Discussion:
"Unmanipulable Majority" strategy criterion
Chris Benham
2008-11-26 18:21:10 UTC
Permalink
I have a suggestion for a new strategy criterion I might call 
"Unmanipulable Majority".

*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B
the winner by altering any of the ballots on which B is voted
above A.*

Does anyone else think that this is highly desirable?

Is it new?

Chris Benham


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Kristofer Munsterhjelm
2008-11-27 18:43:45 UTC
Permalink
I have a suggestion for a new strategy criterion I might call
"Unmanipulable Majority".
*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B
the winner by altering any of the ballots on which B is voted
above A.*
Does anyone else think that this is highly desirable?
Is it new?
I think it's new. I won't say anything about the desirability because I
don't know what it implies; it could be too restrictive (like
Consistency) for all I know.

It would be possible to extend this to a set. For instance: "if the
method elects from a set w, then it must not be possible to make a
candidate X outside w the winner by modifying ballots on which X is
ranked above all in w".

Or a more general case, with constructive and destructive burial.
Constructive burial would be trying to make Y win instead of X.
Destructive burial would be trying to make X not win, though in that
case you would have to consider what kind of ballots could be changed,
since there's no equivalent of B in the destructive burial case.
Destructive burial also sounds too strict, that no useful method could
fulfill it (unless only very specific ballots were permitted to be
changed, e.g those who rank X last).
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Chris Benham
2008-11-28 15:30:24 UTC
Permalink
Kristofer,
Thanks for at least responding.

"...I won't say anything about the desirability because I  don't know what it implies;.."

Only judging criteria by how they fit in with other criteria is obviously circular.

Do you (or anyone) think that judged in isolation this strategy criterion is desirable?

It is true that some desirable/interesting criteria are so "restrictive" (as you put it) that
IMO  compliance with them can only be a redeeming feature of  a method that isn't
one of the best.  (I  put Participation in that category.)

Maybe some people would like me to paraphrase this suggested criterion in language
that is more EM-typical:

'If candidate A majority-strength pairwise beats candidate B, then it must not be possible for B's
supporters (pairwise versus A) to use Burial or Pushover strategy to change the winner from A
to B.'

"Destructive burial would be trying to make X not win,..."

Your "destructive burial"  looks  almost synonymous with *monotonicity*.

Chris Benham
 
 
I have a suggestion for a new strategy criterion I might call
"Unmanipulable Majority".
*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B
the winner by altering any of the ballots on which B is voted
above A.*
Does anyone else think that this is highly desirable?
Is it new?
I think it's new. I won't say anything about the desirability because I
don't know what it implies; it could be too restrictive (like
Consistency) for all I know.

It would be possible to extend this to a set. For instance: "if the
method elects from a set w, then it must not be possible to make a
candidate X outside w the winner by modifying ballots on which X is
ranked above all in w".

Or a more general case, with constructive and destructive burial.
Constructive burial would be trying to make Y win instead of X.
Destructive burial would be trying to make X not win, though in that
case you would have to consider what kind of ballots could be changed,
since there's no equivalent of B in the destructive burial case.
Destructive burial also sounds too strict, that no useful method could
fulfill it (unless only very specific ballots were permitted to be
changed, e.g those who rank X last).



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Raph Frank
2008-11-28 17:06:42 UTC
Permalink
I think you have alot of redundant language, is the criterion
effectively the following?

If the winner is preferred to another candidate on the majority of the
ballots, it must not be possible to make any such candidate win by
modifying the ballots where that candidate is preferred to the winner.

By requiring that at least 3 levels are possible, you are effectively
forcing lots of methods to fail. Also, just because most methods
would meet the criterion in the 2 candidate case isn't a reason to
exclude that case.
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Kevin Venzke
2008-11-28 18:06:33 UTC
Permalink
Hello,
Post by Raph Frank
By requiring that at least 3 levels are possible, you are
effectively
forcing lots of methods to fail.
I'm sure that's the intention, though I'm not sure why. The criterion
wants to limit "cheating" in a sense, and methods like FPP are hard to
cheat under.

I have no problem with the approach... I use a somewhat convoluted
framework to explain why strictly-ranked methods (with no equal ranking
permitted) don't satisfy my take on votes-only FBC, but if I wanted to
be understood quickly I could also just say that a method must allow
equal ranking to satisfy the criterion.
Post by Raph Frank
Also, just because most
methods
would meet the criterion in the 2 candidate case isn't
a reason to
exclude that case.
I'm puzzled on this point also because satisfying the criterion in one
case isn't enough to satisfy it overall, so why state it. I think the
intention must be to just say that three levels are not required, in
cases where there are not three candidates.

Kevin Venzke



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Kristofer Munsterhjelm
2008-11-28 18:57:47 UTC
Permalink
Post by Chris Benham
Kristofer,
Thanks for at least responding.
"...I won't say anything about the desirability because I don't know
what it implies;.."
Only judging criteria by how they fit in with other criteria is obviously circular.
That's true. If we're going to judge criteria by how they fit in with
other criteria, we should have an idea of how relatively desirable they are.

It may also be the case that it the tradeoff would be too great, by
reasoning similar to what I gave in the reply to Juho about your
Dominant Mutual Quarter Burial Resistance property. But if we consider
this in more detail, we don't really know whether such tradeoffs are too
great for, for instance, cloneproof criteria (though I think they are not).
Post by Chris Benham
Do you (or anyone) think that judged in isolation this strategy criterion is desirable?
It is true that some desirable/interesting criteria are so "restrictive"
(as you put it) that
IMO compliance with them can only be a redeeming feature of a method
that isn't
one of the best. (I put Participation in that category.)
In isolation (not affecting anything else), sure. It's desirable because
it limits the burying tricks that can be done.

If you're asking whether I think it's more important than being, say,
cloneproof, I don't think I can answer at the moment. I haven't thought
about the relative desirability of criteria, though I prefer Condorcet
methods to be both Smith and cloneproof.
Post by Chris Benham
Maybe some people would like me to paraphrase this suggested criterion in language
'If candidate A majority-strength pairwise beats candidate B, then it
must not be possible for B's
supporters (pairwise versus A) to use Burial or Pushover strategy to
change the winner from A
to B.'
The mention of pushover strategy there would mean that the method would
have to have some degree of monotonicity, I assume.
Post by Chris Benham
"Destructive burial would be trying to make X not win,..."
Your "destructive burial" looks almost synonymous with *monotonicity*.
Hm, not necessarily. Without qualifications on the criterion,
destructive burial would be constructive burial for *any* candidate, but
also more than that. If A>X voters can cause A to win by rearranging
their ballots, then that would be a form of constructive burial. If, for
instance, some subset of the voters who place X fifth can keep X from
winning by rearranging their first-to-fourth preferences, then that
would be destructive burial.
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Kevin Venzke
2008-11-28 17:57:37 UTC
Permalink
Hi Chris,

--- En date de : Mer 26.11.08, Chris Benham <***@yahoo.com.au> a écrit :
I have a suggestion for a new strategy criterion I might call 
"Unmanipulable Majority".
 
*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B
the winner by altering any of the ballots on which B is voted
above A.*

Does anyone else think that this is highly desirable?
 
Is it new?
[end quote]

I think it's probably new. I have a reservation about how desirable it
is, because you're guaranteeing that this A (preferred by a majority to
B) can hang on to his win, but only when A would win in the first place.
It's hard for me to judge whether A ought to be able to continue to
win when I don't know why he won in the first place. It seems to me I'd
rather state why A's original win should be guaranteed. (I think this
direction may lead to SFC or votes-only SFC.)

All things being equal it is desirable, of course.

Kevin Venzke



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Chris Benham
2008-11-28 18:23:31 UTC
Permalink
Raph,

*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B
the winner by altering any of the ballots on which B is voted
above A.*


"....is the criterion effectively the following?

If the winner is preferred to another candidate on the majority of the
ballots, it must not be possible to make any such candidate win by
modifying the ballots where that candidate is preferred to the winner."

Yes.

"By requiring that at least 3 levels are possible, you are effectively
forcing lots of methods to fail."

Such as?  It is news to me that there are "lots of methods" with ballot
rules that restrict the voter to fewer than three preference-levels.

In the past I've encountered arguments along the lines that Approval
(and/or  vote-for-one plurality) meets some criterion (that it obviously
doesn't) because the ballot rules don't allow me to give an example of
it failing.

So  I've developed the habit of taking care to side-step such sophistry.

My reference to "more than two candidates" was  partly about that I
don't mind if the ballot-rules prevent the voters from expressing more
preference-levels than there are candidates.

Thanks for taking an interest.

Chris Benham




Raph Frank wrote (Fri.Nov.28):
I think you have alot of redundant language, is the criterion
effectively the following?

If the winner is preferred to another candidate on the majority of the
ballots, it must not be possible to make any such candidate win by
modifying the ballots where that candidate is preferred to the winner.

By requiring that at least 3 levels are possible, you are effectively
forcing lots of methods to fail. Also, just because most methods
would meet the criterion in the 2 candidate case isn't a reason to
exclude that case.


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Chris Benham
2008-11-29 16:11:26 UTC
Permalink
Kristofer,

"...your Dominant Mutual Quarter Burial Resistance property."

I don't  remember reading or hearing about anything like that with "Quarter" in the title
anywhere except in your EM  posts.

A few years ago  James Green-Armytage coined the "Mutual Dominant Third" criterion
but never promoted it.  I took it up, but sometimes mistakenly reversed the order of the first
two words. I now think the original order is better, because MDT is analogous with the
better-known older Mutual Majority criterion.

I do remember suggesting  what is in effect "MDT Burial Resistance", because there is an
ok method that meets it while failing Burial Invulnerability: namely Smith,IRV.

I don't know of any method that meets  the MDQBR you refer to that isn't completely in
invulnerable to Burial (do you?), so I don't see how that criterion is presently useful.

In response to my question "is Unmanipulative Majority desirable?"  you wrote:

"In isolation (not affecting anything else), sure. It's desirable because  it limits the burying
tricks that can be done."

I'm glad you think so.

"The mention of pushover strategy there would mean that the method would
have to have some degree of monotonicity, I assume."

Yes.

"If A>X voters can cause A to win by rearranging  their ballots, then that would be a
form of constructive burial. If, for instance, some subset of the voters who place X
fifth can keep X from winning by rearranging their first-to-fourth preferences, then that
would be destructive burial."

If those voters are sincere in ranking X fifth, i.e they sincerely prefer all the candidates
they rank above X to X; then I can't see that that qualifies as "Burial" strategy at all.

Normally the strategy you refer to would qualify as some form of  Compromise strategy.
(Do you have an example that doesn't?)

Chris Benham
Post by Chris Benham
Kristofer,
Thanks for at least responding.
"...I won't say anything about the desirability because I don't know
what it implies;.."
Only judging criteria by how they fit in with other criteria is
obviously circular.
That's true. If we're going to judge criteria by how they fit in with
other criteria, we should have an idea of how relatively desirable they are.

It may also be the case that it the tradeoff would be too great, by
reasoning similar to what I gave in the reply to Juho about your
Dominant Mutual Quarter Burial Resistance property. But if we consider
this in more detail, we don't really know whether such tradeoffs are too
great for, for instance, cloneproof criteria (though I think they are not).
Post by Chris Benham
Do you (or anyone) think that judged in isolation this strategy
criterion is desirable?
It is true that some desirable/interesting criteria are so "restrictive"
(as you put it) that
IMO compliance with them can only be a redeeming feature of a method
that isn't
one of the best. (I put Participation in that category.)
In isolation (not affecting anything else), sure. It's desirable because
it limits the burying tricks that can be done.

If you're asking whether I think it's more important than being, say,
cloneproof, I don't think I can answer at the moment. I haven't thought
about the relative desirability of criteria, though I prefer Condorcet
methods to be both Smith and cloneproof.
Post by Chris Benham
Maybe some people would like me to paraphrase this suggested criterion
in language
'If candidate A majority-strength pairwise beats candidate B, then it
must not be possible for B's
supporters (pairwise versus A) to use Burial or Pushover strategy to
change the winner from A
to B.'
The mention of pushover strategy there would mean that the method would
have to have some degree of monotonicity, I assume.
Post by Chris Benham
"Destructive burial would be trying to make X not win,..."
Your "destructive burial" looks almost synonymous with *monotonicity*.
Hm, not necessarily. Without qualifications on the criterion,
destructive burial would be constructive burial for *any* candidate, but
also more than that. If A>X voters can cause A to win by rearranging
their ballots, then that would be a form of constructive burial. If, for
instance, some subset of the voters who place X fifth can keep X from
winning by rearranging their first-to-fourth preferences, then that
would be destructive burial.



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Kristofer Munsterhjelm
2008-11-29 19:42:55 UTC
Permalink
Post by Chris Benham
Kristofer,
"...your Dominant Mutual Quarter Burial Resistance property."
I don't remember reading or hearing about anything like that with
"Quarter" in the title anywhere except in your EM posts.
A few years ago James Green-Armytage coined the "Mutual Dominant Third"
criterion
but never promoted it. I took it up, but sometimes mistakenly reversed
the order of the first
two words. I now think the original order is better, because MDT is analogous with the
better-known older Mutual Majority criterion.
I do remember suggesting what is in effect "MDT Burial Resistance",
because there is an
ok method that meets it while failing Burial Invulnerability: namely Smith,IRV.
I don't know of any method that meets the MDQBR you refer to that isn't
completely in
invulnerable to Burial (do you?), so I don't see how that criterion is presently useful.
That's odd, because the example I gave in a reply to Juho was yours.
http://listas.apesol.org/pipermail/election-methods-electorama.com/2006-December/019097.html

Note that the method of that post (which I've been referring to as
"first preference Copeland") is neither monotonic nor cloneproof,
although it was claimed to be both. Perhaps it'd be possible to make a
variant of it in some way, though, so that it's both, but it seems that
Burial resistant Condorcet methods tend to be nonmonotonic (unless you
consider Black to resist burial).

This leads me to wonder what monotonic preference ordering methods exist
(that is, methods where A>B differs from A, unlike FPTP), and whether
any of those, modified with one of the minimal "Condorcet-ifying" tweaks
(Condorcet, else; limit to Smith; Smith,,) would also resist burial.
Post by Chris Benham
"If A>X voters can cause A to win by rearranging their ballots, then
that would be a
form of constructive burial. If, for instance, some subset of the voters who place X
fifth can keep X from winning by rearranging their first-to-fourth preferences, then that
would be destructive burial."
If those voters are sincere in ranking X fifth, i.e they sincerely
prefer all the candidates
they rank above X to X; then I can't see that that qualifies as "Burial" strategy at all.
Normally the strategy you refer to would qualify as some form of
Compromise strategy.
(Do you have an example that doesn't?)
I see; yes, it would be a compromise strategy. Perhaps a better kind
would be a setwise constructive burial. Set-limited constructive burial
would take your unmanipulable majority criterion to a set, but the
question is whether, for

"If A is ranked above one or more{1} in S by a majority of the ballots,
then there should be no way for those who rank any{2} in S above A to
rearrange their ballots so that someone in S wins",

if {1} should be "one or more" or "all", and if {2} should be "any" or
"all".

In any event, we could then proceed to create another form of
destructive burial where S is simply the set of all candidates minus the
winner. For that criterion to have any power, {1} should probably be
"one or more" and {2} "any", but then it would seem to be overly
restrictive. So I tried to add the restriction that the strategists
can't add candidates to "push" A lower, but that, as you point out,
turns it into a compromising strategy.

The general idea of destructive burial as a strategy would be "anybody
but Bush" camps cooperating to push off Bush, not minding who they get
instead. You can see the compromising even there; the kind of reasoning
that would lead to such strategy would be "this evil is really evil, I
don't care who I get as long as I don't get this guy", which is a
lesser-evil compromise. You can probably also see that the scenario
would be pretty unrealistic for most real elections, since there'll
always be very minor candidates that nobody wants to have elected,
therefore such a campaign would never be purely destructive burial.
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Abd ul-Rahman Lomax
2008-12-02 21:47:54 UTC
Permalink
I have a suggestion for a new strategy criterion I might call
"Unmanipulable Majority".
*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B
the winner by altering any of the ballots on which B is voted
above A.*
Does anyone else think that this is highly desirable?
Compared to what?

Chris, you know I have a high level of suspicion about all the
"election criteria," though monotonicity seems pretty basic, I mean
it is highly offensive to me that one could cause a candidate to lose
by voting for the candidate.

The Majority Criterion and the Condorcet Criterion, once consider
no-brainers, turn out to be quite defective, preventing an optimal
election outcome, i.e., there are situations, fairly easy to
describe, where all of us would agree that there was a better outcome
than the first preference of a majority or the pairwise winner. It
is, of course, a different question as to whether or not these
criteria are important for large public elections, but voting systems
theory is about *all* elections, not just public ones.

However, what are the implications of this criterion?

Here is what it does.

Range ballot, the only kind that can get around Arrow's Theorem (in
substance). The only kind that directly expresses preference
strength. I can modify the Range method to satisfy the criterion, but
it then becomes a non-deterministic method. WTF are we always wanting
a deterministic method, when this is the major stumbling block to
finding democratically ideal winners?

Anyway, let's just look at two candidates. There are others which
explain the range of votes, but we only need to look at two.

51: A 5, B 4
49: A 4, B 5

A is rated (equivalent to ranked) above B on a majority of ballots.
Alter the 49% to

49: A 0, B 10.

B wins, by a landslide, actually. Was this a better result than if A
continued to win?

Elections like this, with realistic examples behind them, are the
reason why the Majority Criterion, which this is a variation on, are
suspect. Let's assume that those ratings are sincere, in both cases.
In the first case A is, from the votes, a reasonable winner, but it
is close. In the second case, A is *not* a reasonable winner, and
there is a high likelihood that a majority of voters, in a real
runoff, would vote for B.

I've explained elsewhere why.

Allowing weak preferences to overcome strong preference is an obvious
error! It is *not* what we do in real deliberative process or in
making personal decisions, particularly in small groups.

Range does not satisfy the Majority Criterion, and no method which
considers and uses preference strength can, except by a trick.

In the election I described, because preference analysis shows that a
majority preferred a candidate other than the Range winner, I'd have
the election fail. Further process is necessary.

The common way is with a runoff election, where the top two are
listed on the ballot. There are possible variations on this; I have,
for example, proposed that the runoff between the Range winner and a
candidate who is preferred by a majority to the Range winner (if
there exist more than one such -- that should be extraordinarily rare
-- I'd make it be between the Range winner and the highest
sum-of-ratings Condorcet winner or member of the Smith set. I.e., I'd
use the ratings to resolve any Condorcet cycle.

These runoffs would be rare, usually Range chooses the Condorcet winner.

I have also argued that, usually, the Range winner would beat the
Condorcet winner in a real, delayed runoff, because of preference
strength considerations, which affect turnout and which also affect
how many voters change their minds. Have a weak preference -- which
is the situation here -- and it's more likely you will change your
mind. Both of these effects favor the Range winner. Only if the Range
results were distorted, perhaps by unwise strategic voting, would the
Condorcet winner prevail.

This trick turns the overall method into one which satisfies the
Majority Criterion, because that criterion applies, properly, to the
runoff. The first election, really, failed. But it guided ballot
placement in the second, perhaps, and the majority favorite was
guaranteed position on that ballot. All the majority has to do is
persist a little. But they will usually, in a healthy society, I'd
submit, step aside. They will collectively say, well, if you want
that outcome so badly, be our guest. I'm sure you will return the
favor someday.

And that is how real elections in real societies that value unity and
cooperation actually work. Fortunately, the world doesn't run only by
the kind of political division and confrontation that we are accustomed to.

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Chris Benham
2008-12-06 16:56:44 UTC
Permalink
Kristofer,
You wrote addressing me:
"You have some examples showing that RP/Schulze/"etc" fail the criterion."

By my lazy "etc." I just meant  'and the other Condorcet methods that are
all equivalent to MinMax when there are just 3 candidates and Smith//Minmax
when there are not more than 3 candidates in the Smith set'.

"Do they show that Condorcet and UM is incompatible? Or have they just
been constructed on basis of some Condorcet methods, with differing
methods for each?"

My intention was to show that all the methods that take account of more than
one possible voter preference-level (i.e. not Approval or FPP) (and are
well-known and/or advocated by anyone on EM) are vulnerable to UM except
SMD,TP.

"I think I remember that you said Condorcet implies some vulnerability to
burial. Is that sufficient to make it fail UM?"

Probably yes, but I haven't  tried to prove as much.

Returning to this demonstration:


93: A
09: B>A
78: B
14: C>B
02: C>A
04: C
200 ballots

B>A  101-95,  B>C 87-20,  A>C 102-20.
All Condorcet methods, plus MDD,X  and  MAMPO and  ICA elect B.

B has a majority-strength pairwise win against A, but say 82 of the 93A change to
A>C  thus:

82: A>C
11: A
09: B>A
78: B
14: C>B
02: C>A
04: C

B>A  101-95,  C>B 102-87,  A>C 102-20
Approvals: A104, B101, C102
TR scores: A93,   B87,   C 20

Now MDD,A and MDD,TR and MAMPO and ICA and  Schulze/RP/MinMax etc. using
WV or Margins elect A.  So all those methods fail the UM criterion.

Working in exactly the same way as ICA (because no ballots have voted more than one candidate
top), this also applies to  Condorcet//Approval and Smith//Approval and Schwartz//Approval.
So those methods also fail UM.

"I did a bit of calculation and it seems my FPC (first preference
Copeland) variant elects B here, as should plain FPC. Since it's
nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure
whether that can be fixed at all."

My impression is/was that in 3-candidates-in-a-cycle examples that method behaves just like IRV.
The demonstration that I gave of  IRV failing UM certainly also applies to it. 


Chris Benham
 
*If (assuming there are more than two candidates) the ballot
rules don't constrain voters to expressing fewer than three
preference-levels, and A wins being voted above B on more
than half the ballots, then it must not be possible to make B>the winner by altering any of the ballots on which B is voted
above A without raising their ranking or rating of B.*
 
To have any point a criterion must be met by some method.
 
It is met by my recently proposed SMD,TR method, which I introduced
*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).
Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).
Elect the undisqualified candidate with the highest top-ratings score.*
 
[snip examples of methods failing the criterion]

You have some examples showing that RP/Schulze/"etc" fail the criterion.
Do they show that Condorcet and UM is incompatible? Or have they just
been constructed on basis of some Condorcet methods, with differing
methods for each?

I think I remember that you said Condorcet implies some vulnerability to
burial. Is that sufficient to make it fail UM? I wouldn't be surprised
if it is, seeing that you have examples for a very broad range of
election methods.
93: A
09: B>A
78: B
14: C>B
02: C>A
04: C
200 ballots
B>A  101-95,  B>C 87-20,  A>C 102-20.
All Condorcet methods, plus MDD,X  and  MAMPO and  ICA elect B.
B has a majority-strength pairwise win against A, but say 82 of the 93A
change to
82: A>C
11: A
09: B>A
78: B
14: C>B
02: C>A
04: C
 
B>A  101-95,  C>B 102-87,  A>C 102-20
Approvals: A104, B101, C102
TR scores: A93,   B87,   C 20
 
Now MDD,A and MDD,TR and MAMPO and ICA and  Schulze/RP/MinMax etc. using
WV or Margins elect A.  So all those methods fail the UM criterion.
I did a bit of calculation and it seems my FPC (first preference
Copeland) variant elects B here, as should plain FPC. Since it's
nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure
whether that can be fixed at all.



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