Trying to have CD, protect strong top-set, and protect middle candidates too
I meant to ask: Did you say that MTRI doesn't pass FBC? How does FBC
failure happen? In return for FBC, it should beat MDDTR at vulnerability to
burial, and not be vulnerable to truncation.
Anyway, anything you can tell me about the properties comparison between
MTRI & MDDTR would be helpful.
MIchael Ossipoff
On Thu, Nov 17, 2016 at 5:05 PM, Michael Ossipoff email9648742@gmail.com
wrote:
For this method, MTRI, the procedural definition is more understandable
than the recursive definition (though the recursive definition's brevity
could be useful).
So this is what I understand MTRI's procedural definition to be:
-
Order the candidates by their top-count score, with higher scores at
top. -
Switch the lowest pair of adjacent candidates whose lower candidate
pair-beats the higher one.
Repeat till there are no more pairs to switch. The highest candidate in
the order at that time wins.
As a CD rank method, this method is a competitor of MDDTR. What are the
property differences between MTRI & MDDTR?
In particular, how does MTRI compare with MDDTR in regards to protection
of a CWs against truncation & burial?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:55 PM, Forest Simmons fsimmons@pcc.edu wrote:
On Thu, Nov 17, 2016 at 10:54 AM, Michael Ossipoff <
email9648742@gmail.com> wrote:
But wouldn't Smith//Approval, with approval cutoffs in the rankings,
share MDDTR's burial-vullnerability?
...with, additionally, vulnerability to truncation, which MDDTR
doesn't have?
And Smith//Approval trades MDDTR's FBC for Smith, which I consider an
unfavorable trade.
Perhaps make truncation the default approval cutoff, but let voters move
it higher as an option:
45 C
30 A>B or A>>B
25 B
Voting A>>B would be the chicken defense (where sincere is 25 B>A).
Voting A>B would be the truncation defense (where sincere is 45 C>B).
With this option, MDDA would be an FBC compliant method that is
truncation and burial resistant as well as quasi CD compliant.
Is there a way to modify MDDA to make it satisfy mono-add-plump?
How about incorporating some form of power truncation. When you plump X
and reduce the majority victory of Y over Z to a sub-majority, it would
revert to a majority if you counted the common truncation of Y and Z
against each other as even half a point.
Btw, in case you didn't see it, one of my new favorite non-FBC methods is
Most Approved Immune(MAI): Elect the most approved immune candidate.
This means elect the most approved candidate X that is unbeaten pairwise
by the candidate that would win (recursively) if the method were applied to
the same ballot set with X disqualified or withdrawn.
It is the simplest approval based rank method that confers immunity from
second place complaints on its winners.
It is quasi CD compliant if voters can specify their approval cutoffs
above the truncation level when they want to.
A top rank version of this method is fully CD compliant:
Elect the Most Top Ranked Immune candidate. (MTRI)
In other words elect the most top ranked candidate X that is unbeaten
pairwise by the candidate that would win (recursively) if the method were
applied to the same ballot set with X disqualified or withdrawn.
Forest
For most practical purposes (i.e. for a Smith set of fewer than four
members, MTRI is the same as Smith//TR, which is no better than ICT, and
not even as good since it fails FBC.
There are two ways it can fail FBC: Increasing the top count of favorite
can place it in a position to be the only impediment to compromise reaching
the top of the list when favorite doesn't have enough steam to make it
there herself., Or favorite might advance up from below and grab Compromise
pairwise just before fizzling out.
So I don't propose MTRI, but I think that MAI is a good proposal as long as
the default approval cutoff is at the level of truncation, and voters can
raise that when there is a CD threat.
But MAI still fails FBC.
So to me the best proposal is ICA with default approval cutoff at
truncation to help punish burial and truncation with an option to raise the
cutoff to withstand a CD attack.
Here's my version (slightly different from the original):
Candidate X strongly beats candidate Y iff
the number of ballots on which X is ranked over Y is greater than
the number of ballots on which Y is ranked equal to or greater than Y.
[Note Y is not ranked equal to X if Y is not ranked.]
If not all of the candidates are strongly beaten, disqualify all of the
ones who are.
Elect the most approved qualified candidate.
I think that this method has all of the good properties of MDDA with
mono-add-plump to boot.
We still need to explore MDDA with the half power truncation rule, since it
would also satisfy mono-add-plump if I am not mistaken.
I agree with Chris Benham that mono-add-plump failure would be fatal in a
public proposal.
On Thu, Nov 17, 2016 at 2:12 PM, Michael Ossipoff email9648742@gmail.com
wrote:
I meant to ask: Did you say that MTRI doesn't pass FBC? How does FBC
failure happen? In return for FBC, it should beat MDDTR at vulnerability to
burial, and not be vulnerable to truncation.
Anyway, anything you can tell me about the properties comparison between
MTRI & MDDTR would be helpful.
MIchael Ossipoff
On Thu, Nov 17, 2016 at 5:05 PM, Michael Ossipoff email9648742@gmail.com
wrote:
For this method, MTRI, the procedural definition is more understandable
than the recursive definition (though the recursive definition's brevity
could be useful).
So this is what I understand MTRI's procedural definition to be:
-
Order the candidates by their top-count score, with higher scores at
top. -
Switch the lowest pair of adjacent candidates whose lower candidate
pair-beats the higher one.
Repeat till there are no more pairs to switch. The highest candidate in
the order at that time wins.
As a CD rank method, this method is a competitor of MDDTR. What are the
property differences between MTRI & MDDTR?
In particular, how does MTRI compare with MDDTR in regards to protection
of a CWs against truncation & burial?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:55 PM, Forest Simmons fsimmons@pcc.edu wrote:
On Thu, Nov 17, 2016 at 10:54 AM, Michael Ossipoff <
email9648742@gmail.com> wrote:
But wouldn't Smith//Approval, with approval cutoffs in the rankings,
share MDDTR's burial-vullnerability?
...with, additionally, vulnerability to truncation, which MDDTR
doesn't have?
And Smith//Approval trades MDDTR's FBC for Smith, which I consider an
unfavorable trade.
Perhaps make truncation the default approval cutoff, but let voters move
it higher as an option:
45 C
30 A>B or A>>B
25 B
Voting A>>B would be the chicken defense (where sincere is 25 B>A).
Voting A>B would be the truncation defense (where sincere is 45 C>B).
With this option, MDDA would be an FBC compliant method that is
truncation and burial resistant as well as quasi CD compliant.
Is there a way to modify MDDA to make it satisfy mono-add-plump?
How about incorporating some form of power truncation. When you plump X
and reduce the majority victory of Y over Z to a sub-majority, it would
revert to a majority if you counted the common truncation of Y and Z
against each other as even half a point.
Btw, in case you didn't see it, one of my new favorite non-FBC methods
is Most Approved Immune(MAI): Elect the most approved immune candidate.
This means elect the most approved candidate X that is unbeaten pairwise
by the candidate that would win (recursively) if the method were applied to
the same ballot set with X disqualified or withdrawn.
It is the simplest approval based rank method that confers immunity from
second place complaints on its winners.
It is quasi CD compliant if voters can specify their approval cutoffs
above the truncation level when they want to.
A top rank version of this method is fully CD compliant:
Elect the Most Top Ranked Immune candidate. (MTRI)
In other words elect the most top ranked candidate X that is unbeaten
pairwise by the candidate that would win (recursively) if the method were
applied to the same ballot set with X disqualified or withdrawn.
Forest
Forest--
You wrote:
But MAI still fails FBC.
Failing both FBC & CD isn't good.
So to me the best proposal is ICA with default approval cutoff at
truncation to help punish burial and truncation with an option to raise the
cutoff to withstand a CD attack.
But buriers or truncators could raise that approval cutoff too. Someone
could bury X under Z without having to approve Z. That loses the deterrence
that would exist if that burier had to approve Z in order to rank hir over
someone, as would be so if ranking is counted as approval.
So CD still comes at the cost of a lot less protection against burial, or,
in ICT's case, trunction too.
But that just means that it isn't better than MDDTR in that regard. It
doesn't mean that it's worse.
And it doesn't have Mono-Add-Plump failure.
So, the method has CD as MDDTR does, and trades truncation-proofness for
Mono-Add-Plump.
I value strategy protections more than embarrassment criteria. (But I
realize that proposal-opponents can use embarrassment criteria criticisms,
and that proponents aren't likely to be able to afford as much media time,
to answer the criticisms.)
[Replying farther down] :
Here's my version (slightly different from the original):
Candidate X strongly beats candidate Y iff
the number of ballots on which X is ranked over Y is greater than
the number of ballots on which Y is ranked equal to or greater than Y.
[Note Y is not ranked equal to X if Y is not ranked.]
If not all of the candidates are strongly beaten, disqualify all of the
ones who are.
Elect the most approved qualified candidate.
I think that this method has all of the good properties of MDDA with
mono-add-plump to boot.
I've only had a preliminary look at it, but it seems to me, right now, that
the separate approval-cutoff that the voter can raise from the default
spoils protection from burial & truncation.
You wrote:
We still need to explore MDDA with the half power truncation rule, since
it would also satisfy mono-add-plump if I am not mistaken.
Yes, it seems to me that a 1/2 power-truncation would get rid of the
Mono-Add-Plump failure. If, by not ranking a certain 2 candidates, you give
them each at least half of a vote against eachother, that would bring
Mono-Add-Plump compliance, it seems to me.
So maybe it would avoid criticism of MDDA.
But, if used with MDDTR, it would spoil CD.
You wrote:
I agree with Chris Benham that mono-add-plump failure would be fatal in a
public proposal.
What if you're going to rank X last in your ranking. With all the ballots,
including yours, X will win. But then you move X to 1st place in your
ranking, and that makes X lose.
Would that be ok?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:12 PM, Michael Ossipoff email9648742@gmail.com
wrote:
I meant to ask: Did you say that MTRI doesn't pass FBC? How does FBC
failure happen? In return for FBC, it should beat MDDTR at vulnerability to
burial, and not be vulnerable to truncation.
Anyway, anything you can tell me about the properties comparison between
MTRI & MDDTR would be helpful.
MIchael Ossipoff
On Thu, Nov 17, 2016 at 5:05 PM, Michael Ossipoff <email9648742@gmail.com
wrote:
For this method, MTRI, the procedural definition is more understandable
than the recursive definition (though the recursive definition's brevity
could be useful).
So this is what I understand MTRI's procedural definition to be:
-
Order the candidates by their top-count score, with higher scores at
top. -
Switch the lowest pair of adjacent candidates whose lower candidate
pair-beats the higher one.
Repeat till there are no more pairs to switch. The highest candidate in
the order at that time wins.
As a CD rank method, this method is a competitor of MDDTR. What are the
property differences between MTRI & MDDTR?
In particular, how does MTRI compare with MDDTR in regards to protection
of a CWs against truncation & burial?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:55 PM, Forest Simmons fsimmons@pcc.edu
wrote:
On Thu, Nov 17, 2016 at 10:54 AM, Michael Ossipoff <
email9648742@gmail.com> wrote:
But wouldn't Smith//Approval, with approval cutoffs in the rankings,
share MDDTR's burial-vullnerability?
...with, additionally, vulnerability to truncation, which MDDTR
doesn't have?
And Smith//Approval trades MDDTR's FBC for Smith, which I consider an
unfavorable trade.
Perhaps make truncation the default approval cutoff, but let voters
move it higher as an option:
45 C
30 A>B or A>>B
25 B
Voting A>>B would be the chicken defense (where sincere is 25 B>A).
Voting A>B would be the truncation defense (where sincere is 45 C>B).
With this option, MDDA would be an FBC compliant method that is
truncation and burial resistant as well as quasi CD compliant.
Is there a way to modify MDDA to make it satisfy mono-add-plump?
How about incorporating some form of power truncation. When you plump
X and reduce the majority victory of Y over Z to a sub-majority, it would
revert to a majority if you counted the common truncation of Y and Z
against each other as even half a point.
Btw, in case you didn't see it, one of my new favorite non-FBC methods
is Most Approved Immune(MAI): Elect the most approved immune candidate.
This means elect the most approved candidate X that is unbeaten
pairwise by the candidate that would win (recursively) if the method were
applied to the same ballot set with X disqualified or withdrawn.
It is the simplest approval based rank method that confers immunity
from second place complaints on its winners.
It is quasi CD compliant if voters can specify their approval cutoffs
above the truncation level when they want to.
A top rank version of this method is fully CD compliant:
Elect the Most Top Ranked Immune candidate. (MTRI)
In other words elect the most top ranked candidate X that is unbeaten
pairwise by the candidate that would win (recursively) if the method were
applied to the same ballot set with X disqualified or withdrawn.
Forest
I don't mean that IRV isn't ok. IRV's Mono-Raise failure doesn't bother me.
Neither does MDDTR's Mono-Add-Plump failure.
Voting's purpose is probabilistic anyway. You vote to improve the
probability of a better outcome. The possible nonmonotonicity of IRV
& MDDTR doesn't invalidate that.
My point, in asking about when you make someone lose by raising hir from
last place to 1st place, was just that IRV is popular and widely used. It's
been used in Australia for a long time, and it's used in a fair number of
cities in this country. ...and now has been adopted by the state of Maine.
...in spite of its Mono-Raise failure.
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?
There of course have been objections to IRV, some valid, some not. But I
haven't heard any of the IRV critics in the various cities complain about
its nonmonotonicity. They object to implementation complexity. They
invalidly claim voting complexity. They invalidly complain because
supposedly voting is supposed to be by Plurality. They repealed IRV in
Burlington because of the elimination of a CWv. But none of the
complaints that I've heard, in cities using it or considering IRV, have
been about its nonmonotonicity.
Why I say that Mono-Raise failure is more embarrassing:
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.
With IRV, if raising X from bottom to top makes X lose, then X lost for no
other reason than because you helped hir more.
There are 2 kinds of nonmonotonicity:
Did you make X lose in spite of voting favorably for hir?
or
Did you make X lose because you voted hir more favorably?
Of those 2 kinds of nonmonotonicity the 2nd one is more of an embarrassment
to the method. There, the method is more directly acting oppositely to your
action.
Maybe it could be said that the 2nd kind of nonmonotonicity is twice as
embarrassing to the voting-system.
Anyway, if IRV is so widely used and successful, then why would
nonmonotonicity be a problem for MDDTR?
I now feel that IRV's (mitigated) problem isn't an unusually high price for
CD, isn't more than the "going rate" for CD. IRV & its derivatives are at
the top of my ranking of method-merit for electorates who want &/or need
ranking.
Michael Ossipoff
On Fri, Nov 18, 2016 at 1:23 AM, Michael Ossipoff email9648742@gmail.com
wrote:
Forest--
You wrote:
But MAI still fails FBC.
Failing both FBC & CD isn't good.
So to me the best proposal is ICA with default approval cutoff at
truncation to help punish burial and truncation with an option to raise the
cutoff to withstand a CD attack.
But buriers or truncators could raise that approval cutoff too. Someone
could bury X under Z without having to approve Z. That loses the deterrence
that would exist if that burier had to approve Z in order to rank hir over
someone, as would be so if ranking is counted as approval.
So CD still comes at the cost of a lot less protection against burial, or,
in ICT's case, trunction too.
But that just means that it isn't better than MDDTR in that regard. It
doesn't mean that it's worse.
And it doesn't have Mono-Add-Plump failure.
So, the method has CD as MDDTR does, and trades truncation-proofness for
Mono-Add-Plump.
I value strategy protections more than embarrassment criteria. (But I
realize that proposal-opponents can use embarrassment criteria criticisms,
and that proponents aren't likely to be able to afford as much media time,
to answer the criticisms.)
[Replying farther down] :
Here's my version (slightly different from the original):
Candidate X strongly beats candidate Y iff
the number of ballots on which X is ranked over Y is greater than
the number of ballots on which Y is ranked equal to or greater than Y.
[Note Y is not ranked equal to X if Y is not ranked.]
If not all of the candidates are strongly beaten, disqualify all of the
ones who are.
Elect the most approved qualified candidate.
I think that this method has all of the good properties of MDDA with
mono-add-plump to boot.
I've only had a preliminary look at it, but it seems to me, right now,
that the separate approval-cutoff that the voter can raise from the default
spoils protection from burial & truncation.
You wrote:
We still need to explore MDDA with the half power truncation rule, since
it would also satisfy mono-add-plump if I am not mistaken.
Yes, it seems to me that a 1/2 power-truncation would get rid of the
Mono-Add-Plump failure. If, by not ranking a certain 2 candidates, you give
them each at least half of a vote against eachother, that would bring
Mono-Add-Plump compliance, it seems to me.
So maybe it would avoid criticism of MDDA.
But, if used with MDDTR, it would spoil CD.
You wrote:
I agree with Chris Benham that mono-add-plump failure would be fatal in a
public proposal.
What if you're going to rank X last in your ranking. With all the ballots,
including yours, X will win. But then you move X to 1st place in your
ranking, and that makes X lose.
Would that be ok?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:12 PM, Michael Ossipoff <email9648742@gmail.com
wrote:
I meant to ask: Did you say that MTRI doesn't pass FBC? How does FBC
failure happen? In return for FBC, it should beat MDDTR at vulnerability to
burial, and not be vulnerable to truncation.
Anyway, anything you can tell me about the properties comparison between
MTRI & MDDTR would be helpful.
MIchael Ossipoff
On Thu, Nov 17, 2016 at 5:05 PM, Michael Ossipoff <
email9648742@gmail.com> wrote:
For this method, MTRI, the procedural definition is more understandable
than the recursive definition (though the recursive definition's brevity
could be useful).
So this is what I understand MTRI's procedural definition to be:
-
Order the candidates by their top-count score, with higher scores at
top. -
Switch the lowest pair of adjacent candidates whose lower candidate
pair-beats the higher one.
Repeat till there are no more pairs to switch. The highest candidate in
the order at that time wins.
As a CD rank method, this method is a competitor of MDDTR. What are the
property differences between MTRI & MDDTR?
In particular, how does MTRI compare with MDDTR in regards to
protection of a CWs against truncation & burial?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:55 PM, Forest Simmons fsimmons@pcc.edu
wrote:
On Thu, Nov 17, 2016 at 10:54 AM, Michael Ossipoff <
email9648742@gmail.com> wrote:
But wouldn't Smith//Approval, with approval cutoffs in the rankings,
share MDDTR's burial-vullnerability?
...with, additionally, vulnerability to truncation, which MDDTR
doesn't have?
And Smith//Approval trades MDDTR's FBC for Smith, which I consider an
unfavorable trade.
Perhaps make truncation the default approval cutoff, but let voters
move it higher as an option:
45 C
30 A>B or A>>B
25 B
Voting A>>B would be the chicken defense (where sincere is 25 B>A).
Voting A>B would be the truncation defense (where sincere is 45 C>B).
With this option, MDDA would be an FBC compliant method that is
truncation and burial resistant as well as quasi CD compliant.
Is there a way to modify MDDA to make it satisfy mono-add-plump?
How about incorporating some form of power truncation. When you plump
X and reduce the majority victory of Y over Z to a sub-majority, it would
revert to a majority if you counted the common truncation of Y and Z
against each other as even half a point.
Btw, in case you didn't see it, one of my new favorite non-FBC methods
is Most Approved Immune(MAI): Elect the most approved immune candidate.
This means elect the most approved candidate X that is unbeaten
pairwise by the candidate that would win (recursively) if the method were
applied to the same ballot set with X disqualified or withdrawn.
It is the simplest approval based rank method that confers immunity
from second place complaints on its winners.
It is quasi CD compliant if voters can specify their approval cutoffs
above the truncation level when they want to.
A top rank version of this method is fully CD compliant:
Elect the Most Top Ranked Immune candidate. (MTRI)
In other words elect the most top ranked candidate X that is unbeaten
pairwise by the candidate that would win (recursively) if the method were
applied to the same ballot set with X disqualified or withdrawn.
Forest
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.
In fact you could have post-election recriminations reminiscent of those
that were aimed at Nader and those who voted for him supposedly allowing
Bush to
win a few years ago. "Those idiots weren't even really interested in who
won, why didn't they just stay home?!" could be the lament.
Just the knowledge that a failure of Mono-add-Plump is theoretically
possible could reduce people's enthusiasm for voting and make it more
likely that those who like to vote by just plumping for their favourite
will stay home.
Whereas IRV doesn't just meet mono-add-plump. It also meet Mono-add-Top.
C: Failing mono-add-plump is as stupid as a quasi-"intelligent" device
can be, in a pure and starkly obvious way, and with the lamest
possible excuse.
The algorithm/device decides that X should win, and then receives some
more ballots that contain nothing whatsoever but the pure and simple
message:
"You are right! X should win" and responds with the bizarre
malfunction "I've changed my mind, Y should win" and offers the
nonsensical excuse "Hey those
extra ballots didn't just say that X should win. They also increased
the total number of ballots!".
C: What (arguably) desirable properties (or criterion compliances)
are incompatible with meeting Mono-add-Plump?
Mike: FBC, CD, & wv-like strategy are evidently require failing
Mono-Add-Plump, or having MMPO's Hitler-with-2-votes problem.
With MDDTR, the price of FBC, CD & wv-like strategy is Mono-Add-Plump.
C: There are methods that meet FBC and CD and mono-add-plump. So your
proposition boils down to saying that it's worth giving up compliance
with
mono-add-plump just to gain "wv-like strategy".
Chris Benham
On 11/19/2016 3:14 AM, Michael Ossipoff wrote:
I don't mean that IRV isn't ok. IRV's Mono-Raise failure doesn't
bother me.
Neither does MDDTR's Mono-Add-Plump failure.
Voting's purpose is probabilistic anyway. You vote to improve the
probability of a better outcome. The possible nonmonotonicity of IRV
& MDDTR doesn't invalidate that.
My point, in asking about when you make someone lose by raising hir
from last place to 1st place, was just that IRV is popular and widely
used. It's been used in Australia for a long time, and it's used in a
fair number of cities in this country. ...and now has been adopted by
the state of Maine.
...in spite of its Mono-Raise failure.
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?
There of course have been objections to IRV, some valid, some not. But
I haven't heard any of the IRV critics in the various cities complain
about its nonmonotonicity. They object to implementation complexity.
They invalidly claim voting complexity. They invalidly complain
because supposedly voting is supposed to be by Plurality. They
repealed IRV in Burlington because of the elimination of a CWv. But
none of the complaints that I've heard, in cities using it or
considering IRV, have been about its nonmonotonicity.
Why I say that Mono-Raise failure is more embarrassing:
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.
With IRV, if raising X from bottom to top makes X lose, then X lost
for no other reason than because you helped hir more.
There are 2 kinds of nonmonotonicity:
Did you make X lose in spite of voting favorably for hir?
or
Did you make X lose because you voted hir more favorably?
Of those 2 kinds of nonmonotonicity the 2nd one is more of an
embarrassment to the method. There, the method is more directly acting
oppositely to your action.
Maybe it could be said that the 2nd kind of nonmonotonicity is twice
as embarrassing to the voting-system.
Anyway, if IRV is so widely used and successful, then why would
nonmonotonicity be a problem for MDDTR?
I now feel that IRV's (mitigated) problem isn't an unusually high
price for CD, isn't more than the "going rate" for CD. IRV & its
derivatives are at the top of my ranking of method-merit for
electorates who want &/or need ranking.
Michael Ossipoff
On Fri, Nov 18, 2016 at 1:23 AM, Michael Ossipoff
<email9648742@gmail.com mailto:email9648742@gmail.com> wrote:
Forest--
You wrote:
But MAI still fails FBC.
Failing both FBC & CD isn't good.
So to me the best proposal is ICA with default approval cutoff
at truncation to help punish burial and truncation with an
option to raise the cutoff to withstand a CD attack.
But buriers or truncators could raise that approval cutoff too.
Someone could bury X under Z without having to approve Z. That
loses the deterrence that would exist if that burier had to
approve Z in order to rank hir over someone, as would be so if
ranking is counted as approval.
So CD still comes at the cost of a lot less protection against
burial, or, in ICT's case, trunction too.
But that just means that it isn't _better_ than MDDTR in that
regard. It doesn't mean that it's worse.
And it doesn't have Mono-Add-Plump failure.
So, the method has CD as MDDTR does, and trades
truncation-proofness for Mono-Add-Plump.
I value strategy protections more than embarrassment criteria.
(But I realize that proposal-opponents can use embarrassment
criteria criticisms, and that proponents aren't likely to be able
to afford as much media time, to answer the criticisms.)
[Replying farther down] :
Here's my version (slightly different from the original):
Candidate X strongly beats candidate Y iff
the number of ballots on which X is ranked over Y is greater than
the number of ballots on which Y is _/*ranked*/_ equal to or
greater than Y.
[Note Y is not ranked equal to X if Y is not ranked.]
If not all of the candidates are strongly beaten, disqualify
all of the ones who are.
Elect the most approved qualified candidate.
I think that this method has all of the good properties of
MDDA with mono-add-plump to boot.
I've only had a preliminary look at it, but it seems to me, right
now, that the separate approval-cutoff that the voter can raise
from the default spoils protection from burial & truncation.
You wrote:
We still need to explore MDDA with the half power truncation
rule, since it would also satisfy mono-add-plump if I am not
mistaken.
Yes, it seems to me that a 1/2 power-truncation would get rid of
the Mono-Add-Plump failure. If, by not ranking a certain 2
candidates, you give them each at least half of a vote against
eachother, that would bring Mono-Add-Plump compliance, it seems to me.
So maybe it would avoid criticism of MDDA.
But, if used with MDDTR, it would spoil CD.
You wrote:
I agree with Chris Benham that mono-add-plump failure would be
fatal in a public proposal.
What if you're going to rank X last in your ranking. With all the
ballots, including yours, X will win. But then you move X to 1st
place in your ranking, and that makes X lose.
Would that be ok?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:12 PM, Michael Ossipoff
<email9648742@gmail.com <mailto:email9648742@gmail.com>> wrote:
I meant to ask: Did you say that MTRI doesn't pass FBC?
How does FBC failure happen? In return for FBC, it should
beat MDDTR at vulnerability to burial, and not be
vulnerable to truncation.
Anyway, anything you can tell me about the properties
comparison between MTRI & MDDTR would be helpful.
MIchael Ossipoff
On Thu, Nov 17, 2016 at 5:05 PM, Michael Ossipoff
<email9648742@gmail.com <mailto:email9648742@gmail.com>>
wrote:
For this method, MTRI, the procedural definition is
more understandable than the recursive definition
(though the recursive definition's brevity could be
useful).
So this is what I understand MTRI's procedural
definition to be:
1. Order the candidates by their top-count score, with
higher scores at top.
2. Switch the lowest pair of adjacent candidates whose
lower candidate pair-beats the higher one.
Repeat till there are no more pairs to switch. The
highest candidate in the order at that time wins.
-----------------------------------------------
As a CD rank method, this method is a competitor of
MDDTR. What are the property differences between MTRI
& MDDTR?
In particular, how does MTRI compare with MDDTR in
regards to protection of a CWs against truncation &
burial?
Michael Ossipoff
On Thu, Nov 17, 2016 at 2:55 PM, Forest Simmons
<fsimmons@pcc.edu <mailto:fsimmons@pcc.edu>> wrote:
On Thu, Nov 17, 2016 at 10:54 AM, Michael Ossipoff
<email9648742@gmail.com
<mailto:email9648742@gmail.com>> wrote:
But wouldn't Smith//Approval, with approval
cutoffs in the rankings, share MDDTR's
burial-vullnerability?
...with, additionally, vulnerability to
truncation, which MDDTR _doesn't_ have?
And Smith//Approval trades MDDTR's FBC for
Smith, which I consider an unfavorable trade.
Perhaps make truncation the default approval
cutoff, but let voters move it higher as an option:
45 C
30 A>B or A>>B
25 B
Voting A>>B would be the chicken defense (where
sincere is 25 B>A).
Voting A>B would be the truncation defense (where
sincere is 45 C>B).
With this option, MDDA would be an FBC compliant
method that is truncation and burial resistant as
well as quasi CD compliant.
Is there a way to modify MDDA to make it satisfy
mono-add-plump?
How about incorporating some form of power
truncation. When you plump X and reduce the
majority victory of Y over Z to a sub-majority, it
would revert to a majority if you counted the
common truncation of Y and Z against each other as
even half a point.
Btw, in case you didn't see it, one of my new
favorite non-FBC methods is Most Approved
Immune(MAI): Elect the most approved immune candidate.
This means elect the most approved candidate X
that is unbeaten pairwise by the candidate that
would win (recursively) if the method were applied
to the same ballot set with X disqualified or
withdrawn.
It is the simplest approval based rank method that
confers immunity from second place complaints on
its winners.
It is quasi CD compliant if voters can specify
their approval cutoffs above the truncation level
when they want to.
A top rank version of this method is fully CD
compliant:
Elect the Most Top Ranked Immune candidate. (MTRI)
In other words elect the most top ranked candidate
X that is unbeaten pairwise by the candidate that
would win (recursively) if the method were applied
to the same ballot set with X disqualified or
withdrawn.
Forest
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@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
It seems to me that this is the method that you'd rather have named after
you, if it meets FBC, CD, Mono-Add-Plump, and resists truncation & burial.
Michael Ossipoff
On Sat, Nov 19, 2016 at 4:49 PM, Michael Ossipoff email9648742@gmail.com
wrote:
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@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
No hurry. Let's give it some time, and if it survives scrutiny, we can
call it by a descriptive title or the VOBS (Venzke Ossipoff Benham Simmons)
method, like they do in physics.
We might have to change the order of the initials to avoid tempting people
to call it the "Very Old BS method."
On Sat, Nov 19, 2016 at 2:08 PM, Michael Ossipoff email9648742@gmail.com
wrote:
It seems to me that this is the method that you'd rather have named
after you, if it meets FBC, CD, Mono-Add-Plump, and resists truncation &
burial.
Michael Ossipoff
On Sat, Nov 19, 2016 at 4:49 PM, Michael Ossipoff email9648742@gmail.com
wrote:
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@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
On Sat, Nov 19, 2016 at 6:37 PM, Forest Simmons fsimmons@pcc.edu wrote:
No hurry. Let's give it some time, and if it survives scrutiny
Sure, and it seems to be surviving scrutiny better than anything else so
far.
, we can call it by a descriptive title or the VOBS (Venzke Ossipoff
Benham Simmons) method, like they do in physics.
It's true that progress is ultimately collaborative, but of course
eventually one individual notices, finds, puts together the as-yet
un-noticed possibility that is hiding in the discussion, and people
particularly take note of that final arrival at a goal.
We might have to change the order of the initials to avoid tempting people
to call it the "Very Old BS method."
In a debate between Brams (or Fishburn) and the Saari, main Borda advocate,
the Approval advocate called Borda "the Borda System (BS)", and referred to
it as BS throughout the discussion
.
Michael Ossipoff
On Sat, Nov 19, 2016 at 2:08 PM, Michael Ossipoff email9648742@gmail.com
wrote:
It seems to me that this is the method that you'd rather have named
after you, if it meets FBC, CD, Mono-Add-Plump, and resists truncation &
burial.
Michael Ossipoff
On Sat, Nov 19, 2016 at 4:49 PM, Michael Ossipoff <email9648742@gmail.com
wrote:
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@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