in principle, with any possible method, to both protect from chicken-defection by a candidate's voters, and also give hir full truncation & burial protection."

Here's what I tried:

I know of 3 ways of avoiding chicken-dilemma:

1. IRV does it by not sharing any votes unless your top-ranked candidate is eliminated.

2. MDDA(p/2) does it by the A voters denying an approval to B, in the chicken-dilemma example.

3. MMPO does it by the fact that, with C voters treating A & B equally, B can't do better than A,  because the A faction is larger.

It could appear as if #3 is promising, because there's no need for A voters to deny support to B.

The trouble is that,  though the A voters don't need to deny support to B, the support that they give to _anyone_ is iffy. MMPO doesn't really have burial-resistance for _anyone_ you middle-rank. Truncation of the buriers' candidate doesn't prevent hir from successfully burying, any more than it does in MDDTR.

Well, the best that can be said for MMPO, in regards to burial resistance, is that burial isn't quite as easy & safe as it can be in MDDTR.

In MDDTR, the buriers merely need for everyone to be majority-beaten, & for their candidate to have a plurality. In MMPO, the buriers need for all the other candidates to be _more_ beaten than their candidate. So the requirement is a bit harder, making the burial a little less safe & dependable.

The pt/2 provision seems to avoid MMPO's "Hitler with 2 votes" bad-example.

So, between MDDA(pt/2) and MMPO(pt/2), it's a choice between fully protecting middle-ranked candidates whom you don't deny approval to, vs making burial a little harder & less reliable & less safe than in MDDTR (but not really resisted), for all of your middle-ranked candidates.

...Complete protection to all of your middle-ranked to whom you don't deny approval, vs some questionable maybe-protection to all of your middle-ranked.

MDDA(pt/2) gives the choice to the voter, regarding support vs chicken-deterrence, instead of being a crapshoot-compromise like MMPO(pt/2).

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I also considered IC-Smith//MMPO.

Maybe it fails FBC, but I didn't find where it does. It share's MMPO's (& MDDTR's) usual lack of real anti-burial support for any of your middle-ranked candidates.

I guess its advantage over MMPO(pt/2) would be its limitation to the IC-Smith set, if that's really achieved without losing FBC.

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I wanted to mention these possibilities, but I don't regard either of these gamble-support methods as a rival to MDDA(pt/2).

---------------------------------------------------

Michael Ossipoff

On Sun, Nov 20, 2016 at 2:42 AM, Michael Ossipoff <email9648742 at gmail.com> wrote:

Voting, using this method, I might often want to deny approval to a high-ranked candidate (even top?), without denying to the rest of my ranking, approval & full protection from burial & truncation.

Maybe I just don't trust to voters of an excellent candidate whom I rank high, but I have no reason to not want to protect the rest of my ranking from burial or truncation by my unranked candidates' voters.

So I suggest that, in addition to an approval cutoff, a voter should also be able to individually deny approval to any individual candidate(s).

It's probably impossible in principle, with any possible method, to both protect from chicken-defection by a candidate's voters, and also give hir full truncation & burial protection.

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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