Re: [EM] ASM Decisions
Also ...
The Approval Order is essential for finding the order of finish beyond
first place ... first to last with the important Reverse Symmetry property
that is lacking in most other methods.
Approval gives voters the opportunity to get the candidates in roughly the
right order by emphasizing the most important distinctions between
acceptable and unacceptable ... then the pairwise adjustments applied to
the adjacent pairs where the approval order is not as definite (where the
approval margins are statistically less signicant) is a refinement, and
insurance that the Burlington Vermont embarrassment of IRV is impossible
under ASM. It would be technically possible to miss the CW without the
pairwise sorting, but only barely ... quite unlikely ... even with a total
lack of sophistication among voters.
Therefore, as you say, the sorting is a redundant backup ... a safety net
for the sincere Condorcet Candidate. It is redundant, but at no extra cost
... it's free like the symmetry compliant order of finish.
People are always oohing and awing about Kemeny-Young as a supposedly ideal
Condorcet method with Reverse Symmetry, but it cannot hold a candle to ASM
because (1) it is computationally intractable, (2) it fails clone
independence, and (3) it does not take voter preference strengths into
account (because the K-Y ballots do not register that kind of
information)... not even as much as Ranked Pairs, because K-Y requires
complete rankings ... no equal ranks ... no truncations, etc. .... that
allow other Condorcet methods to show a little bit of relative strength of
preference ... though not as simply and directly as ASM.
Supposedly KY is hard to manipulate because it is hard to compute, but that
is a superstitution ... it does nothing to prevent crowding, burial, etc.
The basic defenses against burial are not even available, as can be seen in
the three candidate case ... are we supposed to believe that as the number
of candidates increases that new burial defenses magically appear out of
nowhere?
FWS
El mié., 27 de oct. de 2021 9:57 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:
El mié., 27 de oct. de 2021 9:19 p. m., Ted Stern dodecatheon@gmail.com
escribió:
Hi Forest,
I've been thinking about the modified version of ASM. I think it should
be called Preferred-Acceptable-Insufficient-Reject Sorted
Margins, or PAIR-SM. I don't like movable demarcations, and I think more
than 3 levels within each category would be excessive, so I would go with
10 total levels (score 0 to 9, rank inferred from rating): scores 9, 8, 7
are Preferred, scores 6, 5, 4 are Acceptable, scores 3, 2, 1 are
Insufficient (formerly "compromise": the voter finds candidates at this
level distasteful, but better than the alternative) and score 0 is reject.
And blank is counted as zero, too.
Preferred ratings get 10 points, Acceptable ratings get 5 points,
Insufficient candidates get 0 points but have pairwise votes over lower
rated Insufficient candidates and all Rejected candidates. Then Sorted
margins is run using those points.
PAIR-SM could also be run with only 2 levels within each of the approved
categories, for a total of 7 levels, if you want to retain an odd number of
ratings.
Small scale elections could get by with seven levels, but rigid
demarcations work better with ten imho.
The one problem I've had on the EndFPTP subreddit is explaining how the
ranking is more important than approval. While the Approval level is in
fact what sets up the seed ordering, it is practically irrelevant unless
there is a Condorcet cycle. It's a little hard to explain that the Approval
rating is more of an insurance that it won't be needed.
On Wed, Oct 27, 2021 at 6:31 PM Forest Simmons <
forest.simmons21@gmail.com> wrote:
I prefer Ted Stern's version of Approval Sorted Margins over any other
single-winner public proposal I've seen lately, other than simple asset
voting as proposed by Charles Dodgson in the 19th century, and more
recently a symmetrical version of Majority Judgment currently in the works
if it can be simplified adequately w/o sacrificing its integrity.
Ted's version of ASM uses a version of what we used to call "3-slot
approval" to seed the finish order which is then sorted pairwise with
pairs that show the least discrepancy in their 3-slot scores getting
priority for pairwise rectification. It is important to note that the
ordinal information is inferred from six slots, twice as many as those used
for the cardinal seeding.
This is valuable for several (including psychological) reasons. One is
that 3-slots are not enough for the ordinal information to fully
distinguish the pairwise preferences important to the voters. But
increasing the score slots (as in STAR) is not the answer, for several
reasons ... STAR voters aware of optimal approval strategy (vote only at
the extremes) would feel too much tension between the need to make use of
the intermediate score levels for ordinal information and the need to avoid
those levels for optimal cardinal strategy.
But for non-perfect information elections, even sophisticated approval
voters might welcome a middle slot.
I like three slots because, personally I would reserve the top and
bottom slots for definite approvals and disapproval, respectively. [Bottom
also takes care of blank or no opinion to obviate darkhorse candidates].
How do you know if you "definitely" approve or disapprove of a candidate?
Easy ... if you don't know that you do, then you don't. If you are not
sure, or if you have to ask, then your approval or disapproval is
definitely not definite.
So it's easy to know how to vote honestly under that rule, which should
be part of the instructions to the voters.
People who think they can out wit the devil may be tempted to vote
dishonestly, but at least they have the option of voting honestly if those
"definite instructions" are the official instructions.
So Ted Stern's version of ASM is one of the best possible public
proposals IMHO.
However personally, I would rather have it implemented in the format of
a Ranked Ranking ballot, so that the voter has more freedom in defining the
cutoffs demarcating the three slots, and making more ordinal distinctions
within the three approval levels if needed to distinguish among clones in a
large election:
A>B1>B2>C>>U>V>W1>W2>W3>>X>Y>Z...
BORDA is quoted as saying that his method was only intended for "honest
men." But honestly would not fix the greater design flaw ... clone
dependence ... in particular, clone loser. Cardinal Ratings is a partial
solution ... with all of the caveats expressed in Kristofer's reservations.
A solution nearer to the spirit of Borda would be a point system based
on Ranked Rankings.
Borda can be thought of as a way of converting rankings into a
score/point system ... sacrificing clone dependence.
A minimal tweak of Borda (to restore clone independence) would be to
base a point system on Ranked Rankings ... with weaker rankings reflected
in smaller point/score gaps.
This idea is not my favorite way of using Ranked Rankings ... but it may
help some people to see the value of a different kind of ordinal ballot ...
more expressive than ordinary rankings without the strategic and
psychological burden (including cognitive dissonance) of the (obviously
exaggerated) implied numerical precision of ratings.
El mar., 26 de oct. de 2021 8:26 a. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:
On 10/25/21 2:35 AM, fdpk69p6uq@snkmail.com wrote:
Why does their identity matter? Discuss the facts, not ad hominems.
Also, I'm surprised and a bit saddened that you haven't come around
to
cardinal systems yet. :/
The goal of democracy is to elect the candidate who best represents
the
will of the voters. My near-indifference between two candidates
shouldn't arbitrarily be given the same weight as your strong
preference
between them.
Let me make a ranked voting advocate (ordinalist?) argument here. I'll
be referring to "simple cardinal methods", by which I mean things like
Range, and not so much things that I'm fumbling towards in my utility
posts.
Cardinal supporters tend to use two arguments to argue for the
superiority of cardinal methods over ordinal ones.
The first is that cardinal methods support strength of preference; and
the second is that, because they pass FBC (and IIA), they inherently
are
more robust to strategy.
My response to these are, much abbreviated, that first, the "strength
of
preference" that these methods gather is probably ambiguous, and if it
weren't, it would come with significant disadvantages.
And second, that the methods' IIA and FBC compliance take a form that
shoves what used to be tactical voting into a mush that's kind of
honest, kind of not; and that once that's made clear, it's obvious that
the methods no longer achieve the impossible. But because it doesn't
look like ranked voting strategy, cardinal advocates can shift between
a
position that the methods permit everybody to vote "honestly" (an easy
position) and that the methods are strategy-proof (a hard, incorrect
position).
So for the first point, let's use Range as the standard cardinal
method.
Range asks for a set of ratings that are intended to represent utility,
so that your rating is proportional to the utility you achieve from
seeing this candidate elected. That's what's being demonstrated in
examples like the pizza election: that the meat eaters show that their
utility from getting mushroom pizza is not that far off from the
utility
of getting pepperoni, so that the method elects the pizza that
satisfies
all.
But here's a problem. I can't know that my scale is calibrated the same
way as yours. In philosophy, this is known as the problem of
incommensurability. Suppose I happen to feel more pleasure (and pain)
than you, but due to growing up in the same society as you, I
mistakenly
appear to use the same scale as you. It's then quite hard to know that
when I say 6/10 I mean what you would consider twice as good as that.
At first it would seem, though, that Range has dodged a bullet. Because
if utility were directly comparable on an absolute scale, then there
might exist "pleasure wizards"[1] who obtain so much utility from a
choice that they effectively become dictators. By insisting on a 0-1
scale (in its continuous version), Range limits the power any one voter
has and so enforces a weak type of one man, one vote. It is what I
called a type three method - voters might voluntarily decide to forego
some of their power to make the outcome better for others (again, as in
the pizza election).
But the problem with this is that Range supposes that there's a common
scale where there isn't. As a consequence, the concept of just what is
a
honest vote becomes blurred. E.g. suppose that I consider the sure
election of Y to be equally good as a 50-50 shot of either X or Z
winning. Do I rate X 1, Y 0.5, and Z 0? Or do I rate X 0.5, Y 0.25, and
Z 0? Because there's no way to answer that question (unless it somehow
becomes possible to get at utility information), there's more than one
honest vote, and a honest voter is faced with the burden of having to
decide which one. (It is assumed that voters will answer the question
by normalizing[2], but this leads to strategy problems which I'll get
to.)
My attempts to generalize STAR came from asking "what if we want to be
truly honest about what information it makes sense to ask of voters,
while respecting OMOV?". Well, we could ask the voters about
preferences
over lotteries (as the 50-50 vs certainty example above). Doing so, the
method acknowledges the ambiguity of comparing utility. Perhaps there's
more we can do - e.g. by following MJ's reasoning of a common standard,
or by separating "worse than nothing happening" events from "better
than
nothing happening" ones.
But all of this is better than just saying "it means what you want it
to
mean", and then sweeping the resulting ambiguity in honest voters under
the carpet.
As for the point that e.g. Range is superior to ordinal methods because
Range passes IIA and the ordinal ones don't, I always feel like that's
a
bit of a sleight of hand. To explain, let's divide the ballot types
into
three:
-
The highest information honest ballot (ranking candidates in order
of
preference, reporting relative utility values in Range). -
Other honest ballots: some monotone transformation of this.
-
Tactical/dishonest ballots (order reversal).
Ranked methods have a very obvious category one, and going for some
category two ballot instead (e.g. equal rank or truncation) doesn't
usually produce much harm. Cardinal methods like Range replaces most of
category three with category two because they pass FBC and IIA.
As I've argued above, there's not really a category one for Range
because it asks for more than the voter can provide. And we know from
Gibbard's theorem that no deterministic voting method (cardinal or
ordinal) is entirely free of strategy. So both categories one and three
collapse into category two in Range: the former because there's no one
honest ballot, and the latter because order-reversal isn't necessary
(the famous FBC compliance, but it's actually stronger than just FBC).
So, in ranked voting methods, voting strategy consists of choosing an
appropriate category three ballot. In methods like Range, it consists
of
choosing an appropriate category two ballot.
But here's the problem: having a clearly defined category one and a
narrow category two means that a voter who values honesty as such can
just choose the one honest ballot and then go home without regrets. But
in Range, because "every ballot is honest", he has to carefully
deliberate which honest vote to choose. And if he chooses wrong (e.g.
in a Burr dilemma), he'll sure come to regret it.
That kind of peril should only exist, IMHO, for voters who decide to
play rough by choosing a category three ballot.
And thus the sleight of hand: in a ranked method, "honest" means more
or
less category one[3]. So cardinal voting proponents can say "oh, but
our
category three is empty because of FBC!", but all they're really doing
is shifting the Gibbard-mandated instrumental voting from category
three
over to category two. This lets them say "you can just vote honestly",
thus giving the impression there's no risk in Range. But it's actually
the other way around: it's not only determined strategic voters who may
regret the strategy they chose, but also honest voters who just want to
vote honestly and go home.
This also poisons the value of IIA. If IIA is to be practically
meaningful, it must mean that the outcome doesn't change when a
candidate who didn't win drops out. But if every voter is deliberating
which type-two ballot to go for, the ballots may change even if the
sentiment doesn't.
In other words: if enough voters normalize in Approval, then Approval's
IIA compliance isn't worth much at all in practice. E.g. first round
ballots:
25: A>B>>C
40: B>C>>A
35: C>A>>B
The Approval winner is C.
But now let A drop out, and the voters renormalize (as Warren suggests
everybody would):
25: B>>C
40: B>>C
35: C>>B
and then B wins, so even though Approval passes IIA de jure, it looks
rather different de facto. Telling the voters to perform a particular
algorithm on their ballots before submitting them, and then claiming
the
inputs to the method satisfies IIA, doesn't mean the method plus the
manual algorithm passes IIA!
So the problem, in summing up, is that there's too much vagueness to
hide subtleties in. Cardinal methods measure utility (but they don't,
so
what do they measure?). Cardinal methods let you vote honestly (but
honest doesn't mean the same thing anymore). Cardinal methods pass IIA
and FBC (but it does them much less good than ranked methods). Bayesian
regret evaluations show Range as superior to ranked methods (but
questionable assumptions about voter strategy may invalidate the
results).
It's better to be honest about the limitations that exist. If we can
only get lottery information, then the method should reflect that. If
we
can get more, then the method should show how we can get it. That way,
there won't be anything up its sleeve.
-km
[1]
https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780195189254.001.0001/oxfordhb-9780195189254-e-020
or, if you're more in a funny mood,
https://www.smbc-comics.com/comic/2012-04-03 :-)
[2] E.g. Warren Smith says voters will do so because they're not
"strategic idiots", and that voters who don't normalize in a
two-candidate election are simply "idiots".
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-December/084357.html
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-January/084662.html
respectively.
[3] There's a caveat here because equal-rank/truncation seem to be in
category two, and so a response to this reasoning would be "ranked
ballots have category two too!". But there's very little regret in
choosing category one instead of two, in practice. However, some ranked
methods that pass FBC do so by making equal-rank stronger than strict
ranking, and those reintroduce the problem.
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
On 10/27/2021 11:27 PM, Forest Simmons wrote:
People are always oohing and awing about Kemeny-Young as a supposedly
ideal Condorcet method ...
... (3) it does not take voter preference
strengths into account (because the K-Y ballots do not register that
kind of information)... not even as much as Ranked Pairs, because K-Y
requires complete rankings ... no equal ranks ... no truncations, etc.
The Condorcet-Kemeny method does not require complete rankings. A voter
can mark multiple candidates at the same preference order, and the voter
can leave candidates unmarked. These conventions have been running on
the VoteFair survey service for a decade.
(1) it is computationally intractable,
Actually it's easy, and fair in real elections (as opposed to software
test simulations), to quickly eliminate all but the top 12 candidates
and quickly do the calculations for the top 12. Or the top 6 if a
minute or two is too long to wait. The VoteFair service sets a limit of
6 choices as the default, but I increase the limit to 12 when that's needed.
(2) it fails clone independence,
It has a nice balance between clone independence and independence of
irrelevant alternatives. "Fails" just means the failure rates are not zero.
Richard Fobes
The VoteFair guy
On 10/27/2021 11:27 PM, Forest Simmons wrote:
Also ...
The Approval Order is essential for finding the order of finish beyond
first place ... first to last with the important Reverse Symmetry
property that is lacking in most other methods.
Approval gives voters the opportunity to get the candidates in roughly
the right order by emphasizing the most important distinctions between
acceptable and unacceptable ... then the pairwise adjustments applied to
the adjacent pairs where the approval order is not as definite (where
the approval margins are statistically less signicant) is a refinement,
and insurance that the Burlington Vermont embarrassment of IRV is
impossible under ASM. It would be technically possible to miss the CW
without the pairwise sorting, but only barely ... quite unlikely ...
even with a total lack of sophistication among voters.
Therefore, as you say, the sorting is a redundant backup ... a safety
net for the sincere Condorcet Candidate. It is redundant, but at no
extra cost ... it's free like the symmetry compliant order of finish.
People are always oohing and awing about Kemeny-Young as a supposedly
ideal Condorcet method with Reverse Symmetry, but it cannot hold a
candle to ASM because (1) it is computationally intractable, (2) it
fails clone independence, and (3) it does not take voter preference
strengths into account (because the K-Y ballots do not register that
kind of information)... not even as much as Ranked Pairs, because K-Y
requires complete rankings ... no equal ranks ... no truncations, etc.
.... that allow other Condorcet methods to show a little bit of relative
strength of preference ... though not as simply and directly as ASM.
Supposedly KY is hard to manipulate because it is hard to compute, but
that is a superstitution ... it does nothing to prevent crowding,
burial, etc. The basic defenses against burial are not even available,
as can be seen in the three candidate case ... are we supposed to
believe that as the number of candidates increases that new burial
defenses magically appear out of nowhere?
FWS
El mié., 27 de oct. de 2021 9:57 p. m., Forest Simmons
<forest.simmons21@gmail.com mailto:forest.simmons21@gmail.com> escribió:
El mié., 27 de oct. de 2021 9:19 p. m., Ted Stern
<dodecatheon@gmail.com <mailto:dodecatheon@gmail.com>> escribió:
Hi Forest,
I've been thinking about the modified version of ASM. I think it
should be called
*P*referred-*A*cceptable-*I*nsufficient-*R*eject Sorted Margins,
or PAIR-SM. I don't like movable demarcations, and I think more
than 3 levels within each category would be excessive, so I
would go with 10 total levels (score 0 to 9, rank inferred from
rating): scores 9, 8, 7 are Preferred, scores 6, 5, 4 are
Acceptable, scores 3, 2, 1 are Insufficient (formerly
"compromise": the voter finds candidates at this level
distasteful, but better than the alternative) and score 0 is reject.
And blank is counted as zero, too.
Preferred ratings get 10 points, Acceptable ratings get 5
points, Insufficient candidates get 0 points but have pairwise
votes over lower rated Insufficient candidates and all Rejected
candidates. Then Sorted margins is run using those points.
PAIR-SM could also be run with only 2 levels within each of the
approved categories, for a total of 7 levels, if you want to
retain an odd number of ratings.
Small scale elections could get by with seven levels, but rigid
demarcations work better with ten imho.
The one problem I've had on the EndFPTP subreddit is explaining
how the ranking is more important than approval. While the
Approval level is in fact what sets up the seed ordering, it is
practically irrelevant unless there is a Condorcet cycle. It's a
little hard to explain that the Approval rating is more of an
insurance that it won't be needed.
On Wed, Oct 27, 2021 at 6:31 PM Forest Simmons
<forest.simmons21@gmail.com <mailto:forest.simmons21@gmail.com>>
wrote:
I prefer Ted Stern's version of Approval Sorted Margins over
any other single-winner public proposal I've seen lately,
other than simple asset voting as proposed by Charles
Dodgson in the 19th century, and more recently a symmetrical
version of Majority Judgment currently in the works if it
can be simplified adequately w/o sacrificing its integrity.
Ted's version of ASM uses a version of what we used to call
"3-slot approval" to seed the finish order which is then
sorted pairwise with pairs that show the least discrepancy
in their 3-slot scores getting priority for pairwise
rectification. It is important to note that the ordinal
information is inferred from six slots, twice as many as
those used for the cardinal seeding.
This is valuable for several (including psychological)
reasons. One is that 3-slots are not enough for the ordinal
information to fully distinguish the pairwise preferences
important to the voters. But increasing the score slots (as
in STAR) is not the answer, for several reasons ... STAR
voters aware of optimal approval strategy (vote only at the
extremes) would feel too much tension between the need to
make use of the intermediate score levels for ordinal
information and the need to avoid those levels for optimal
cardinal strategy.
But for non-perfect information elections, even
sophisticated approval voters might welcome a middle slot.
I like three slots because, personally I would reserve the
top and bottom slots for definite approvals and disapproval,
respectively. [Bottom also takes care of blank or no
opinion to obviate darkhorse candidates].
How do you know if you "definitely" approve or disapprove of
a candidate?
Easy ... if you don't know that you do, then you don't. If
you are not sure, or if you have to ask, then your approval
or disapproval is definitely not definite.
So it's easy to know how to vote honestly under that rule,
which should be part of the instructions to the voters.
People who think they can out wit the devil may be tempted
to vote dishonestly, but at least they have the option of
voting honestly if those "definite instructions" are the
official instructions.
So Ted Stern's version of ASM is one of the best possible
public proposals IMHO.
However personally, I would rather have it implemented in
the format of a Ranked Ranking ballot, so that the voter has
more freedom in defining the cutoffs demarcating the three
slots, and making more ordinal distinctions within the three
approval levels if needed to distinguish among clones in a
large election:
A>B1>B2>C>>U>V>W1>W2>W3>>X>Y>Z...
BORDA is quoted as saying that his method was only intended
for "honest men." But honestly would not fix the greater
design flaw ... clone dependence ... in particular, clone
loser. Cardinal Ratings is a partial solution ... with all
of the caveats expressed in Kristofer's reservations.
A solution nearer to the spirit of Borda would be a point
system based on Ranked Rankings.
Borda can be thought of as a way of converting rankings into
a score/point system ... sacrificing clone dependence.
A minimal tweak of Borda (to restore clone independence)
would be to base a point system on Ranked Rankings ... with
weaker rankings reflected in smaller point/score gaps.
This idea is not my favorite way of using Ranked Rankings
... but it may help some people to see the value of a
different kind of ordinal ballot ... more expressive than
ordinary rankings without the strategic and psychological
burden (including cognitive dissonance) of the (obviously
exaggerated) implied numerical precision of ratings.
El mar., 26 de oct. de 2021 8:26 a. m., Kristofer
Munsterhjelm <km_elmet@t-online.de
<mailto:km_elmet@t-online.de>> escribió:
On 10/25/21 2:35 AM, fdpk69p6uq@snkmail.com
<mailto:fdpk69p6uq@snkmail.com> wrote:
Why does their identity matter? Discuss the facts,
not ad hominems.
Also, I'm surprised and a bit saddened that you
haven't come around to
cardinal systems yet. :/
The goal of democracy is to elect the candidate who
best represents the
will of the voters. My near-indifference between two
candidates
shouldn't arbitrarily be given the same weight as your
strong preference
between them.
Let me make a ranked voting advocate (ordinalist?)
argument here. I'll
be referring to "simple cardinal methods", by which I
mean things like
Range, and not so much things that I'm fumbling towards
in my utility posts.
Cardinal supporters tend to use two arguments to argue
for the
superiority of cardinal methods over ordinal ones.
The first is that cardinal methods support strength of
preference; and
the second is that, because they pass FBC (and IIA),
they inherently are
more robust to strategy.
My response to these are, much abbreviated, that first,
the "strength of
preference" that these methods gather is probably
ambiguous, and if it
weren't, it would come with significant disadvantages.
And second, that the methods' IIA and FBC compliance
take a form that
shoves what used to be tactical voting into a mush
that's kind of
honest, kind of not; and that once that's made clear,
it's obvious that
the methods no longer achieve the impossible. But
because it doesn't
look like ranked voting strategy, cardinal advocates can
shift between a
position that the methods permit everybody to vote
"honestly" (an easy
position) and that the methods are strategy-proof (a
hard, incorrect
position).
-
So for the first point, let's use Range as the standard
cardinal method.
Range asks for a set of ratings that are intended to
represent utility,
so that your rating is proportional to the utility you
achieve from
seeing this candidate elected. That's what's being
demonstrated in
examples like the pizza election: that the meat eaters
show that their
utility from getting mushroom pizza is not that far off
from the utility
of getting pepperoni, so that the method elects the
pizza that satisfies
all.
But here's a problem. I can't know that my scale is
calibrated the same
way as yours. In philosophy, this is known as the
problem of
incommensurability. Suppose I happen to feel more
pleasure (and pain)
than you, but due to growing up in the same society as
you, I mistakenly
appear to use the same scale as you. It's then quite
hard to know that
when I say 6/10 I mean what you would consider twice as
good as that.
At first it would seem, though, that Range has dodged a
bullet. Because
if utility were directly comparable on an absolute
scale, then there
might exist "pleasure wizards"[1] who obtain so much
utility from a
choice that they effectively become dictators. By
insisting on a 0-1
scale (in its continuous version), Range limits the
power any one voter
has and so enforces a weak type of one man, one vote. It
is what I
called a type three method - voters might voluntarily
decide to forego
some of their power to make the outcome better for
others (again, as in
the pizza election).
But the problem with this is that Range supposes that
there's a common
scale where there isn't. As a consequence, the concept
of just what is a
honest vote becomes blurred. E.g. suppose that I
consider the sure
election of Y to be equally good as a 50-50 shot of
either X or Z
winning. Do I rate X 1, Y 0.5, and Z 0? Or do I rate X
0.5, Y 0.25, and
Z 0? Because there's no way to answer that question
(unless it somehow
becomes possible to get at utility information), there's
more than one
honest vote, and a honest voter is faced with the burden
of having to
decide *which one*. (It is assumed that voters will
answer the question
by normalizing[2], but this leads to strategy problems
which I'll get to.)
My attempts to generalize STAR came from asking "what if
we want to be
truly honest about what information it makes sense to
ask of voters,
while respecting OMOV?". Well, we could ask the voters
about preferences
over lotteries (as the 50-50 vs certainty example
above). Doing so, the
method acknowledges the ambiguity of comparing utility.
Perhaps there's
more we can do - e.g. by following MJ's reasoning of a
common standard,
or by separating "worse than nothing happening" events
from "better than
nothing happening" ones.
But all of this is better than just saying "it means
what you want it to
mean", and then sweeping the resulting ambiguity in
honest voters under
the carpet.
-
As for the point that e.g. Range is superior to ordinal
methods because
Range passes IIA and the ordinal ones don't, I always
feel like that's a
bit of a sleight of hand. To explain, let's divide the
ballot types into
three:
1. The highest information honest ballot (ranking
candidates in order of
preference, reporting relative utility values in Range).
2. Other honest ballots: some monotone transformation of
this.
3. Tactical/dishonest ballots (order reversal).
Ranked methods have a very obvious category one, and
going for some
category two ballot instead (e.g. equal rank or
truncation) doesn't
usually produce much harm. Cardinal methods like Range
replaces most of
category three with category two because they pass FBC
and IIA.
As I've argued above, there's not really a category one
for Range
because it asks for more than the voter can provide. And
we know from
Gibbard's theorem that no deterministic voting method
(cardinal or
ordinal) is entirely free of strategy. So both
categories one and three
collapse into category two in Range: the former because
there's no one
honest ballot, and the latter because order-reversal
isn't necessary
(the famous FBC compliance, but it's actually stronger
than just FBC).
So, in ranked voting methods, voting strategy consists
of choosing an
appropriate category three ballot. In methods like
Range, it consists of
choosing an appropriate category two ballot.
But here's the problem: having a clearly defined
category one and a
narrow category two means that a voter who values
honesty *as such* can
just choose the one honest ballot and then go home
without regrets. But
in Range, because "every ballot is honest", he has to
carefully
deliberate *which* honest vote to choose. And if he
chooses wrong (e.g.
in a Burr dilemma), he'll sure come to regret it.
That kind of peril should only exist, IMHO, for voters
who decide to
play rough by choosing a category three ballot.
And thus the sleight of hand: in a ranked method,
"honest" means more or
less category one[3]. So cardinal voting proponents can
say "oh, but our
category three is empty because of FBC!", but all
they're really doing
is shifting the Gibbard-mandated instrumental voting
from category three
over to category two. This lets them say "you can just
vote honestly",
thus giving the impression there's no risk in Range. But
it's actually
the other way around: it's not only determined strategic
voters who may
regret the strategy they chose, but also honest voters
who just want to
vote honestly and go home.
This also poisons the value of IIA. If IIA is to be
practically
meaningful, it must mean that the outcome doesn't change
when a
candidate who didn't win drops out. But if every voter
is deliberating
which type-two ballot to go for, the ballots may change
even if the
sentiment doesn't.
In other words: if enough voters normalize in Approval,
then Approval's
IIA compliance isn't worth much at all in practice. E.g.
first round
ballots:
25: A>B>>C
40: B>C>>A
35: C>A>>B
The Approval winner is C.
But now let A drop out, and the voters renormalize (as
Warren suggests
everybody would):
25: B>>C
40: B>>C
35: C>>B
and then B wins, so even though Approval passes IIA de
jure, it looks
rather different de facto. Telling the voters to perform
a particular
algorithm on their ballots before submitting them, and
then claiming the
inputs to the method satisfies IIA, doesn't mean the
method plus the
manual algorithm passes IIA!
So the problem, in summing up, is that there's too much
vagueness to
hide subtleties in. Cardinal methods measure utility
(but they don't, so
what do they measure?). Cardinal methods let you vote
honestly (but
honest doesn't mean the same thing anymore). Cardinal
methods pass IIA
and FBC (but it does them much less good than ranked
methods). Bayesian
regret evaluations show Range as superior to ranked
methods (but
questionable assumptions about voter strategy may
invalidate the results).
It's better to be honest about the limitations that
exist. If we can
only get lottery information, then the method should
reflect that. If we
can get more, then the method should show how we can get
it. That way,
there won't be anything up its sleeve.
-km
[1]
https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780195189254.001.0001/oxfordhb-9780195189254-e-020
or, if you're more in a funny mood,
https://www.smbc-comics.com/comic/2012-04-03 :-)
[2] E.g. Warren Smith says voters will do so because
they're not
"strategic idiots", and that voters who don't normalize
in a
two-candidate election are simply "idiots".
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-December/084357.html
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-January/084662.html
respectively.
[3] There's a caveat here because equal-rank/truncation
seem to be in
category two, and so a response to this reasoning would
be "ranked
ballots have category two too!". But there's very little
regret in
choosing category one instead of two, in practice.
However, some ranked
methods that pass FBC do so by making equal-rank
stronger than strict
ranking, and those reintroduce the problem.
----
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https://electorama.com/em for list info
----
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https://electorama.com/em for list info
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On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:
(2) it fails clone independence,
It has a nice balance between clone independence and independence of
irrelevant alternatives. "Fails" just means the failure rates are not
zero.
I'd rather pick a Condorcet method with Condorcet methods' IIA
resilience (when there is a CW) and full clone independence, than one
with the former but not the latter. :-)
Since that option is available, I mean.
-km
Richard,
Twenty years ago I was excited to learn about K-Y because a topologist is
always on the lookout for interesting metrics on multidimensional spaces.
The NP complete intractability intrigued me without discouraging me because
in practice with hundreds of ballots the one among them with the minimum
average distance to the other ballots would be the actual global minimum or
very close to it ... after all, billions of such averages can be calculated
every second ... the problem is the sheer number of finish orders that need
to be checked to be absolutely sure that you got the right one .... for 30
finalists it would be about 2.65 times 10^32 different orders ... but that
is just a messy inconvenience for picky people to worry about ... anybody
who thinks they have found a better solution can easily check it ... and
then (if it pans out) easily prove it by one additional average distance
calculation ... a drop in the bucket compared with the millions of such
calculations required for an exhaustive search for the winning order, even
in an election with only ten candidates, for example.
So the intractability issue is mostly an inconvenience ... but the clone
dependence is a deal breaker ... the whole impetus for single winner
election method reform is the spoiler problem ... an example of clone
winner failure.
K-Y fails clone winner because the Kemeny distance itself, the fundamental
basis of the method, is distorted by cloning.
There is a way to declone the Kemeny metric, but at a sacrifice of
monotonicity and simplicity .... in fact, any Universal Domain metric will
result in a monotonicity failure, a clone independence failure, or both.
What is needed is a way of reducing the cost of shuffling clones around
within their own clone set ... ranking clones equally would do that, but
with a loss of ability to help decide which of them wins if the set had a
chance of producing a winner. Also is needed a way for non-clones to pass
through the clone set at a discount.
However, going outside of Universal Domain by allowing one or more approval
cutoff (or other virtual) candidates (as ASM does) makes decloning more or
less automatic as long as clone sets more or less respect these cutoffs,
and in the case of Kemeny distance, a transposition with a cutoff candidate
is significantly more costly than a normal transposition....[The Kemeny
Distance between two candidate rankings is the number of transpositions
required to convert one into the other.]
K-Y started out in the old Universal Domain ... strict rankings required...
so I am happy to hear that it has been adapted to the relaxed UD rules
allowing equal rankings and truncations ... but that is not far enough to
solve the clone problem of K-Y or to distinguish between ballot sets
resulting from burial attacks and chicken attacks ... even clone-free UD
constrained methods like River, CSSD, and Ranked Pairs are incapable of
making that distinction, as I have reminded readers of the EM list many
times.
The next step in UD rules relaxation should be either general allowance of
virtual candidates or else Ranked Rankings ballots that allow expressions
of relative strength of preference to be utilized.
Then, for example, clone free metrics can be used, and Borda can be
decloned without sacrificing monotonicity. Many of the excuses for the
(purportedly psychologically stressful) requirement of cardinal ratings
would vanish.
So that you can judge for yourself rather than rely on what somebody else
told you about the seriousness of K-Y's spoiler problem, here is an example
...
40 A>B>C
30 B>C>A
30 C>A>B
A wins according to K-Y rules and any other method anybody has ever
invented based on Universal Domain rules.
So according to clone-winner, a member of A's clone set should win if A is
cloned.
Suppose the A faction ranks the clone members in the order a1>a2> ... a9,
but the other factions rank this clone set in the opposite order a9>...>a1.
This will be the Kemeny order among the clones ... in fact, to change from
one clone order to the other takes a minimum of 36 transpositions... so
changing all 60 of the reverse orders would require 6036 while changing
the other 40 ballots would require only 4036. The difference is 36*20 or
720, a great cost (i.e.distance) saving by rejecting the A faction order.
This puts the A faction ballots at a significant disadvantage compared with
the other two orders, so one of them will be the winning order after the
dust clears.
The A faction would claim that a2, a3, ...a9 spoiled the chances of their
favorite a1. That's why clone winner failure is referred to as the spoiler
effect.
That's not the only kind of clone dependence suffered under K-Y ... it also
suffers from crowding, for example; If B were cloned, and the C and B
faction ranked the clones in the same order and A in a significantly
different order, that could cost A the election.
On the other hand if we were not constrained by UD, the factions could vote
40 a1>a2> ...a9>>B>C
30 B>C>>a9>...>a1
30 C>>a9>...>a1>>B
for example, and the extra cost of moving {A} around could save the first
faction order.
Does that help clarify the situation?
Thanks!
El vie., 29 de oct. de 2021 4:29 p. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:
On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:
(2) it fails clone independence,
It has a nice balance between clone independence and independence of
irrelevant alternatives. "Fails" just means the failure rates are not
zero.
I'd rather pick a Condorcet method with Condorcet methods' IIA
resilience (when there is a CW) and full clone independence, than one
with the former but not the latter. :-)
Since that option is available, I mean.
-km
Election-Methods mailing list - see https://electorama.com/em for list
info
On 10/31/2021 5:04 PM, Forest Simmons wrote:
So the intractability issue is mostly an inconvenience ...
I'm pleased that you, unlike many others, realize that the
Condorcet-Kemeny method's long computation time for some possible cases
is just an inconvenience, not a deal breaker.
but the clone dependence is a deal breaker ...
I disagree that a non-zero failure rate for clone independence is a
deal-breaker.
The Beatpath (aka Schulze) method achieves a zero failure rate for clone
independence, but I suspect that, as a result, it has a significantly
higher failure rate for IIA -- Independence of Irrelevant Alternatives.
This characteristic would match what happens with IRV -- instant-runoff
voting. It has a zero failure rate for clone independence, but it has a
high failure rate for IIA.
The follow scatter plot shows this pattern:
https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg
FYI, the upper right corner is where there are zero clone failures and
zero IIA failures. Most of the plotted methods, with the notable
exception of plurality, can correctly handle two-candidate cases.
If the Condorcet-Kemeny method were modified to reduce the failure rate
for clone independence, that would increase its IIA failure rate.
I believe this obviously follows from the fact that Arrow's theorum and
other proofs tell us that no method can have zero failure rates for all
of a set of specific desirable fairness criteria. So it follows that
decreasing the failure rate for one fairness criterion will increase the
failure rate for at least one other fairness criterion.
This is why I've spent time calculating failure rates and plotting them
on a scatter plot. I want to know the failure RATES, not just whether
the failure rate is zero or non-zero.
In my opinion the scatter plot clearly shows that the Condorcet-Kemeny
method has the best compromise for clone independence and IIA.
Specifically, look at the distance of the points from the upper right
corner. The Condorcet-Kemeny points are closer than the other methods.
As a clarification about the data for the STAR method: These
calculations simulate sincere voting -- with no tactical voting -- so
the points for STAR voting are idealized compared to actual elections
where tactical voting would be involved.
In contrast, the Kemeny, IPE (Instant Pairwise Elimination), and RCIPE
(Ranked Choice Including Pairwise Elimination) method are more resistant
to tactical voting compared to STAR voting, so tactical voting would not
increase the failure rates for the same cases.
Since these calculations are based on randomly generated ballots, the
failure rates in real elections would be lower than this data measures.
That's because most real elections have clearer patterns regarding
popularity of candidates. So these simulations are like stress tests
that look at performance under challenging cases.
So, I disagree that "clone dependence is a deal breaker." Yes, clone
independence is very important, but so is IIA.
In fact, the failure of IRV in Burlington is an IIA failure! I regard
that IIA failure to be more important than the failure to elect the
Condorcet winner. Of course in that case if the "Condorcet loser"
(actually the "pairwise losing candidate") had been eliminated instead
of eliminating the Condorcet winner, then the Condorcet winner would
have won.
In other words, it was the presence of an irrelevant candidate (the
pairwise losing candidate) in the top 3 that blocked the Condorcet
winner from reaching the top 2.
The elimination of "pairwise losing candidates" is why the RCIPE method
performs better than IRV.
And because the Condorcet-Kemeny method looks so deeply into ALL the
ballot preferences on all the ballots, I suspect that it eliminates
"irrelevant alternatives" better than a method that has a zero failure
rate for clone independence.
Also consider that when an election has rock-paper-scissors (Condorcet)
cycles (that involve the most popular candidates), ignoring irrelevant
alternatives helps the method deal with near clones.
Admittedly I'm less concerned about the handling of exact clones
because those are almost impossible in a real election.
Yet if an election did have almost exact clones, I'm willing to accept
electing the wrong clone. That's better than if a method gets "confused"
by an irrelevant alternative.
Richard Fobes
The VoteFair guy
On 10/31/2021 5:04 PM, Forest Simmons wrote:
Richard,
Twenty years ago I was excited to learn about K-Y because a topologist
is always on the lookout for interesting metrics on multidimensional
spaces. The NP complete intractability intrigued me without discouraging
me because in practice with hundreds of ballots the one among them with
the minimum average distance to the other ballots would be the actual
global minimum or very close to it ... after all, billions of such
averages can be calculated every second ... the problem is the sheer
number of finish orders that need to be checked to be absolutely sure
that you got the right one .... for 30 finalists it would be about 2.65
times 10^32 different orders ... but that is just a messy inconvenience
for picky people to worry about ... anybody who thinks they have found a
better solution can easily check it ... and then (if it pans out) easily
prove it by one additional average distance calculation ... a drop in
the bucket compared with the millions of such calculations required for
an exhaustive search for the winning order, even in an election with
only ten candidates, for example.
So the intractability issue is mostly an inconvenience ... but the clone
dependence is a deal breaker ... the whole impetus for single winner
election method reform is the spoiler problem ... an example of clone
winner failure.
K-Y fails clone winner because the Kemeny distance itself, the
fundamental basis of the method, is distorted by cloning.
There is a way to declone the Kemeny metric, but at a sacrifice of
monotonicity and simplicity .... in fact, any Universal Domain metric
will result in a monotonicity failure, a clone independence failure, or
both. What is needed is a way of reducing the cost of shuffling clones
around within their own clone set ... ranking clones equally would do
that, but with a loss of ability to help decide which of them wins if
the set had a chance of producing a winner. Also is needed a way for
non-clones to pass through the clone set at a discount.
However, going outside of Universal Domain by allowing one or more
approval cutoff (or other virtual) candidates (as ASM does) makes
decloning more or less automatic as long as clone sets more or less
respect these cutoffs, and in the case of Kemeny distance, a
transposition with a cutoff candidate is significantly more costly than
a normal transposition....[The Kemeny Distance between two candidate
rankings is the number of transpositions required to convert one into
the other.]
K-Y started out in the old Universal Domain ... strict rankings
required... so I am happy to hear that it has been adapted to the
relaxed UD rules allowing equal rankings and truncations ... but that is
not far enough to solve the clone problem of K-Y or to distinguish
between ballot sets resulting from burial attacks and chicken attacks
... even clone-free UD constrained methods like River, CSSD, and Ranked
Pairs are incapable of making that distinction, as I have reminded
readers of the EM list many times.
The next step in UD rules relaxation should be either general allowance
of virtual candidates or else Ranked Rankings ballots that allow
expressions of relative strength of preference to be utilized.
Then, for example, clone free metrics can be used, and Borda can be
decloned without sacrificing monotonicity. Many of the excuses for the
(purportedly psychologically stressful) requirement of cardinal ratings
would vanish.
So that you can judge for yourself rather than rely on what somebody
else told you about the seriousness of K-Y's spoiler problem, here is an
example ...
40 A>B>C
30 B>C>A
30 C>A>B
A wins according to K-Y rules and any other method anybody has ever
invented based on Universal Domain rules.
So according to clone-winner, a member of A's clone set should win if A
is cloned.
Suppose the A faction ranks the clone members in the order a1>a2> ...
a9, but the other factions rank this clone set in the opposite order
a9>...>a1. This will be the Kemeny order among the clones ... in fact,
to change from one clone order to the other takes a minimum of 36
transpositions... so changing all 60 of the reverse orders would require
6036 while changing the other 40 ballots would require only 4036. The
difference is 36*20 or 720, a great cost (i.e.distance) saving by
rejecting the A faction order.
This puts the A faction ballots at a significant disadvantage compared
with the other two orders, so one of them will be the winning order
after the dust clears.
The A faction would claim that a2, a3, ...a9 spoiled the chances of
their favorite a1. That's why clone winner failure is referred to as
the spoiler effect.
That's not the only kind of clone dependence suffered under K-Y ... it
also suffers from crowding, for example; If B were cloned, and the C and
B faction ranked the clones in the same order and A in a significantly
different order, that could cost A the election.
On the other hand if we were not constrained by UD, the factions could vote
40 a1>a2> ...a9>>B>C
30 B>C>>a9>...>a1
30 C>>a9>...>a1>>B
for example, and the extra cost of moving {A} around could save the
first faction order.
Does that help clarify the situation?
Thanks!
El vie., 29 de oct. de 2021 4:29 p. m., Kristofer Munsterhjelm
<km_elmet@t-online.de mailto:km_elmet@t-online.de> escribió:
On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:
(2) it fails clone independence,
It has a nice balance between clone independence and independence of
irrelevant alternatives. "Fails" just means the failure rates are
not
zero.
I'd rather pick a Condorcet method with Condorcet methods' IIA
resilience (when there is a CW) *and* full clone independence, than one
with the former but not the latter. :-)
Since that option is available, I mean.
-km
----
Election-Methods mailing list - see https://electorama.com/em for
list info
Richard,
Clone winner failure is not about electing the wrong clone ... it's about
none of the clones of the erstwhile winner being elected. That is the
spoiler problem.
If you want a method that is both clone winner compliant and IIAC
compliant, Approval Sorted Margins (ASM), or Majority Judgment Sorted
Margins (MJSM) is what you need.
FWS
El mar., 2 de nov. de 2021 9:02 p. m., Richard, the VoteFair guy <
electionmethods@votefair.org> escribió:
On 10/31/2021 5:04 PM, Forest Simmons wrote:
So the intractability issue is mostly an inconvenience ...
I'm pleased that you, unlike many others, realize that the
Condorcet-Kemeny method's long computation time for some possible cases
is just an inconvenience, not a deal breaker.
but the clone dependence is a deal breaker ...
I disagree that a non-zero failure rate for clone independence is a
deal-breaker.
The Beatpath (aka Schulze) method achieves a zero failure rate for clone
independence, but I suspect that, as a result, it has a significantly
higher failure rate for IIA -- Independence of Irrelevant Alternatives.
This characteristic would match what happens with IRV -- instant-runoff
voting. It has a zero failure rate for clone independence, but it has a
high failure rate for IIA.
The follow scatter plot shows this pattern:
https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg
FYI, the upper right corner is where there are zero clone failures and
zero IIA failures. Most of the plotted methods, with the notable
exception of plurality, can correctly handle two-candidate cases.
If the Condorcet-Kemeny method were modified to reduce the failure rate
for clone independence, that would increase its IIA failure rate.
I believe this obviously follows from the fact that Arrow's theorum and
other proofs tell us that no method can have zero failure rates for all
of a set of specific desirable fairness criteria. So it follows that
decreasing the failure rate for one fairness criterion will increase the
failure rate for at least one other fairness criterion.
This is why I've spent time calculating failure rates and plotting them
on a scatter plot. I want to know the failure RATES, not just whether
the failure rate is zero or non-zero.
In my opinion the scatter plot clearly shows that the Condorcet-Kemeny
method has the best compromise for clone independence and IIA.
Specifically, look at the distance of the points from the upper right
corner. The Condorcet-Kemeny points are closer than the other methods.
As a clarification about the data for the STAR method: These
calculations simulate sincere voting -- with no tactical voting -- so
the points for STAR voting are idealized compared to actual elections
where tactical voting would be involved.
In contrast, the Kemeny, IPE (Instant Pairwise Elimination), and RCIPE
(Ranked Choice Including Pairwise Elimination) method are more resistant
to tactical voting compared to STAR voting, so tactical voting would not
increase the failure rates for the same cases.
Since these calculations are based on randomly generated ballots, the
failure rates in real elections would be lower than this data measures.
That's because most real elections have clearer patterns regarding
popularity of candidates. So these simulations are like stress tests
that look at performance under challenging cases.
So, I disagree that "clone dependence is a deal breaker." Yes, clone
independence is very important, but so is IIA.
In fact, the failure of IRV in Burlington is an IIA failure! I regard
that IIA failure to be more important than the failure to elect the
Condorcet winner. Of course in that case if the "Condorcet loser"
(actually the "pairwise losing candidate") had been eliminated instead
of eliminating the Condorcet winner, then the Condorcet winner would
have won.
In other words, it was the presence of an irrelevant candidate (the
pairwise losing candidate) in the top 3 that blocked the Condorcet
winner from reaching the top 2.
The elimination of "pairwise losing candidates" is why the RCIPE method
performs better than IRV.
And because the Condorcet-Kemeny method looks so deeply into ALL the
ballot preferences on all the ballots, I suspect that it eliminates
"irrelevant alternatives" better than a method that has a zero failure
rate for clone independence.
Also consider that when an election has rock-paper-scissors (Condorcet)
cycles (that involve the most popular candidates), ignoring irrelevant
alternatives helps the method deal with near clones.
Admittedly I'm less concerned about the handling of exact clones
because those are almost impossible in a real election.
Yet if an election did have almost exact clones, I'm willing to accept
electing the wrong clone. That's better than if a method gets "confused"
by an irrelevant alternative.
Richard Fobes
The VoteFair guy
On 10/31/2021 5:04 PM, Forest Simmons wrote:
Richard,
Twenty years ago I was excited to learn about K-Y because a topologist
is always on the lookout for interesting metrics on multidimensional
spaces. The NP complete intractability intrigued me without discouraging
me because in practice with hundreds of ballots the one among them with
the minimum average distance to the other ballots would be the actual
global minimum or very close to it ... after all, billions of such
averages can be calculated every second ... the problem is the sheer
number of finish orders that need to be checked to be absolutely sure
that you got the right one .... for 30 finalists it would be about 2.65
times 10^32 different orders ... but that is just a messy inconvenience
for picky people to worry about ... anybody who thinks they have found a
better solution can easily check it ... and then (if it pans out) easily
prove it by one additional average distance calculation ... a drop in
the bucket compared with the millions of such calculations required for
an exhaustive search for the winning order, even in an election with
only ten candidates, for example.
So the intractability issue is mostly an inconvenience ... but the clone
dependence is a deal breaker ... the whole impetus for single winner
election method reform is the spoiler problem ... an example of clone
winner failure.
K-Y fails clone winner because the Kemeny distance itself, the
fundamental basis of the method, is distorted by cloning.
There is a way to declone the Kemeny metric, but at a sacrifice of
monotonicity and simplicity .... in fact, any Universal Domain metric
will result in a monotonicity failure, a clone independence failure, or
both. What is needed is a way of reducing the cost of shuffling clones
around within their own clone set ... ranking clones equally would do
that, but with a loss of ability to help decide which of them wins if
the set had a chance of producing a winner. Also is needed a way for
non-clones to pass through the clone set at a discount.
However, going outside of Universal Domain by allowing one or more
approval cutoff (or other virtual) candidates (as ASM does) makes
decloning more or less automatic as long as clone sets more or less
respect these cutoffs, and in the case of Kemeny distance, a
transposition with a cutoff candidate is significantly more costly than
a normal transposition....[The Kemeny Distance between two candidate
rankings is the number of transpositions required to convert one into
the other.]
K-Y started out in the old Universal Domain ... strict rankings
required... so I am happy to hear that it has been adapted to the
relaxed UD rules allowing equal rankings and truncations ... but that is
not far enough to solve the clone problem of K-Y or to distinguish
between ballot sets resulting from burial attacks and chicken attacks
... even clone-free UD constrained methods like River, CSSD, and Ranked
Pairs are incapable of making that distinction, as I have reminded
readers of the EM list many times.
The next step in UD rules relaxation should be either general allowance
of virtual candidates or else Ranked Rankings ballots that allow
expressions of relative strength of preference to be utilized.
Then, for example, clone free metrics can be used, and Borda can be
decloned without sacrificing monotonicity. Many of the excuses for the
(purportedly psychologically stressful) requirement of cardinal ratings
would vanish.
So that you can judge for yourself rather than rely on what somebody
else told you about the seriousness of K-Y's spoiler problem, here is an
example ...
40 A>B>C
30 B>C>A
30 C>A>B
A wins according to K-Y rules and any other method anybody has ever
invented based on Universal Domain rules.
So according to clone-winner, a member of A's clone set should win if A
is cloned.
Suppose the A faction ranks the clone members in the order a1>a2> ...
a9, but the other factions rank this clone set in the opposite order
a9>...>a1. This will be the Kemeny order among the clones ... in fact,
to change from one clone order to the other takes a minimum of 36
transpositions... so changing all 60 of the reverse orders would require
6036 while changing the other 40 ballots would require only 4036. The
difference is 36*20 or 720, a great cost (i.e.distance) saving by
rejecting the A faction order.
This puts the A faction ballots at a significant disadvantage compared
with the other two orders, so one of them will be the winning order
after the dust clears.
The A faction would claim that a2, a3, ...a9 spoiled the chances of
their favorite a1. That's why clone winner failure is referred to as
the spoiler effect.
That's not the only kind of clone dependence suffered under K-Y ... it
also suffers from crowding, for example; If B were cloned, and the C and
B faction ranked the clones in the same order and A in a significantly
different order, that could cost A the election.
On the other hand if we were not constrained by UD, the factions could
vote
40 a1>a2> ...a9>>B>C
30 B>C>>a9>...>a1
30 C>>a9>...>a1>>B
for example, and the extra cost of moving {A} around could save the
first faction order.
Does that help clarify the situation?
Thanks!
El vie., 29 de oct. de 2021 4:29 p. m., Kristofer Munsterhjelm
<km_elmet@t-online.de mailto:km_elmet@t-online.de> escribió:
On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:
(2) it fails clone independence,
It has a nice balance between clone independence and independence
of
irrelevant alternatives. "Fails" just means the failure rates are
not
zero.
I'd rather pick a Condorcet method with Condorcet methods' IIA
resilience (when there is a CW) *and* full clone independence, than
one
with the former but not the latter. :-)
Since that option is available, I mean.
-km
----
Election-Methods mailing list - see https://electorama.com/em for
list info
Election-Methods mailing list - see https://electorama.com/em for list
info
By the way, I'm referring to Ted Stern's most recent version of ASM that he
calls PAIR-SM from his 27October EM message.
As for MJ-SM, be sure to use a symmetric version of MJ for Reverse Symmetry
Criterion compliance.
By the way, what makes you think that the use of a couple of extra strength
rank relations to fix K-Y's spoiler problem would impair IIAC compliance?
It works great for PAIR-SM.
You invoked Arrow, but Arrow never said that Clone Winner and IIAC were
incompatible. He did say that IIAC and the Majority Criterion are
incompatible, and it is easy to prove ...
Consider for example ...
40 A>B>C
30 B>C>A
30 C>A>B
If A wins, as in Kemeny-Young, River, Ranked Pairs, CSSD, Borda, Bucklin,
IRV, etc. then B is an irrelevant alternative.
But when B is removed, C becomes the Majority Winner 60 to 40.
Perhaps in your simulations you threw out cycles like these ... but that
would give all Condorcet Compliant methods perfect scores for IIAC. I am
curious how you came up with the idea that K-Y trades in Clone Winner
compliance for better IIAC compliance.
FWS
El mar., 2 de nov. de 2021 10:50 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:
Richard,
Clone winner failure is not about electing the wrong clone ... it's about
none of the clones of the erstwhile winner being elected. That is the
spoiler problem.
If you want a method that is both clone winner compliant and IIAC
compliant, Approval Sorted Margins (ASM), or Majority Judgment Sorted
Margins (MJSM) is what you need.
FWS
El mar., 2 de nov. de 2021 9:02 p. m., Richard, the VoteFair guy <
electionmethods@votefair.org> escribió:
On 10/31/2021 5:04 PM, Forest Simmons wrote:
So the intractability issue is mostly an inconvenience ...
I'm pleased that you, unlike many others, realize that the
Condorcet-Kemeny method's long computation time for some possible cases
is just an inconvenience, not a deal breaker.
but the clone dependence is a deal breaker ...
I disagree that a non-zero failure rate for clone independence is a
deal-breaker.
The Beatpath (aka Schulze) method achieves a zero failure rate for clone
independence, but I suspect that, as a result, it has a significantly
higher failure rate for IIA -- Independence of Irrelevant Alternatives.
This characteristic would match what happens with IRV -- instant-runoff
voting. It has a zero failure rate for clone independence, but it has a
high failure rate for IIA.
The follow scatter plot shows this pattern:
https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg
FYI, the upper right corner is where there are zero clone failures and
zero IIA failures. Most of the plotted methods, with the notable
exception of plurality, can correctly handle two-candidate cases.
If the Condorcet-Kemeny method were modified to reduce the failure rate
for clone independence, that would increase its IIA failure rate.
I believe this obviously follows from the fact that Arrow's theorum and
other proofs tell us that no method can have zero failure rates for all
of a set of specific desirable fairness criteria. So it follows that
decreasing the failure rate for one fairness criterion will increase the
failure rate for at least one other fairness criterion.
This is why I've spent time calculating failure rates and plotting them
on a scatter plot. I want to know the failure RATES, not just whether
the failure rate is zero or non-zero.
In my opinion the scatter plot clearly shows that the Condorcet-Kemeny
method has the best compromise for clone independence and IIA.
Specifically, look at the distance of the points from the upper right
corner. The Condorcet-Kemeny points are closer than the other methods.
As a clarification about the data for the STAR method: These
calculations simulate sincere voting -- with no tactical voting -- so
the points for STAR voting are idealized compared to actual elections
where tactical voting would be involved.
In contrast, the Kemeny, IPE (Instant Pairwise Elimination), and RCIPE
(Ranked Choice Including Pairwise Elimination) method are more resistant
to tactical voting compared to STAR voting, so tactical voting would not
increase the failure rates for the same cases.
Since these calculations are based on randomly generated ballots, the
failure rates in real elections would be lower than this data measures.
That's because most real elections have clearer patterns regarding
popularity of candidates. So these simulations are like stress tests
that look at performance under challenging cases.
So, I disagree that "clone dependence is a deal breaker." Yes, clone
independence is very important, but so is IIA.
In fact, the failure of IRV in Burlington is an IIA failure! I regard
that IIA failure to be more important than the failure to elect the
Condorcet winner. Of course in that case if the "Condorcet loser"
(actually the "pairwise losing candidate") had been eliminated instead
of eliminating the Condorcet winner, then the Condorcet winner would
have won.
In other words, it was the presence of an irrelevant candidate (the
pairwise losing candidate) in the top 3 that blocked the Condorcet
winner from reaching the top 2.
The elimination of "pairwise losing candidates" is why the RCIPE method
performs better than IRV.
And because the Condorcet-Kemeny method looks so deeply into ALL the
ballot preferences on all the ballots, I suspect that it eliminates
"irrelevant alternatives" better than a method that has a zero failure
rate for clone independence.
Also consider that when an election has rock-paper-scissors (Condorcet)
cycles (that involve the most popular candidates), ignoring irrelevant
alternatives helps the method deal with near clones.
Admittedly I'm less concerned about the handling of exact clones
because those are almost impossible in a real election.
Yet if an election did have almost exact clones, I'm willing to accept
electing the wrong clone. That's better than if a method gets "confused"
by an irrelevant alternative.
Richard Fobes
The VoteFair guy
On 10/31/2021 5:04 PM, Forest Simmons wrote:
Richard,
Twenty years ago I was excited to learn about K-Y because a topologist
is always on the lookout for interesting metrics on multidimensional
spaces. The NP complete intractability intrigued me without discouraging
me because in practice with hundreds of ballots the one among them with
the minimum average distance to the other ballots would be the actual
global minimum or very close to it ... after all, billions of such
averages can be calculated every second ... the problem is the sheer
number of finish orders that need to be checked to be absolutely sure
that you got the right one .... for 30 finalists it would be about 2.65
times 10^32 different orders ... but that is just a messy inconvenience
for picky people to worry about ... anybody who thinks they have found a
better solution can easily check it ... and then (if it pans out) easily
prove it by one additional average distance calculation ... a drop in
the bucket compared with the millions of such calculations required for
an exhaustive search for the winning order, even in an election with
only ten candidates, for example.
So the intractability issue is mostly an inconvenience ... but the clone
dependence is a deal breaker ... the whole impetus for single winner
election method reform is the spoiler problem ... an example of clone
winner failure.
K-Y fails clone winner because the Kemeny distance itself, the
fundamental basis of the method, is distorted by cloning.
There is a way to declone the Kemeny metric, but at a sacrifice of
monotonicity and simplicity .... in fact, any Universal Domain metric
will result in a monotonicity failure, a clone independence failure, or
both. What is needed is a way of reducing the cost of shuffling clones
around within their own clone set ... ranking clones equally would do
that, but with a loss of ability to help decide which of them wins if
the set had a chance of producing a winner. Also is needed a way for
non-clones to pass through the clone set at a discount.
However, going outside of Universal Domain by allowing one or more
approval cutoff (or other virtual) candidates (as ASM does) makes
decloning more or less automatic as long as clone sets more or less
respect these cutoffs, and in the case of Kemeny distance, a
transposition with a cutoff candidate is significantly more costly than
a normal transposition....[The Kemeny Distance between two candidate
rankings is the number of transpositions required to convert one into
the other.]
K-Y started out in the old Universal Domain ... strict rankings
required... so I am happy to hear that it has been adapted to the
relaxed UD rules allowing equal rankings and truncations ... but that is
not far enough to solve the clone problem of K-Y or to distinguish
between ballot sets resulting from burial attacks and chicken attacks
... even clone-free UD constrained methods like River, CSSD, and Ranked
Pairs are incapable of making that distinction, as I have reminded
readers of the EM list many times.
The next step in UD rules relaxation should be either general allowance
of virtual candidates or else Ranked Rankings ballots that allow
expressions of relative strength of preference to be utilized.
Then, for example, clone free metrics can be used, and Borda can be
decloned without sacrificing monotonicity. Many of the excuses for the
(purportedly psychologically stressful) requirement of cardinal ratings
would vanish.
So that you can judge for yourself rather than rely on what somebody
else told you about the seriousness of K-Y's spoiler problem, here is an
example ...
40 A>B>C
30 B>C>A
30 C>A>B
A wins according to K-Y rules and any other method anybody has ever
invented based on Universal Domain rules.
So according to clone-winner, a member of A's clone set should win if A
is cloned.
Suppose the A faction ranks the clone members in the order a1>a2> ...
a9, but the other factions rank this clone set in the opposite order
a9>...>a1. This will be the Kemeny order among the clones ... in fact,
to change from one clone order to the other takes a minimum of 36
transpositions... so changing all 60 of the reverse orders would require
6036 while changing the other 40 ballots would require only 4036. The
difference is 36*20 or 720, a great cost (i.e.distance) saving by
rejecting the A faction order.
This puts the A faction ballots at a significant disadvantage compared
with the other two orders, so one of them will be the winning order
after the dust clears.
The A faction would claim that a2, a3, ...a9 spoiled the chances of
their favorite a1. That's why clone winner failure is referred to as
the spoiler effect.
That's not the only kind of clone dependence suffered under K-Y ... it
also suffers from crowding, for example; If B were cloned, and the C and
B faction ranked the clones in the same order and A in a significantly
different order, that could cost A the election.
On the other hand if we were not constrained by UD, the factions could
vote
40 a1>a2> ...a9>>B>C
30 B>C>>a9>...>a1
30 C>>a9>...>a1>>B
for example, and the extra cost of moving {A} around could save the
first faction order.
Does that help clarify the situation?
Thanks!
El vie., 29 de oct. de 2021 4:29 p. m., Kristofer Munsterhjelm
<km_elmet@t-online.de mailto:km_elmet@t-online.de> escribió:
On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:
(2) it fails clone independence,
It has a nice balance between clone independence and independence
of
irrelevant alternatives. "Fails" just means the failure rates are
not
zero.
I'd rather pick a Condorcet method with Condorcet methods' IIA
resilience (when there is a CW) *and* full clone independence, than
one
with the former but not the latter. :-)
Since that option is available, I mean.
-km
----
Election-Methods mailing list - see https://electorama.com/em for
list info
Election-Methods mailing list - see https://electorama.com/em for list
info
Richard,
You have shown by your EM postings that you are not content to just
regurgitate the opinions and pronouncements of the "experts". You want
fundamental understanding so that you have the tools to form and defend
your own opinions with alacrity.. which you have done with admirable valor
based on above average curiosity and willingness to think carefully while
searching for truth.
That's why I want to dig a little more into Independence from Irrelevant
Alternatives... We have seen that no method based solely on ranked choice
ballots can satisfy the IIAC except by failing the Majority Criterion....
in fact, if a majority prefers A over B and another majority prefers B over
C, and another majority prefers C over A, then no matter which of these is
the method winner X the removal/withdrawal of the one majority beaten by X
will change the winner from X to the one that beats X by a majority.
So how do MJ and some versions of Cardinal Ratings satisfy IIAC? By going
outside Universal Domain .. i.e. by using ballot information beyond mere
ordinal information ... information that is supposed to be absolute, unlike
rankings which are fundamentally relative.
Does Approval satisfy IIAC? Technically yes ... sincere approval is not
supposed to be relative .. you either approve of X or you don't ...
according to your own standards, independent of your approval of other
people. Approval in a zero info environment would satisfy it ... as would
even FPTP if a candidate withdrew after the ballots were already submitted.
But not so with any ranked preference method ... re-counting the ballots
after the withdrawal can change the IRV winner, the Kemeny-Young winner,
etc ... but not the MJ winner, the FPTP winner, the Range winner, or the
Approval winner.
This is the best objective test fo IIAC compliance: if after all of the
ballots have been submitted and counted a losing candidate X withdraws ...
would a recount of the exact same ballots with X crossed out on all ballots
necessarily result in the same winner?
If so, then the method passes IIAC.
Now what about the Sorted Margins versions of IIAC compliant methods ... do
they satisfy the IIAC?
No, but like Kemeny-Young, they all satisfy "Local IIAC", which means that
if you transpose just one pair of candidates in the finish order, the
average Kemeny distance of that order from the ballot rankings will be
increased ... i.e. the finish order distance is a local minimum in the
Kemeny distance from the ballots.
Sorting the finish order pairwise as a last step confers local IIAC
compliance on any method that has both a finish order and a way of making
pairwise comparisons.
This kind of sorting of the finish order is sometimes referred to as
Kemenization, especially if the local minimum obtained therefrom is at
minimal distance from the original finish order.
In the case of ASM (or MJ) the original (base method) finish order already
satisfies the IIAC without necessarily being at a local or global minimal
average distance to the ballot rankings.
Ironically, since pairwise comparisons are generally based on relative
ordinal infornation only, this afterburner add-on can scuttle the absolute
IIAC compliance of the original finish order.
So as Ted Stern has pointed out, the sorting step is more of a guarantee
that the ballot CW cannot lose, like the necessary redundancy in an error
correcting code ... where the allowable code words (i.e. finish orders in
this context) are local minima of the Kemeny distance from the ballots.
This analogy is precise ... a non-code word "signal" W, when received and
detected is taken as contaminated by error/noise. The most likely intended
message word is the code word closest to W.
For example, if the cyclic pairwise beat order is ABCA, then the "code
words" (allowable rankings) are ABC, BCA, and CAB.
Suppose that the base method (say IRV) finish order is CBA. Then the
question becomes which code word is closest to the contaminated signal CBA
that was received after passing through IRV and the other elements of the
noisy, error fraught election system/environment?
Changing CBA to codeword BAC or to CAB involves one transposition in the
finish order, but on how many ballots?
That depends on the respective absolute margins of defeat of B>A and of
A>B, respectly.
Hence, Approval Sorted Margins, MJ Sorted Margins, etc.
Just one detail, in practice the "margins" in question can be pairwise
approval margins or pairwise range margins, etc ... whatever kind of
margins are most convenient ... as in Galerkin's method of error
minimization.
FWS
El mar., 2 de nov. de 2021 11:50 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:
By the way, I'm referring to Ted Stern's most recent version of ASM that
he calls PAIR-SM from his 27October EM message.
As for MJ-SM, be sure to use a symmetric version of MJ for Reverse
Symmetry Criterion compliance.
By the way, what makes you think that the use of a couple of extra
strength rank relations to fix K-Y's spoiler problem would impair IIAC
compliance? It works great for PAIR-SM.
You invoked Arrow, but Arrow never said that Clone Winner and IIAC were
incompatible. He did say that IIAC and the Majority Criterion are
incompatible, and it is easy to prove ...
Consider for example ...
40 A>B>C
30 B>C>A
30 C>A>B
If A wins, as in Kemeny-Young, River, Ranked Pairs, CSSD, Borda, Bucklin,
IRV, etc. then B is an irrelevant alternative.
But when B is removed, C becomes the Majority Winner 60 to 40.
Perhaps in your simulations you threw out cycles like these ... but that
would give all Condorcet Compliant methods perfect scores for IIAC. I am
curious how you came up with the idea that K-Y trades in Clone Winner
compliance for better IIAC compliance.
FWS
El mar., 2 de nov. de 2021 10:50 p. m., Forest Simmons <
forest.simmons21@gmail.com> escribió:
Richard,
Clone winner failure is not about electing the wrong clone ... it's about
none of the clones of the erstwhile winner being elected. That is the
spoiler problem.
If you want a method that is both clone winner compliant and IIAC
compliant, Approval Sorted Margins (ASM), or Majority Judgment Sorted
Margins (MJSM) is what you need.
FWS
El mar., 2 de nov. de 2021 9:02 p. m., Richard, the VoteFair guy <
electionmethods@votefair.org> escribió:
On 10/31/2021 5:04 PM, Forest Simmons wrote:
So the intractability issue is mostly an inconvenience ...
I'm pleased that you, unlike many others, realize that the
Condorcet-Kemeny method's long computation time for some possible cases
is just an inconvenience, not a deal breaker.
but the clone dependence is a deal breaker ...
I disagree that a non-zero failure rate for clone independence is a
deal-breaker.
The Beatpath (aka Schulze) method achieves a zero failure rate for clone
independence, but I suspect that, as a result, it has a significantly
higher failure rate for IIA -- Independence of Irrelevant Alternatives.
This characteristic would match what happens with IRV -- instant-runoff
voting. It has a zero failure rate for clone independence, but it has a
high failure rate for IIA.
The follow scatter plot shows this pattern:
https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg
FYI, the upper right corner is where there are zero clone failures and
zero IIA failures. Most of the plotted methods, with the notable
exception of plurality, can correctly handle two-candidate cases.
If the Condorcet-Kemeny method were modified to reduce the failure rate
for clone independence, that would increase its IIA failure rate.
I believe this obviously follows from the fact that Arrow's theorum and
other proofs tell us that no method can have zero failure rates for all
of a set of specific desirable fairness criteria. So it follows that
decreasing the failure rate for one fairness criterion will increase the
failure rate for at least one other fairness criterion.
This is why I've spent time calculating failure rates and plotting them
on a scatter plot. I want to know the failure RATES, not just whether
the failure rate is zero or non-zero.
In my opinion the scatter plot clearly shows that the Condorcet-Kemeny
method has the best compromise for clone independence and IIA.
Specifically, look at the distance of the points from the upper right
corner. The Condorcet-Kemeny points are closer than the other methods.
As a clarification about the data for the STAR method: These
calculations simulate sincere voting -- with no tactical voting -- so
the points for STAR voting are idealized compared to actual elections
where tactical voting would be involved.
In contrast, the Kemeny, IPE (Instant Pairwise Elimination), and RCIPE
(Ranked Choice Including Pairwise Elimination) method are more resistant
to tactical voting compared to STAR voting, so tactical voting would not
increase the failure rates for the same cases.
Since these calculations are based on randomly generated ballots, the
failure rates in real elections would be lower than this data measures.
That's because most real elections have clearer patterns regarding
popularity of candidates. So these simulations are like stress tests
that look at performance under challenging cases.
So, I disagree that "clone dependence is a deal breaker." Yes, clone
independence is very important, but so is IIA.
In fact, the failure of IRV in Burlington is an IIA failure! I regard
that IIA failure to be more important than the failure to elect the
Condorcet winner. Of course in that case if the "Condorcet loser"
(actually the "pairwise losing candidate") had been eliminated instead
of eliminating the Condorcet winner, then the Condorcet winner would
have won.
In other words, it was the presence of an irrelevant candidate (the
pairwise losing candidate) in the top 3 that blocked the Condorcet
winner from reaching the top 2.
The elimination of "pairwise losing candidates" is why the RCIPE method
performs better than IRV.
And because the Condorcet-Kemeny method looks so deeply into ALL the
ballot preferences on all the ballots, I suspect that it eliminates
"irrelevant alternatives" better than a method that has a zero failure
rate for clone independence.
Also consider that when an election has rock-paper-scissors (Condorcet)
cycles (that involve the most popular candidates), ignoring irrelevant
alternatives helps the method deal with near clones.
Admittedly I'm less concerned about the handling of exact clones
because those are almost impossible in a real election.
Yet if an election did have almost exact clones, I'm willing to accept
electing the wrong clone. That's better than if a method gets "confused"
by an irrelevant alternative.
Richard Fobes
The VoteFair guy
On 10/31/2021 5:04 PM, Forest Simmons wrote:
Richard,
Twenty years ago I was excited to learn about K-Y because a topologist
is always on the lookout for interesting metrics on multidimensional
spaces. The NP complete intractability intrigued me without
discouraging
me because in practice with hundreds of ballots the one among them with
the minimum average distance to the other ballots would be the actual
global minimum or very close to it ... after all, billions of such
averages can be calculated every second ... the problem is the sheer
number of finish orders that need to be checked to be absolutely sure
that you got the right one .... for 30 finalists it would be about 2.65
times 10^32 different orders ... but that is just a messy inconvenience
for picky people to worry about ... anybody who thinks they have found
a
better solution can easily check it ... and then (if it pans out)
easily
prove it by one additional average distance calculation ... a drop in
the bucket compared with the millions of such calculations required for
an exhaustive search for the winning order, even in an election with
only ten candidates, for example.
So the intractability issue is mostly an inconvenience ... but the
clone
dependence is a deal breaker ... the whole impetus for single winner
election method reform is the spoiler problem ... an example of clone
winner failure.
K-Y fails clone winner because the Kemeny distance itself, the
fundamental basis of the method, is distorted by cloning.
There is a way to declone the Kemeny metric, but at a sacrifice of
monotonicity and simplicity .... in fact, any Universal Domain metric
will result in a monotonicity failure, a clone independence failure, or
both. What is needed is a way of reducing the cost of shuffling clones
around within their own clone set ... ranking clones equally would do
that, but with a loss of ability to help decide which of them wins if
the set had a chance of producing a winner. Also is needed a way for
non-clones to pass through the clone set at a discount.
However, going outside of Universal Domain by allowing one or more
approval cutoff (or other virtual) candidates (as ASM does) makes
decloning more or less automatic as long as clone sets more or less
respect these cutoffs, and in the case of Kemeny distance, a
transposition with a cutoff candidate is significantly more costly than
a normal transposition....[The Kemeny Distance between two candidate
rankings is the number of transpositions required to convert one into
the other.]
K-Y started out in the old Universal Domain ... strict rankings
required... so I am happy to hear that it has been adapted to the
relaxed UD rules allowing equal rankings and truncations ... but that
is
not far enough to solve the clone problem of K-Y or to distinguish
between ballot sets resulting from burial attacks and chicken attacks
... even clone-free UD constrained methods like River, CSSD, and Ranked
Pairs are incapable of making that distinction, as I have reminded
readers of the EM list many times.
The next step in UD rules relaxation should be either general allowance
of virtual candidates or else Ranked Rankings ballots that allow
expressions of relative strength of preference to be utilized.
Then, for example, clone free metrics can be used, and Borda can be
decloned without sacrificing monotonicity. Many of the excuses for the
(purportedly psychologically stressful) requirement of cardinal ratings
would vanish.
So that you can judge for yourself rather than rely on what somebody
else told you about the seriousness of K-Y's spoiler problem, here is
an
example ...
40 A>B>C
30 B>C>A
30 C>A>B
A wins according to K-Y rules and any other method anybody has ever
invented based on Universal Domain rules.
So according to clone-winner, a member of A's clone set should win if A
is cloned.
Suppose the A faction ranks the clone members in the order a1>a2> ...
a9, but the other factions rank this clone set in the opposite order
a9>...>a1. This will be the Kemeny order among the clones ... in fact,
to change from one clone order to the other takes a minimum of 36
transpositions... so changing all 60 of the reverse orders would
require
6036 while changing the other 40 ballots would require only 4036. The
difference is 36*20 or 720, a great cost (i.e.distance) saving by
rejecting the A faction order.
This puts the A faction ballots at a significant disadvantage compared
with the other two orders, so one of them will be the winning order
after the dust clears.
The A faction would claim that a2, a3, ...a9 spoiled the chances of
their favorite a1. That's why clone winner failure is referred to as
the spoiler effect.
That's not the only kind of clone dependence suffered under K-Y ... it
also suffers from crowding, for example; If B were cloned, and the C
and
B faction ranked the clones in the same order and A in a significantly
different order, that could cost A the election.
On the other hand if we were not constrained by UD, the factions could
vote
40 a1>a2> ...a9>>B>C
30 B>C>>a9>...>a1
30 C>>a9>...>a1>>B
for example, and the extra cost of moving {A} around could save the
first faction order.
Does that help clarify the situation?
Thanks!
El vie., 29 de oct. de 2021 4:29 p. m., Kristofer Munsterhjelm
<km_elmet@t-online.de mailto:km_elmet@t-online.de> escribió:
On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:
(2) it fails clone independence,
It has a nice balance between clone independence and
independence of
irrelevant alternatives. "Fails" just means the failure rates
are
not
zero.
I'd rather pick a Condorcet method with Condorcet methods' IIA
resilience (when there is a CW) *and* full clone independence,
than one
with the former but not the latter. :-)
Since that option is available, I mean.
-km
----
Election-Methods mailing list - see https://electorama.com/em for
list info
Election-Methods mailing list - see https://electorama.com/em for list
info
On 11/3/21 5:02 AM, Richard, the VoteFair guy wrote:
On 10/31/2021 5:04 PM, Forest Simmons wrote:
So the intractability issue is mostly an inconvenience ...
I'm pleased that you, unlike many others, realize that the
Condorcet-Kemeny method's long computation time for some possible cases
is just an inconvenience, not a deal breaker.
but the clone dependence is a deal breaker ...
I disagree that a non-zero failure rate for clone independence is a
deal-breaker.
The Beatpath (aka Schulze) method achieves a zero failure rate for clone
independence, but I suspect that, as a result, it has a significantly
higher failure rate for IIA -- Independence of Irrelevant Alternatives.
This characteristic would match what happens with IRV -- instant-runoff
voting. It has a zero failure rate for clone independence, but it has a
high failure rate for IIA.
I wouldn't trust IRV's clone independence all that much. James
Green-Armytage showed that, although IRV strictly passes clone
independence, it has serious candidate exit incentive, which means that
some allied candidates have an incentive to drop out, similar to Plurality.
A much better comparison to Kemeny is Ranked Pairs; see below.
The follow scatter plot shows this pattern:
https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg
FYI, the upper right corner is where there are zero clone failures and
zero IIA failures. Most of the plotted methods, with the notable
exception of plurality, can correctly handle two-candidate cases.
If the Condorcet-Kemeny method were modified to reduce the failure rate
for clone independence, that would increase its IIA failure rate.
I believe this obviously follows from the fact that Arrow's theorum and
other proofs tell us that no method can have zero failure rates for all
of a set of specific desirable fairness criteria. So it follows that
decreasing the failure rate for one fairness criterion will increase the
failure rate for at least one other fairness criterion.
That only holds if you're on the Pareto front and the two criteria
aren't aligned, which needs to be separately argued. Your graph shows
that it's possible to considerably improve your IIA compliance by losing
only a sliver of clone independence - that's what RCIPE does. So I
wouldn't consider it impossible that what you're seeing is just IRV
being bad, rather than clone independence and IIA inherently being
subject to a trade-off.
One could even argue that IIA should benefit from clone independence,
because clone independence is a form of IIA: Removing a clone who
doesn't win changes who actually wins. So a clone failure is an IIA
failure.[1]
This is why I've spent time calculating failure rates and plotting them
on a scatter plot. I want to know the failure RATES, not just whether
the failure rate is zero or non-zero.
In your plot, does 2 candidates clone independence mean that you have
two candidates and then you clone one of them and see if the winner
changes, or that you start off with one candidate and then you clone
that candidate?
Because if it's the former, then Borda should have nonzero clone
independence failure, e.g. this example:
6: A>B
3: B>A
A wins. Now clone B:
6: A>B1>B2
3: B1>B2>A
B1 wins, clone failure.
And if it's the latter, then Plurality should also be cloneproof.
So, I disagree that "clone dependence is a deal breaker." Yes, clone
independence is very important, but so is IIA.
I'll take both, thanks :-)
I know: I can't have IIA with a ranked method. But I can have ISDA, or
even River's IPDA and independence of strongly dominated alternatives.
And because the Condorcet-Kemeny method looks so deeply into ALL the
ballot preferences on all the ballots, I suspect that it eliminates
"irrelevant alternatives" better than a method that has a zero failure
rate for clone independence.
Kemeny is a method that seeks to optimize a certain scoring function of
the pairwise matchups that agree with the returned social outcome. (WLOG
I'll phrase it as maximizing, not minimizing.) The Kemeny objective
function is the sum of the strength of all the pairwise match-ups that
agree with the output ranking.
Another method can be phrased this way: Ranked Pairs. Its objective
function is just the strength of the strongest victory consistent with
the outcome, with ties broken by second strongest, then third strongest,
etc. Leximax.
Both these methods look deeply enough into all the ballots that they
pass both LIIA and ISDA. The difference is that Ranked Pairs is
computable in polynomial time... and happens to be cloneproof.
I don't see why should a method that is cloneproof necessarily look less
deeply into all the ballots than one that fails clone independence, just
because IRV happens to be that way.
-km
[1] I suspect that clone independence won't have much of a bearing on
(other) IIA failures because two candidates just happening to be clones
is vanishingly rare in the space of all possible elections. But by that
reasoning, any constraint relating clone independence to (other) IIA
failures should also be very weak unless the implications of passing the
property propagate throughout most of election space.
On ..., Forest Simmons wrote:
You have shown by your EM postings that you are not content
to just regurgitate the opinions and pronouncements of the
"experts". You want fundamental understanding so that you
have the tools to form and defend your own opinions with
alacrity.. which you have done with admirable valor based
on above average curiosity and willingness to think
carefully while searching for truth.
Yes, I'm trying to look beneath the surface to see what lies deeper.
This is why I'm frustrated that many people are content to judge
election methods based on the simplistic pass-versus-fail "grading" system.
We have seen that no method based solely on ranked choice ballots can
satisfy the IIAC except by failing the Majority Criterion....
You invoked Arrow, but Arrow never said that Clone Winner and IIAC
were incompatible.
I referred to Arrow's theorem as an example of a broader concept. That
concept is that if a method has a zero failure rate for specific
fairness criteria, then there are specific other criteria that cannot
have a zero failure rate.
As you point out, there are proofs that support this concept for
specific combinations of characteristics.
In my opinion we don't need to wait for more theorems to extend this
concept to the broader concept: There are going to be other combinations
of fairness criteria for which getting a zero failure rate for one of
them means that we cannot get a zero failure rate for another one.
... I am curious how you came up with the idea that K-Y trades in
Clone Winner compliance for better IIAC compliance.
Hopefully I've just answered this question.
Expressed non-mathematically: "You can't have it all."
I'm attempting to use measurements to quantify the answer to the
question: "How close can we get to identifying a method that has a nice
balance of low failure rates across the most important fairness criteria?"
Clone winner failure is not about electing the wrong clone ... it's
about none of the clones of the erstwhile winner being elected.
...
That is the spoiler problem.
As I understand it, the word "spoiler" overlaps with the clone
independence (CI) criterion and the IIA (independence of irrelevant
alternatives) criterion. Specifically:
-
CI refers to the effect of adding candidates.
-
IIA refers to the effect of removing candidates.
I think the word spoiler can refer to either an added candidate or a
removed candidate changing the results, right?
This relates to a comment from Kristofer:
"One could even argue that IIA should benefit from clone independence,
because clone independence is a form of IIA: Removing a clone who
doesn't win changes who actually wins. So a clone failure is an IIA
failure."
The Wikipedia definition of clone independence says:
"... the winner must not change due to the addition of a non-winning
candidate who is similar to a candidate already present."
After an expert on Reddit pointed out that a different clone winning
(instead of the originally winning clone) is not really a failure, I
changed the software to handle it as you say, where a different clone
winning is not a clone independence failure.
I admit I'm trying to look deeper. Especially into the criteria related
to "strategic nomination." That's because money can be used to
"nominate" and basically un-nominate candidates. My goal is to find
election systems that reduce the currently excessive influence of money
on politics.
If you want a method that is both clone winner compliant and IIAC
compliant, Approval Sorted Margins (ASM), or Majority Judgment Sorted
Margins (MJSM) is what you need.
To repeat, I'm not looking for zero failure rates. I'm looking for a
nice combination of low failure rates.
Also, very importantly, I'm not interested in methods that use
rating/cardinal ballots.
That's because ranked choice ballots are already appearing on ballots in
various states in the United States.
A method that uses a rating/cardinal ballot would eventually lead to
overlap. Specifically a voter would be asked to do both ranking and
rating on the same ballot. That would be unacceptable.
In other words, in the U.S., ranked-choice ballots have already won the
battle against rating/score ballots.
I do agree that in the distant future there will be situations where
rating/score ballots are used, and useful. But voters would be way too
confused to be introduced to both kinds at the beginning, which is where
we are now.
Perhaps in your simulations you threw out cycles like these ...
The simulations ignore tied results. They do not ignore Condorcet
(rock-paper-scissors) cycles -- unless that produces a tie for the winner.
Again, thank you Forest for your feedback. It helps to keep my thinking
clear.
Richard Fobes
On 11/3/2021 2:44 PM, Forest Simmons wrote:
Richard,
You have shown by your EM postings that you are not content to just
regurgitate the opinions and pronouncements of the "experts". You want
fundamental understanding so that you have the tools to form and defend
your own opinions with alacrity.. which you have done with admirable
valor based on above average curiosity and willingness to think
carefully while searching for truth.
...