Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Chris, --- En date de : Ven 23.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : I can't see what's so highly absurd about failing mono-append. It's basically a limited case of mono-raise, and one that doesn't seem especially more important. Is it absurd to fail mono-raise? The absurdity of failing mono-append is compounded by the cheapness of meeting it. As with mono-add-plump the quasi-intelligent device is given simple and pure new information. Being confused by it is simply unforgivable *stupidity* on the part of the quasi-intelligent device. I find it unclear how to decide whether something is unforgivably stupid in your view, or instead mitigated by something like this: Regards mono-raise, I would say that failing it is obviously 'positionally absurd' and 'pairwise absurd' but perhaps not 'LNH absurd'. We know that it isn't absurd in the sense that mono-add-plump and mono-append is, because it is failed by a method that has a maximal set of (IMO) desirable criterion compliances . It seems to me like a real problem that the absurdity of failing a criterion can depend on whether better criteria require that it be failed. I think this is just cheapness again. Failing mono-raise isn't absurd, because mono-raise is relatively expensive. I think there ought to be a clear distinction between criteria whose violation is absurd no matter what the circumstances, and criteria whose violation is absurd due to other available options. There are very few (named) criteria whose failure I'd call absurd no matter what. Can I take it then that you no longer like CDTT,Random Ballot, which does award a probability pie? Sure. Does your question mean that this really is how you view the difference between CDTT and Mutual Majority, is in terms of the candidates of the winning set sharing a probability pie? Not exactly. No-one has ever suggested MM,Random Ballot as a good method and few have suggested that sometimes the clearly most appropriate winner is not in the MM set (as I have regarding the CDTT set). I think that either isn't relevant or doesn't help your case. The question is about why you view MM's behavior as qualitatively different from CDTT's behavior, when in practice, in a real method, it's exactly the same behavior. If the important thing is how many people suggest that the clearly best winner is not in the MM or CDTT sets, then there doesn't seem to be a good reason to bring up mono-add-plump. The criterion/standard is an end in itself. Not everything is about the strategy game. Higer SU with sincere voting and sparing the method common-sense (at least) difficult -to-counter complaints from the positional-minded are worthwhile accomplisments. This strikes me as an unusual amount of paranoia that the method's results can't be explained to the public's satisfaction unless it's similar to Approval. It isn't just the public. It is myself wearing my common-sense positional hat. And it isn't just Approval, it's 'Approval and/or FPP'. Well, supposing that the public decided to accept a method that failed a positional criterion, I guess at that time I would drop that criterion. Hypothetically if the public were willing to accept any method I would propose to them, and not question any of its results, then I wouldn't care about appearances. I would just give them the method that I felt would perform the best. Kevin Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Kevin, I can't see what's so highly absurd about failing mono-append. It's basically a limited case of mono-raise, and one that doesn't seem especially more important. Is it absurd to fail mono-raise? The absurdity of failing mono-append is compounded by the cheapness of meeting it. As with mono-add-plump the quasi-intelligent device is given simple and pure new information. Being confused by it is simply unforgivable *stupidity* on the part of the quasi-intelligent device. Regards mono-raise, I would say that failing it is obviously 'positionally absurd' and 'pairwise absurd' but perhaps not 'LNH absurd'. We know that it isn't absurd in the sense that mono-add-plump and mono-append is, because it is failed by a method that has a maximal set of (IMO) desirable criterion compliances . Can I take it then that you no longer like CDTT,Random Ballot, which does award a probability pie? Sure. Does your question mean that this really is how you view the difference between CDTT and Mutual Majority, is in terms of the candidates of the winning set sharing a probability pie? Not exactly. No-one has ever suggested MM,Random Ballot as a good method and few have suggested that sometimes the clearly most appropriate winner is not in the MM set (as I have regarding the CDTT set). The criterion/standard is an end in itself. Not everything is about the strategy game. Higer SU with sincere voting and sparing the method common-sense (at least) difficult -to-counter complaints from the positional-minded are worthwhile accomplisments. This strikes me as an unusual amount of paranoia that the method's results can't be explained to the public's satisfaction unless it's similar to Approval. It isn't just the public. It is myself wearing my common-sense positional hat. And it isn't just Approval, it's 'Approval and/or FPP'. Chris Benham Hi Chris, --- En date de : Jeu 15.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : Kevin, You wrote (12 Jan 2009): Why do we *currently* ever bother to satisfy difficult criteria? What do we mean when we say we value a criterion? Surely not just that we feel it's cheap? When simultaneously a criterion's satisfaction's cost falls below a certain level and its failure reaches a certain level of absurdity/silliness I start to lose sight of the distinction between important for its own sake and very silly not to have because it's so cheap. Mono-add-plump (like mono-append) is way inside that territory. I see. I don't think I value criteria for this sort of reason. If I insist on a criterion like Plurality, it's because I don't think the public will accept the alternative. And these two criteria are relative, so that in order to complain about a violation you have to illustrate a hypothetical scenario in addition to what really occurred. I can't see what's so highly absurd about failing mono-append. It's basically a limited case of mono-raise, and one that doesn't seem especially more important. Is it absurd to fail mono-raise? If you need to identify majorities, then the fact that a ballot shows no preference between Y and Z, is relevant information. In my view a voting method *doesn't* need to specifically identify majorities, so it isn't. (The voting method can and should meet majority-related criteria 'naturally' and obliquely.) But we aren't even talking about voting methods, we're talking about sets. You have basically criticized Schulze(wv) even though it naturally and obliquely satisfies majority-related criteria. But even if the quasi-intelligent device is mistaken in treating them as relevant, then that is a much more understandable and much less serious a blunder than the mono-add-plump failure. Ok. I still don't really see why, or what makes the difference. Imagine the quasi-intelligent device is the captain of a democracy bus that takes on passengers and then decides on its course/destination after polling the passengers. Imagine that as in situation 1 it provisionally decides to go to C, and then as in situation 2 a group of new passengers get on (swelling the total by about 28%) and they are openly polled and they all say we want to go to C, and have nothing else to say and then the captain announces in that case I'll take the bus to B. Would you have confidence that that captain made rational decisions on the most democratic (best representing the passengers' expressed wishes) decisions? I and I think many others would not, and would conclude that the final B decision can only be right if the original C decision was completely ridiculous. Or would you be impressed by the captain's wisdom in being properly swayed by the new passengers' indecision between A and B? However I answer doesn't make any difference, because the question is why this crosses the boundary of clear badness while failures of mono-add-top and
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Chris, --- En date de : Lun 12.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : Kevin, You wrote (11 Jan 2009): There are reasons for criteria to be important other than how easy they are to satisfy. Otherwise why would we ever bother to satisfy the difficult criteria? Well, if as I said none of the criteria were incompatible with each other then presumably none of the criteria would be difficult. That's not what I meant. I meant: Why do we *currently* ever bother to satisfy difficult criteria? What do we mean when we say we value a criterion? Surely not just that we feel it's cheap? With mono-add-top and Participation, the quasi-intelligent device in reviewing its decision to elect X gets (possibly relevant) information about other candidates besides X. How can it be relevant? X was winning and X is the preferred candidate on the new ballots. You know that Condorcet is incompatible with mono-add-top (and so of course Participation), Condorcet isn't incompatible with mono-add-top. Only top tiers probably are. so if we value compliance with the Condorcet criterion information about candidates ranked below X must sometimes be relevant. I didn't realize that whether information is relevant depends on whether a valued criterion requires the information. If you need to identify majorities, then the fact that a ballot shows no preference between Y and Z, is relevant information. But even if the quasi-intelligent device is mistaken in treating them as relevant, then that is a much more understandable and much less serious a blunder than the mono-add-plump failure. Ok. I still don't really see why, or what makes the difference. It's absurd that ballots that plump for X should in any way be considered relevant to the strength of the pairwise comparison between two other candidates. This absurdity only arises from the algorithm specifically using (and relying on) a majority threshold. We have Mutual Majority and beatpath GMC displaying the same phenomenon. No. I don't accept that 'being tossed out of the favoured (not excluded from winning) set' is exactly the same phenomenon as 'being joined by others in the favoured set'. The latter is obviously far less serious. In an actual election method it would be exactly the same phenomenon. Removed from that context it isn't clear how any of this is serious, let alone obviously far more/less serious. The logical problem is the same, that according to you, the new ballots only contain information on one candidate and should only affect that one candidate. I guess you imagine the win as a pie that has to be split up, and it's better for the candidate to get a smaller piece than none at all. Never mind, that the logic causing this is still just as bad, or that real elections don't award divisible pies. Anyway, you already said there was no way to explain why it isn't completely absurd for Mutual Majority to behave as it does. I don't think that whether Mutual Majority's behavior is absurd should depend on whether you remember that Mutual Majority has this behavior. I don't feel there's an advantage to tending to elect candidates with more approval, because in turn this should just make voters approve fewer candidates when they doubt how the method will use their vote. And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- vulnerable-to-Burial Condocet methods, I think it is better if they have a watch who you rank because you could help elect them Approval flavour. This is a negative because it suggests that your positional criterion will be self-defeating. How can it possibly be self-defeating? What is there to defeat? I thought there was some intention behind your criterion. You talk about the clearly strongest candidate so I assumed this idea is important to you. If insisting on electing the clearly strongest candidate creates incentives that *change* who this candidate is, then what have you accomplished? From your earlier post: In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the CDTT. Why? Because in the three-candidate case this is likely to be a failure of MD or SFC, or close to it. I'm happy to have MD, and I don't care about SFC or close failures of MD. Regarding SFC: It's a bit strange to elect Y when a majority of the voters prefer X to Y, but there's no majority that prefers anybody to X. There could be a good reason for it, but that doesn't mean it wouldn't be better if we never had to do that. I would say that I don't think the CDTT is that much more valuable, than the combination of MD and SFC, especially if you use pairwise definitions of these two. In the three-candidate case it's also compatible with LNHarm. By adding a vote for your second choice, you can't inadvertently remove your first preference from the CDTT.
Re: [EM] Beatpath GMC compliance a mistaken standard?
Paul Kislanko wrote:
This still makes no sense to me, since C has no more a majority in case 2
than it had in case 1.
If mutual majority selects (A B) in case 1 and (A B C) in case 2, it makes
no sense at all and should never be mentioned again.
Mutual majority can still be useful. Let's make an analogy to Condorcet.
The Condorcet criterion elects the CW if there is one. In other words,
if there is a CW and that CW is candidate X, then the set from which
Condorcet methods elect is { X }. If there is no CW, and the candidates
for election are {A B C ... X }, then the set from which Condorcet
methods elect is {A B C ... X }.
Thus, Condorcet is useful when there is indeed a CW, but does nothing
when there isn't.
So it is with mutual majority as well. When there's a set that a
majority ranks above all the others, then a method that passes mutual
majority must elect from that set. When there is no such set, the method
is free to pick any candidate yet still pass mutual majority.
In that light, mutual majority seems very reasonable indeed: if there is
a set so that a majority prefers that set to all others outside the set,
then a candidate within that set should be elected. It's simply
majority transported to sets.
(And on another note, sorry for not mailing you this directly as well,
Paul, but airmail.net seems to think my ISP is a dirty spammer.)
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
This is the post that confused me, and got everbody yelling at me because I
was confused. I call attention to theis bit:
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
--
My original question was how does that make sense? The only answers have
been addressed to me, and haven't addressed the question. The assertion that
mutual majority elects was made by Kevin Venzke, so I guess my question
directed to him.
-Original Message-
From: election-methods-boun...@lists.electorama.com
[mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Kevin
Venzke
Sent: Saturday, January 10, 2009 1:25 PM
To: election-meth...@electorama.com
Subject: Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Chris,
--- En date de : Sam 10.1.09, Chris Benham cbenha...@yahoo.com.au a
écrit :
De: Chris Benham cbenha...@yahoo.com.au
Objet: [EM] Beatpath GMC compliance a mistaken standard?
À: EM election-methods@lists.electorama.com, Kevin Venzke
step...@yahoo.fr
Cc: Markus Schulze markus.schu...@alumni.tu-berlin.de
Date: Samedi 10 Janvier 2009, 0h31
Kevin,
You wrote (9 Jan 2009):
Well, with Mutual Majority, when X may
win, it's possible that by
adding bullet votes for X, then every other candidate
becomes able to
win.
No it isn't. (Can you give an example?)
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
By the way, it's very easy to define a single-winner method that
satisfies Mutual Majority and which elects A in the first scenario and
C in the second.
Is there any way to explain, why it isn't
completely absurd, that adding
bullet votes for X should cause other candidates to become
eligible to
win?
No.
Ok.
Why is mono-add-plump important?
Because as an election method algorithm that fails it
simply can't have any
credibility as a quasi-intelligent device (which is what it
is supposed to be)
and because satisfying it should be (and is) very cheap.
I feel that cheapness isn't relevant to whether a criterion is important,
and certainly not to whether failing it is absurd. I save the term
absurd for ideas that are bad regardless of what else is available.
Regarding your first reason: Why is it acceptable to fail mono-add-top
or Participation, but not acceptable to fail mono-add-plump? I guess
that you based this distinction almost entirely on the relative cheapness
of the criteria.
If we view CDTT somehow as an election method, then
when it fails
mono-add-plump, the bullet votes for X are not simply
strengthening
X, they are also *weakening* some pairwise victory of Y
over Z, which X
had relied upon in order to have a majority beatpath to
Z.
That just testifies to the absurdity of an algorithm
specifically putting some
special significance on majority beatpaths
versus other beatpaths.
You're saying it's absurd, but what is absurd about it? The only reason
X is allowed to win in the first place is due to a decisive YZ win
providing a path from X to Z. Why is it clear that X should be entitled
to remain a possible winner irrespective of the status of this win?
I agree it would be better if this were possible, but I don't see anything
essential about it.
Of course, you can always use the mechanics of the
method to explain why
something has happened. But it seems to me that the bullet
voters aren't
purely strengthening X, they are also weakening
Y and thereby also X.
This contention that bullet voters for X aren't
purely strengthening X but are
in some way also weakening X is completely
absurd.
The strengthening and weakening are in two different senses. The
strengthening is in terms of bullet votes. The weakening is in terms
of losing a majority beatpath to a candidate that the voters decisively
prefer.
This is an oddity inherent to beatpaths, really
I think only to beatpaths that measure defeat
strengths in a silly way.
I don't agree. Just because the use of beatpaths doesn't naturally
cause problems with mono-add-plump, doesn't mean there aren't other
oddities. Why should a candidate's ability to win, ever depend on the
strength of a contest between two other candidates?
But I contend that here in my situation 2
election Beatpath GMC does exclude
the clearly strongest candidate C.
You're attacking a lot more than just beatpath
GMC with this scenario.
Excluding C is required by SFC (the 51 B voters are
basically assured
LNHarm when voting for C, since B might be the sincere CW)
and also
basically any WV method.
Yes, you catch on quick.
It's just a bit puzzling that this thread is phrased as an attack on
beatpath GMC, if the bottom line is that beatpath GMC isn't compatible
with the positional criterion.
In other words the CDTT set can fail to include the
candidate that on overwhelming
common-sense (mostly
Re: [EM] Beatpath GMC compliance a mistaken standard?
--- On Sun, 11/1/09, Paul Kislanko kisla...@airmail.net wrote:
Arrr. Explain, someone, anyone, how MM can change an (A
B) to an (A B C)
possible winner set by adding voters for A.
One way to say this is that since in the
first example there was a set of voters
(26 AB, 25 BA) that had a mutual majority
opinion on candidate set {A, B} the winner
must come from this set. In the second
example there is no such majority set of
voters that would prefer some set of
candidates, so the criterion says nothing.
There is thus no requirement not to allow
C to win. There is also no requirement to
allow C to win.
Note also that set {A, B, C} refers to all
candidates, i.e. {A, B, C, D, ... ,Z} (if
there are more candidates than the three
mentioned three).
There are methods that meet mutual majority
and are not very good. A method that would
elect a random candidate from the set of all
candidates but limiting the choice using the
mutual majority criterion would be problematic
in in the way you mention. Bullet votes would
add C to the set of potential winners.
Typically methods that meet mutual majority
have however also other rules (or algorithm)
that would elect the most sensible candidate
from the sets {A, B} and {A, B, C}. Mutual
majority could be just one of the criteria
that the method meets.
The behaviour of the methods is also often
smooth in the sense that if there is almost
mutual majority then the method elects a
candidate that is (almost) in the mutual
majority candidate set. So, even if some
criterion may not apply in some set of votes
the criterion may still roughly point out the
direction where the winner will be found.
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
Here words Now Mutual Majority elects
{A,B,C} are a bit confusing since mutual
majority doesn't set any requirements on
who should be elected (nor elect anyone).
There also seems to be a hidden assumption
that there are no other candidates than A,
B and C. Maybe it would be clearer to just
say that any candidate can be elected (A,
B, C or any other).
Juho
P.S. Also my direct mail to you was returned
back to me (and this happened also with
Kristofer Munsterhjelm some time ago).
-Original Message-
From: election-methods-boun...@lists.electorama.com
[mailto:election-methods-boun...@lists.electorama.com] On
Behalf Of
Kristofer Munsterhjelm
Sent: Sunday, January 11, 2009 2:23 AM
To: election-meth...@electorama.com
Cc: 'Markus Schulze'
Subject: Re: [EM] Beatpath GMC compliance a
mistaken standard?
Paul Kislanko wrote:
This still makes no sense to me, since C has no more a
majority in case 2
than it had in case 1.
If mutual majority selects (A B) in case 1 and (A B C)
in case 2, it makes
no sense at all and should never be mentioned again.
Mutual majority can still be useful. Let's make an
analogy to Condorcet.
The Condorcet criterion elects the CW if there is one. In
other words,
if there is a CW and that CW is candidate X, then the set
from which
Condorcet methods elect is { X }. If there is no CW, and
the candidates
for election are {A B C ... X }, then the set from which
Condorcet
methods elect is {A B C ... X }.
Thus, Condorcet is useful when there is indeed a CW, but
does nothing
when there isn't.
So it is with mutual majority as well. When there's a
set that a
majority ranks above all the others, then a method that
passes mutual
majority must elect from that set. When there is no such
set, the method
is free to pick any candidate yet still pass mutual
majority.
In that light, mutual majority seems very reasonable
indeed: if there is
a set so that a majority prefers that set to all others
outside the set,
then a candidate within that set should be elected.
It's simply
majority transported to sets.
(And on another note, sorry for not mailing you this
directly as well,
Paul, but airmail.net seems to think my ISP is a dirty
spammer.)
Election-Methods mailing list - see
http://electorama.com/em for list info
Election-Methods mailing list - see
http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Paul,
Regarding mutual majority:
The problem is that the BA voters cannot be counted as solidly committed
to {A}. They can only be counted to {B} and {A,B}. The additional A
bullet voters can only be counted to {A}. C was excluded in scenario 1
because {A,B} possessed a majority. The new A voters increase the
requirement for a majority but don't increase the strength of {A,B}.
And {A} alone is not strong enough.
It's certainly possible to criticize that the BA voters should be
allowed to help {A} somehow.
Regarding minimal defense (and I apologize for confusing the issue if
I did so, by bringing up a second criterion):
--- En date de : Sam 10.1.09, Paul Kislanko kisla...@airmail.net a écrit :
A criterion more similar to what you have in mind, and
which I consider
more essential and effective than mutual majority, is this
rendition of
minimal defense:
If a majority of the voters vote for X and don't
vote for Y, then Y must
not win.
Although, the effect of that criterion is that {A,B} are
the possible
winners in both scenarios.
I am still not understanding. In the second scenario only A
has a majority
of voters' support. So how does B get included in the
second scenario?
A's majority support serves to disqualify C, but can't disqualify B,
because too much of A's support is also B's support. There's no majority
that votes for a common candidate and doesn't vote for B.
A criterion which said: If any candidate receives votes from a majority
of the voters, then the winner must be one of these candidates,
would be controversial because in a scenario like this:
49 AB
3 B
48 C
This hypothetical criterion would require that B be elected, when many
of us would rather say that A should win this election, because A can
defeat the other candidates pairwise. Also, if B wins, then the A voters
will feel that it wasn't safe to vote for B.
Kevin Venzke
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? JL
Hi Juho,
--- En date de : Dim 11.1.09, Juho Laatu juho4...@yahoo.co.uk a écrit :
Now Mutual Majority elects {A,B,C}.
Here words Now Mutual Majority elects
{A,B,C} are a bit confusing since mutual
majority doesn't set any requirements on
who should be elected (nor elect anyone).
...
Maybe it would be clearer to just
say that any candidate can be elected (A,
B, C or any other).
Yes, that would be clearer. However, given the subject of the thread
that this comes from, it was necessary to treat Mutual Majority as a
method and not a criterion.
If I thought it was a novel discovery that carelessly electing from
the set of candidates permissible by Mutual Majority, could violate
mono-add-plump, then I would have used better wording.
Kevin Venzke
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Juho Laatu wrote:
--- On Sun, 11/1/09, Kristofer Munsterhjelm km-el...@broadpark.no wrote:
Let's consider the first election first, with
truncation extended to full preference:
26: A B C
25: B A C
49: C A = B
A B C: 100 prefer {A B C} to the empty set
This case is interesting (not that it
would have any impact on the ongoing
mutual majority discussion but just
for theoretical interest).
The number of candidates was not exactly
stated in the example. If there are e.g.
four candidates then the votes would be:
26: A B C = D
25: B A C = D
49: C A = B = D
Set {A, B, C} has in this case no support.
Let's assume that there are also other
citizens (=potential candidates who
are however not candidates) than the
named candidates. The opinions of the
first 26 voters could be as follows.
26: X1 A B X2 C = D = X3 X4
The point here is that the voters have
not said that they would prefer A, B, C
and D to the other citizens / potential
candidates (X1, X2,...).
It is ok to say that if there are no
mutual majorities the winner can be
elected from the whole set of candidates
{A, B, C} or {A, B, C, D} or whatever set.
One can not say that the voters would
prefer the all the candidates (or those
that are named on the ballots) to other
citizens. What is the meaning of saying
that they prefer these candidates to an
empty set?
There is no real meaning - it's just an artifact of taking the process
to its conclusion. The only thing it means is that all voters who voted,
voted for the candidates they voted for, which is a tautology.
Smaller unanimity sets can only exist if there's a candidate or a
candidate set that everybody ranks last.
Also note that changing a vote from A B to X1 A B can dissolve
what would otherwise be a majority for {A B}. Mutual majority isn't
complete - it only says that in certain cases (majority support for a
set), certain things should happen (the method should elect from the
set). In that respect, it's kind of like independence of clones. You can
make a method that technically passes mutual majority yet wouldn't be
any good, just like you can prefix a method with remove clones yet it
would be a bad method if a single voter didn't vote clones in strict
clone order.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
--- On Sun, 11/1/09, Kristofer Munsterhjelm km-el...@broadpark.no wrote:
Juho Laatu wrote:
--- On Sun, 11/1/09, Kristofer Munsterhjelm
km-el...@broadpark.no wrote:
Let's consider the first election first, with
truncation extended to full preference:
26: A B C
25: B A C
49: C A = B
A B C: 100 prefer {A B C} to the empty set
This case is interesting (not that it
would have any impact on the ongoing
mutual majority discussion but just
for theoretical interest).
The number of candidates was not exactly
stated in the example. If there are e.g.
four candidates then the votes would be:
26: A B C = D
25: B A C = D
49: C A = B = D
Set {A, B, C} has in this case no support.
Let's assume that there are also other
citizens (=potential candidates who
are however not candidates) than the
named candidates. The opinions of the
first 26 voters could be as follows.
26: X1 A B X2 C = D = X3 X4
The point here is that the voters have
not said that they would prefer A, B, C
and D to the other citizens / potential
candidates (X1, X2,...).
It is ok to say that if there are no
mutual majorities the winner can be
elected from the whole set of candidates
{A, B, C} or {A, B, C, D} or whatever set.
One can not say that the voters would
prefer the all the candidates (or those
that are named on the ballots) to other
citizens. What is the meaning of saying
that they prefer these candidates to an
empty set?
There is no real meaning - it's just an artifact of
taking the process to its conclusion. The only thing it
means is that all voters who voted, voted for the candidates
they voted for, which is a tautology.
Smaller unanimity sets can only exist if there's a
candidate or a candidate set that everybody ranks last.
Also note that changing a vote from A B to X1 A
B can dissolve what would otherwise be a majority for
{A B}. Mutual majority isn't complete - it only says
that in certain cases (majority support for a set), certain
things should happen (the method should elect from the set).
In that respect, it's kind of like independence of
clones. You can make a method that technically passes mutual
majority yet wouldn't be any good, just like you can
prefix a method with remove clones yet it would
be a bad method if a single voter didn't vote clones in
strict clone order.
Yes. I wish we had a more stable definitions and terms
for discussing about criteria and how they are applied
(e.g. just to meet the criterion or also its spirit
when working outside of the defined scope of the
criterion).
Since all criteria can not be met I'd also like to have
terminology for almost meeting some criteria, and
following the spirit in most cases although not fully
and formally meeting the criterion.
(One example. Minmax(margins) doesn't meet independence
of clones nor mutual majority, but it is very close to
meeting both. It elects the candidate with weakest
opposition instead (= their strength over the defenders
when compared pairwise to any of the other candidates),
and wile following this good principle is forced to
violate the other good principles.)
All methods violate some criteria. Typically we need a
good balance of the violations and appropriate level of
violation of each criterion.
Juho
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? JL
Hi Juho, --- En date de : Dim 11.1.09, Juho Laatu juho4...@yahoo.co.uk a écrit : If there is a set of voters that form a majority and they all prefer all candidates of set A to all candidates of set B then candidates of set B should not win. This helps A (as requested) by at least eliminating some of the candidates from competing with A. This criterion may also eliminate all candidates. In such situations the rule of course will not apply. I haven't really thought what implications there are. Any comments? I would say you're close to inventing again either MDD or beatpath GMC / CDTT. All you've essentially said is that if A has a majority over B, B can't win. Because, each candidate could make up their own set. Having multiple candidates in a set doesn't make any difference. Under MDD the candidates of set B cannot be elected unless all candidates can be placed in a set B. This is inherently not cloneproof. Under beatpath GMC / CDTT the candidates of set B cannot be elected unless they have a majority-strength beatpath to all the candidates of set A. However, lacking this, the candidates of set B can also be disqualified when the candidates of set A merely have a majority-strength beatpath to the candidates of set B. A few years ago I considered a set where it wouldn't be enough for set A to merely have a beatpath to set B, in order to disqualify those candidates. But from what I remember, there were monotonicity problems. I guess there are probably clone problems also. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? JL
Ok, that relaxed version of mutual majority degraded faster to basic majority than I expected. Need to think more if there is something to conclude from the BA votes. Juho --- On Mon, 12/1/09, Kevin Venzke step...@yahoo.fr wrote: From: Kevin Venzke step...@yahoo.fr Subject: Re: [EM] Beatpath GMC compliance a mistaken standard? JL To: election-meth...@electorama.com Date: Monday, 12 January, 2009, 12:20 AM Hi Juho, --- En date de : Dim 11.1.09, Juho Laatu juho4...@yahoo.co.uk a écrit : If there is a set of voters that form a majority and they all prefer all candidates of set A to all candidates of set B then candidates of set B should not win. This helps A (as requested) by at least eliminating some of the candidates from competing with A. This criterion may also eliminate all candidates. In such situations the rule of course will not apply. I haven't really thought what implications there are. Any comments? I would say you're close to inventing again either MDD or beatpath GMC / CDTT. All you've essentially said is that if A has a majority over B, B can't win. Because, each candidate could make up their own set. Having multiple candidates in a set doesn't make any difference. Under MDD the candidates of set B cannot be elected unless all candidates can be placed in a set B. This is inherently not cloneproof. Under beatpath GMC / CDTT the candidates of set B cannot be elected unless they have a majority-strength beatpath to all the candidates of set A. However, lacking this, the candidates of set B can also be disqualified when the candidates of set A merely have a majority-strength beatpath to the candidates of set B. A few years ago I considered a set where it wouldn't be enough for set A to merely have a beatpath to set B, in order to disqualify those candidates. But from what I remember, there were monotonicity problems. I guess there are probably clone problems also. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Chris,
--- En date de : Dim 11.1.09, Chris Benham cbenha...@yahoo.com.au a écrit :
Kevin,
You wrote (10 Jan 2009):
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
Oops! (I knew that!) Sorry for falsely contradicting
you.
I guessed you must have known that.
Why is mono-add-plump important?
Because as an election method algorithm that fails it
simply can't have any credibility as a
quasi-intelligent
device (which is what it is supposed to be) and
because
satisfying it should be (and is) very cheap.
I feel that cheapness isn't relevant to whether a
criterion is important,
and certainly not to whether failing it is absurd. I save
the term
absurd for ideas that are bad regardless of
what else is available.
Well I don't. If none of the election criteria were
incompatible with each
other, wouldn't we say that nearly all of them are
important?
I don't think so. There are reasons for criteria to be important
other than how easy they are to satisfy. Otherwise why would we ever
bother to satisfy the difficult criteria?
Regarding your first reason: Why is it acceptable to
fail mono-add-top
or Participation, but not acceptable to fail
mono-add-plump? I guess
that you based this distinction almost entirely on the
relative cheapness
of the criteria.
No. With mono-add-top and Participation, the
quasi-intelligent device in
reviewing its decision to elect X gets (possibly
relevant) information about
other candidates besides X.
How can it be relevant? X was winning and X is the preferred candidate
on the new ballots.
With mono-add-plump it gets
nothing but information
about and purely in favour of X, so it has no excuse at all
for changing its mind
about electing X.
I don't think the information is purely about X. The method also learns
about indecision between Y and Z.
If we view CDTT somehow as an election method,
then when it fails
mono-add-plump, the bullet votes for X are not simply
strengthening
X, they are also *weakening* some pairwise victory of Y
over Z, which X
had relied upon in order to have a majority beatpath
to Z.
That just testifies to the absurdity of an algorithm
specifically putting some
special significance on majority beatpaths
versus other beatpaths.
You're saying it's absurd, but what is absurd
about it?
It's absurd that ballots that plump for X should in any
way be considered relevant
to the strength of the pairwise comparison
between two other candidates.
This absurdity only arises from the
algorithm specifically using (and relying on) a
majority threshold.
Instead of strength you could view it as decisiveness.
This is moot anyway, isn't it? We have Mutual Majority and beatpath GMC
displaying the same phenomenon. Clearly there's no problem since neither
criterion requires failures of mono-add-plump.
It would be better, as in less arbitrary, if you
simply criticized that beatpath GMC is
incompatible with ratings summation.
So is Condorcet. I don't think it's particularly
arbitrary to value electing a voted
Shwartz winner. I'm still a bit confused as to why
anyone would be interested in
beatpath GMC.
Well, it's a majority-rule criterion that is compatible with clone
independence and monotonicity. In the three-candidate case it's also
compatible with LNHarm. By adding a vote for your second choice, you
can't inadvertently remove your first preference from the CDTT.
So essentially, Schwartz//Approval is preferable to
any method that satisfies SMD,
Schwartz, and beatpath GMC.
Yes, much preferable to any method that satisfies
beatpath GMC period
I don't feel there's an advantage to tending
to elect candidates with more approval, because
in turn this should just make voters approve fewer
candidates when they doubt how the method
will use their vote.
And why is that a negative? I value LNHarm as an absolute
guarantee, but in inherently-
vulnerable-to-Burial Condocet methods, I think it is
better if they have a watch who you rank
because you could help elect them Approval flavour.
This is a negative because it suggests that your positional criterion
will be self-defeating. If you want to write a criterion about burial,
that would probably be better.
From your earlier post:
In the three-candidate case, at least, I think
it's a problem to elect a candidate who isn't in the
CDTT.
Why?
Because in the three-candidate case this is likely to be a failure
of MD or SFC, or close to it.
25: AB
26: BC
23: CA
26: C
In this situation 2 election from my
demonstration, can you seriously contend (with a straight
face)
that electing C is a problem?
It's not ideal. You have to use the BC votes contrary to the wishes of
those voters, and for little purpose that isn't self-defeating
considering that voters will just truncate, accomplishing the same result
as
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
Kevin Venzke wrote (10 Jan 2009):
[Situation #1]
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
[Situation #2]
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
You wrote (10 Jan 2009):
I guess I don't understand mutual majority, then,
because after adding 5 votes it takes 53 votes to
have a majority, and only A has a majority. B is
51/105 and C is 45/105.
Five bullet-votes for A appear to change (A,B) to (A).
Mutual majority says: When a majority of the voters
strictly prefers every candidate of a given set of
candidates to every candidate outside this set of
candidates, then the winner must be chosen from this
set of candidates.
column1 = set of candidates
column2 = number of voters who strictly prefer every
candidate in column1 to every candidate outside column1
For situation #1, we get:
column1 / column2
A / 26
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says that the winner must be
chosen from {A,B}.
For situation #2, we get:
column1 / column2
A / 31
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says nothing.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
How can mutual majority say nothing? Only if no combination has a
majority. But A is in the AB, BA, and new A's, so A is on 56 ballots,
which is a majority of ballots (and no one else is)
If a majority of voters (with the new voters, and where did they come from
anyway) the only candidate with a majority win is A. Using
Mutual majority says: When a majority of the voters
strictly prefers every candidate of a given set of
candidates to every candidate outside this set of
candidates, then the winner must be chosen from this
set of candidates.
we get after adding five voters from theoretical space, only A meets this
criterion.
-Original Message-
From: election-methods-boun...@lists.electorama.com
[mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Markus
Schulze
Sent: Saturday, January 10, 2009 2:45 PM
To: election-meth...@electorama.com
Subject: Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
Kevin Venzke wrote (10 Jan 2009):
[Situation #1]
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
[Situation #2]
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
You wrote (10 Jan 2009):
I guess I don't understand mutual majority, then,
because after adding 5 votes it takes 53 votes to
have a majority, and only A has a majority. B is
51/105 and C is 45/105.
Five bullet-votes for A appear to change (A,B) to (A).
Mutual majority says: When a majority of the voters
strictly prefers every candidate of a given set of
candidates to every candidate outside this set of
candidates, then the winner must be chosen from this
set of candidates.
column1 = set of candidates
column2 = number of voters who strictly prefer every
candidate in column1 to every candidate outside column1
For situation #1, we get:
column1 / column2
A / 26
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says that the winner must be
chosen from {A,B}.
For situation #2, we get:
column1 / column2
A / 31
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says nothing.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
I wrote (10 Jan 2009):
For situation #2, we get:
column1 / column2
A / 31
B / 25
C / 49
AB / 51
AC / 0
BC / 0
So mutual majority says nothing.
You wrote (10 Jan 2009):
How can mutual majority say nothing? Only
if no combination has a majority. But A is in
the AB, BA, and new A's, so A is on 56 ballots,
which is a majority of ballots (and no one else is)
There are 105 voters. So a majority
requires at least 53 voters.
I have listed all solid coalitions.
And there is no solid coalition with
at least 53 voters.
So mutual majority says nothing.
There are only 31 voters who strictly prefer
candidate A to every other candidate. And
there are only 51 voters who strictly prefer
every candidate in {A,B} to every candidate
outside {A,B}.
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Paul,
--- En date de : Sam 10.1.09, Paul Kislanko kisla...@airmail.net a écrit :
If a majority of voters (with the new voters, and where did
they come from
anyway)
You can view them as voters who are debating staying home instead of
voting. The issue is whether this can benefit them and whether it matters.
the only candidate with a majority win is A.
A criterion more similar to what you have in mind, and which I consider
more essential and effective than mutual majority, is this rendition of
minimal defense:
If a majority of the voters vote for X and don't vote for Y, then Y must
not win.
Although, the effect of that criterion is that {A,B} are the possible
winners in both scenarios.
Kevin Venzke
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
I am still not understanding. In the second scenario only A has a majority
of voters' support. So how does B get included in the second scenario?
-Original Message-
From: election-methods-boun...@lists.electorama.com
[mailto:election-methods-boun...@lists.electorama.com] On Behalf Of Kevin
Venzke
Sent: Saturday, January 10, 2009 4:07 PM
To: election-meth...@electorama.com
Subject: Re: [EM] Beatpath GMC compliance a mistaken standard?
Hi Paul,
--- En date de : Sam 10.1.09, Paul Kislanko kisla...@airmail.net a écrit :
If a majority of voters (with the new voters, and where did
they come from
anyway)
You can view them as voters who are debating staying home instead of
voting. The issue is whether this can benefit them and whether it matters.
the only candidate with a majority win is A.
A criterion more similar to what you have in mind, and which I consider
more essential and effective than mutual majority, is this rendition of
minimal defense:
If a majority of the voters vote for X and don't vote for Y, then Y must
not win.
Although, the effect of that criterion is that {A,B} are the possible
winners in both scenarios.
Kevin Venzke
Election-Methods mailing list - see http://electorama.com/em for list info
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko, you wrote (10 Jan 2009): The second scenario is 26 AB 25 BA 49 C 5 A which has 105 voters. 56 include A on any ballot and that's a majority. 51 include B, and that's not a majority. So how is B a possible winner under the second scenario? Mutual majority doesn't ask: How many voters rank all the candidates of set S? Mutual majority asks: How many voters rank all the candidates of set S ahead of all the candidates outside the set S? There are 56 voters who rank candidate A. But there are only 31 voters who rank candidate A ahead of every other candidate. Therefore, mutual majority says nothing in the scenario above. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
I ask again, in the post I replied to, it was claimed mutual majority selected (A,B,C) in the 2nd case. I wondered how that was possible, and you agree that it isn't. -Original Message- From: Markus Schulze [mailto:markus.schu...@alumni.tu-berlin.de] Sent: Saturday, January 10, 2009 8:06 PM To: kisla...@airmail.net; election-meth...@electorama.com Subject: Re: [EM] Beatpath GMC compliance a mistaken standard? Dear Paul Kislanko, you wrote (10 Jan 2009): The second scenario is 26 AB 25 BA 49 C 5 A which has 105 voters. 56 include A on any ballot and that's a majority. 51 include B, and that's not a majority. So how is B a possible winner under the second scenario? Mutual majority doesn't ask: How many voters rank all the candidates of set S? Mutual majority asks: How many voters rank all the candidates of set S ahead of all the candidates outside the set S? There are 56 voters who rank candidate A. But there are only 31 voters who rank candidate A ahead of every other candidate. Therefore, mutual majority says nothing in the scenario above. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard?
Dear Paul Kislanko,
you wrote (10 Jan 2009):
The second scenario is
26 AB
25 BA
49 C
5 A
I ask again, in the post I replied to, it was claimed
mutual majority selected (A,B,C) in the 2nd case. I
wondered how that was possible, and you agree that it
isn't.
Kevin Venzke wrote: Mutual Majority elects {A,B,C}.
I wrote: Mutual majority says nothing in the scenario
above.
There is no contradiction between Kevin Venzke and me.
When the set of candidates is {A,B,C}, then saying that
the winner is chosen from {A,B,C} (Kevin Venzke) is the
same as saying that mutual majority says nothing (Markus
Schulze).
Markus Schulze
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)
Dear Chris Benham, you are the only one who uses the fact, that criterion X doesn't imply criterion Y, as an argument against criterion X. That's the same as rejecting monotonicity for not implying independence of clones. Your argumentation is not complicated. It is simply false. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)
Dear Chris Benham, you wrote (29 Dec 2008): I think that compliance with GMC is a mistaken standard in the sense that the best methods should fail it. The GMC concept is spectacularly vulnerable to Mono-add-Plump! [Situation #1] 25: AB 26: BC 23: CA 04: C 78 ballots (majority threshold = 40) BC 51-27, CA 53-25, AB 48-26. All three candidates have a majority beat-path to each other, so GMC says that any of them are allowed to win. [Situation #2] But say we add 22 ballots that plump for C: 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-49, CA 75-25, AB 48-26. Now B has majority beatpaths to each of the other candidates but neither of them have one back to B, so the GMC says that now the winner must be B. The GMC concept is also naturally vulnerable to Irrelevant Ballots. Suppose we now add 3 new ballots that plump for an extra candidate X. [Situation #3] 25: AB 26: BC 23: CA 26: C 03: X 103 ballots (majority threshold = 52) Now B no longer has a majority-strength beat-path to C, so now GMC says that C (along with B) is allowed to win again. (BTW this whole demonstration also applies to Majority-Defeat Disqualification(MDD) and if we pretend that the C-plumping voters are truncating their sincere preference for B over A then it also applies to Eppley's Truncation Resistance and Ossipoff's SFC and GFSC criteria.) I wrote (29 Dec 2008): Your argumentation is incorrect. Example: In many scientific papers, the Smith set is criticized because the Smith set can contain Pareto-dominated candidates. However, to these criticisms I usually reply that the fact, that the Smith criterion doesn't imply the Pareto criterion, is not a problem as long as the used tie-breaker guarantees that none of these Pareto-dominated candidates is elected. It would be a problem only if the Smith criterion and the Pareto criterion were incompatible. You made the same mistake as the authors of these papers. You didn't demonstrate that the GMC concept is spectacularly vulnerable to mono-add-plump. You only demonstrated that beatpath GMC doesn't imply mono-add-plump. However, the fact, that Schulze(winning votes) satisfies mono-add-plump and always chooses from the CDTT set and isn't vulnerable to irrelevant ballots, shows that these properties are not incompatible. In all three situations, Schulze(winning votes) chooses candidate B. Therefore, you demonstrated neither a spectacular failure of mono-add-plump nor a vulnerability to irrelevant ballots for methods that satisfy beatpath GMC. You wrote: All three candidates have a majority beatpath to each other, so GMC says that any of them are allowed to win. No! Beatpath GMC doesn't say that any of them are allowed to win; beatpath GMC only doesn't exclude any of them from winning. Similarly, the Smith criterion doesn't say that even Pareto-dominated candidates must be allowed to win; that would have meant that the Smith criterion and the Pareto criterion were incompatible; the Smith criterion only doesn't imply the Pareto criterion. You wrote (8 Jan 2009): I can't see that the distinction between allowed to win and not excluded from winning is anything more than that between the glass is half full and the glass is half empty, so I reject your semantic quibble. Any candidate that a criterion C doesn't exclude from winning is (as far as C is concerned) allowed to win. Statement #1: Criterion X does not imply criterion Y. Statement #2: Criterion X and criterion Y are incompatible. Statement #1 does not imply statement #2. But in your 29 Dec 2008 mail, you mistakenly assume that statement #1 implies statement #2. Example: X = Smith criterion. Y = Pareto criterion. Then statement #1 is true and statement #2 is false. The fact, that statement #1 does not imply statement #2, is not semantic quibble. You proved only that beatpath GMC does not imply mono-add-plump; but then you mistakenly concluded that this means that beatpath GMC and mono-add-plump were incompatible (spectacularly vulnerable to mono-add-plump, spectacular failure of mono-add-plump). However, the fact, that Schulze(winning votes) satisfies beatpath GMC and mono-add-plump, demonstrates that these two criteria are not incompatible. Example: The Smith criterion does not imply the Pareto criterion; that means that it can happen that a Pareto-dominated candidate is not excluded from winning by the Smith criterion. However, this doesn't mean that the Smith criterion implies that even Pareto-dominated candidates must be allowed to win. You wrote (8 Jan 2009): Perhaps you misunderstand my use of the word concept. Beatpath GMC says that the winner must come from a certain set S, but a candidate X can fall out of S if a relatively large number of new ballots are added, all plumping (bullet-voting) for X. Is there any other
