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

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

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

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.

Related to this, one issue I'd like your thoughts on is how CD is defined
on the wiki: Chicken Dilemma Criterion - Electowiki
http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion

Chicken Dilemma Criterion - Electowiki
http://wiki.electorama.com/wiki/Chicken_Dilemma_Criterion

Premise item 4 used to say "Voting is sincere, except that the 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 C
4 A>B
3 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@gmail.com
À : Forest Simmons fsimmons@pcc.edu
Cc : EM election-methods@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).

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.

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@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@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

Election-Methods mailing list - see http://electorama.com/em for list info

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

On 11/19/2016 3:14 AM, Michael Ossipoff wrote:

If the more embarrassing Mono-Raise failure doesn't give IRV any
acceptance or enactment problem, then why should the less embarrassing
Mono-Add-Plump failure of MDDTR give MDDTR an acceptance or enactment
problem?

Because what you consider more or less "embarrassing" I am sure isn't in
accord with what most people would find unacceptably ridiculous.

With MDDTR, if your plump for X makes X lose, it's because you added a
ballot. It has nothing whatsoever to do with the fact that you voted
favorably to X.

That's right. "You" should have found some way to vote for X without
adding a ballot. Unfortunately removing someone else's ballot when you are
in the
polling station is usually impossible or legally risky.

Anyway, if IRV is so widely used and successful, then why would
nonmonotonicity be a problem for MDDTR?

Because IRV has a traditional and (for many) intuitive algorithm

, and a solid "maximal"  set of criterion compliances and MDDTR doesn't.

Earlier you attempted to ridicule my observation that MDDTR fails
Irrelevant Ballots Independence by suggesting that might indirectly
motivate a higher
turnout.

Well, just as some might have an interest in promoting that (for voters
who'll ignore the competitive/viable candidates) so as to wash away
an otherwise likely majority-defeat disqualification so would opposed
forces have an interest in doing the opposite.