Why All the Fuss?
On 2/26/2023 9:47 PM, Forest Simmons wrote:
Here's my question: do simulations carry any weight
with the public? Or do they just care about choice
of buzz words and phrases like democracy; majority
rule, etc?
I have not seen hardly anyone in the "public" realm who initially seems
to care about simulations.
Mostly they care about "who will win?" "which party does it favor?"
"does it empower minorities?" and most of all: "Can I understand it? And
does it make sense?"
For the latter, the FairVote organization has popularized the notion of
eliminating one candidate at a time. It's easier to comprehend.
Especially compared to something like the Smith set. Even the Condorcet
winner concept is difficult for many, many voters to understand.
Aside: I've had success educating "the public" about the idea that a
"pairwise losing candidate" -- which is a simpler variation of
"Condorcet loser" -- deserves to be eliminated. A soccer analogy helps:
if a soccer team loses against every other team then it shouldn't be
possible for that team to win. (This is one of the two refinements over
IRV that the RCIPE method, mentioned below, offers. The other
refinement is to count ballots that the FairVote folks wants to discard
as an "overvote.")
Yet simulations can be useful IF the results are presented as a
GRAPHIC that compares "your" methods with familiar methods.
I created a graphic (at the following link) that shows failure rates for
RCIPE (ranked choice including pairwise elimination) and IPE (instant
pairwise elimination) plotted along with IRV, plurality, Borda, and
Kemeny. That graphic has been helpful to some people who already
understand IRV and have heard about Condorcet methods.
http://votefair.org/clone_iia_success_rates.png
In this sense such a graphic is like a Yee diagram. Most people
intuitively recognize that the Yee diagram for IRV reveals that method
has serious flaws. (However, trying to explain Yee diagrams is not
fruitful.)
The fans of STAR voting have gotten lots of mileage from their graphs of
VSE (voter satisfaction efficiency). Alas most people don't realize
that the "efficiency" is meaningful among a group of friends or
cooperative people, but is not meaningful in governmental elections
where strength of opinion violates the principle of "one person one vote."
In summary, graphics that show many thousands of simulations for
multiple methods are useful among informed voters.
Such graphics are also useful for us, the experts. It reveals the
extent to which a method is better than other methods.
In other words, just looking at specific cases to identify failure
possibilities is of limited use. In contrast, quantitative graphics
that allow failure rates to be compared with familiar methods are quite
useful.
Not as "proofs" but as supporting evidence for claims about being "better."
And such graphics answer the question "Is this 'better' method worth the
extra effort it takes to understand it and calculate it?" If there is
only a small gain, most people will say "no it's not worth the extra
complication."
Forest, I've enjoyed your speculations about better methods. It would
be interesting to see graphics that show specific failure rates -- such
as IIA, clone independence, burial resistance, chicken resistance, etc.
Such graphic comparisons will reveal whether your improvements are big
improvements or tiny improvements, and which methods excel at which
characteristics.
Then it will become easier to find a balance between mathematically
ideal and "good enough" for use in real elections.
Richard Fobes
The VoteFair guy
Voter Choice Massachusetts reported that over 200 academics in conjunction with The New York Times urged Congress to adopt personally (proportionally) representative multi-member constituencies. (Something like Cambridge) Singlemember constituencies can never be this. They are monopolistic and not competitive, as generally required of an allegedly democratic society. That is to say, single members cannot meet more than a minimal measure of democracy, which is what a single member majority is.
A real obstacle to progress is the tunnel vision with regard to the "majority" concept, which is always confined to single majority. Whereas proportional counts, like the Hare quota, or the Droop quota, or my averaging of them, the Harmonic Mean quota, generalise the concept of the majority from single member majority to multi-member majority, or from minimally representative to maximally representative or democratic.
A distinction might be made between a democratic election method and a rational election method. Single members single member majorities cannot be more than minimally democratic, for above reason given. The use of Binomial STV offers a rational procedure for single members, because it has a rational exclusion count, as well as a rational election count, but that does not make it, like any other system, more than minimally democratic for single member elections.
Regards,
Richard Lung.
On 28 Feb 2023, at 12:35 am, Richard, the VoteFair guy electionmethods@votefair.org wrote:
On 2/26/2023 9:47 PM, Forest Simmons wrote:
Here's my question: do simulations carry any weight
with the public? Or do they just care about choice
of buzz words and phrases like democracy; majority
rule, etc?
I have not seen hardly anyone in the "public" realm who initially seems to care about simulations.
Mostly they care about "who will win?" "which party does it favor?" "does it empower minorities?" and most of all: "Can I understand it? And does it make sense?"
For the latter, the FairVote organization has popularized the notion of eliminating one candidate at a time. It's easier to comprehend. Especially compared to something like the Smith set. Even the Condorcet winner concept is difficult for many, many voters to understand.
Aside: I've had success educating "the public" about the idea that a "pairwise losing candidate" -- which is a simpler variation of "Condorcet loser" -- deserves to be eliminated. A soccer analogy helps: if a soccer team loses against every other team then it shouldn't be possible for that team to win. (This is one of the two refinements over IRV that the RCIPE method, mentioned below, offers. The other refinement is to count ballots that the FairVote folks wants to discard as an "overvote.")
Yet simulations can be useful IF the results are presented as a GRAPHIC that compares "your" methods with familiar methods.
I created a graphic (at the following link) that shows failure rates for RCIPE (ranked choice including pairwise elimination) and IPE (instant pairwise elimination) plotted along with IRV, plurality, Borda, and Kemeny. That graphic has been helpful to some people who already understand IRV and have heard about Condorcet methods.
http://votefair.org/clone_iia_success_rates.png
In this sense such a graphic is like a Yee diagram. Most people intuitively recognize that the Yee diagram for IRV reveals that method has serious flaws. (However, trying to explain Yee diagrams is not fruitful.)
The fans of STAR voting have gotten lots of mileage from their graphs of VSE (voter satisfaction efficiency). Alas most people don't realize that the "efficiency" is meaningful among a group of friends or cooperative people, but is not meaningful in governmental elections where strength of opinion violates the principle of "one person one vote."
In summary, graphics that show many thousands of simulations for multiple methods are useful among informed voters.
Such graphics are also useful for us, the experts. It reveals the extent to which a method is better than other methods.
In other words, just looking at specific cases to identify failure possibilities is of limited use. In contrast, quantitative graphics that allow failure rates to be compared with familiar methods are quite useful.
Not as "proofs" but as supporting evidence for claims about being "better."
And such graphics answer the question "Is this 'better' method worth the extra effort it takes to understand it and calculate it?" If there is only a small gain, most people will say "no it's not worth the extra complication."
Forest, I've enjoyed your speculations about better methods. It would be interesting to see graphics that show specific failure rates -- such as IIA, clone independence, burial resistance, chicken resistance, etc. Such graphic comparisons will reveal whether your improvements are big improvements or tiny improvements, and which methods excel at which characteristics.
Then it will become easier to find a balance between mathematically ideal and "good enough" for use in real elections.
Richard Fobes
The VoteFair guy
Election-Methods mailing list - see https://electorama.com/em for list info
On Mon, Feb 27, 2023, 4:35 PM Richard, the VoteFair guy <
electionmethods@votefair.org> wrote:
On 2/26/2023 9:47 PM, Forest Simmons wrote:
Here's my question: do simulations carry any weight
with the public? Or do they just care about choice
of buzz words and phrases like democracy; majority
rule, etc?
I have not seen hardly anyone in the "public" realm who initially seems
to care about simulations.
Mostly they care about "who will win?" "which party does it favor?"
"does it empower minorities?" and most of all: "Can I understand it? And
does it make sense?"
These two questions should be important to everyone ... especially method
designers.
Another important question is efficiency and transparency of tally... a big
weakness of IRV.
Also ... is sincere strategy optimal? Or do voters have to reverse their
ballot preferences to protect their sincere preferences.
For the latter, the FairVote organization has popularized the notion of
eliminating one candidate at a time. It's easier to comprehend.
Especially compared to something like the Smith set. Even the Condorcet
winner concept is difficult for many, many voters to understand.
Aside: I've had success educating "the public" about the idea that a
"pairwise losing candidate" -- which is a simpler variation of
"Condorcet loser" -- deserves to be eliminated. A soccer analogy helps:
if a soccer team loses against every other team then it shouldn't be
possible for that team to win. (This is one of the two refinements over
IRV that the RCIPE method, mentioned below, offers. The other
refinement is to count ballots that the FairVote folks wants to discard
as an "overvote.")
Great work!
What did you think about the Martin Harper solution to the "over vote"
problem?
Yet simulations can be useful IF the results are presented as a
GRAPHIC that compares "your" methods with familiar methods.
I created a graphic (at the following link) that shows failure rates
What constitutes "failure"? If we have notions of success and failure that
appeal to voters we can design our methods around them. Which criteria of
success and failure measures by your graphics appeal the most to them?
for
RCIPE (ranked choice including pairwise elimination) and IPE (instant
pairwise elimination)
How is IPE received? That is the focus of my recent efforts ... nominal
elimination criteria backed up with pairwise confirmation when possible ...
else pairwise over-ridden ... in a way that makes burial, chicken
defection, and other insincere manipulations likely to backfire.
Does the public care about that?
I ask because that is the main focus of our simulations.
plotted along with IRV, plurality, Borda, and
Kemeny. That graphic has been helpful to some people who already
understand IRV and have heard about Condorcet methods.
http://votefair.org/clone_iia_success_rates.png
In this sense such a graphic is like a Yee diagram. Most people
intuitively recognize that the Yee diagram for IRV reveals that method
has serious flaws. (However, trying to explain Yee diagrams is not
fruitful.)
Too bad ... it's pretty simple as far as graphics go ... the color of each
pixel is the color that identifies the candidate who would win if the
voters were distributed symmetrically about that pixel.
It's a huge mistake to introduce two dimensional Yee diagrams without first
getting students comfortable with one dimensional Yee diagrams.
If you do a good job in the one dimensional case, the two dimensional case
is pretty much optional ... Galileo didn't need the Hubble telescope to get
the basic picture ... nor did Van Leeuwenhoek need an electron scanning
microscope.
The fans of STAR voting have gotten lots of mileage from their graphs of
VSE (voter satisfaction efficiency). Alas most people don't realize
that the "efficiency" is meaningful among a group of friends or
cooperative people, but is not meaningful in governmental elections
where strength of opinion violates the principle of "one person one vote."
But STAR is a runoff like IRV in which the winner is determined by which
candidate gets a majority preference in the final pairwise contest. Each
participating voter has one vote in that contest ... all of the previous
stages are clumsy jockeying to see who the two finalists are for the actual
one-person-one-vote contest.
But, you say, "Every stage of IRV serves to shuttle the voter's 'vote' from
the first stage to the final stage."
But those stages form a very lossy channel for the "vote" signal.
Those stages are plagued by vote splitting, center squeeze, etc.... Without
the pairwise check of RCIPE they have very little democratic validity ...
just superficial correlation with suitability for continued participation
versus elimination.
[Martin Harper invented his method to disentangle the ultimate over-vote ..
approval itself, to find the logical destination of the "one vote" of the
"one person" who voted a given approval ballot. His solution was to add it
to the total of the ballot approved candidate with the most support from
the other voters. Your one vote goes to the candidate you approve with the
best chance of winning. The generalized Martin Harper rule accomplishes the
same disentanglement for score ballots ... to give them "one ballot, one
vote" compliance ... a way of deducing who "got the vote" of the person who
submitted the ballot.]
As far as unequal vote strength goes ...
Just as score gives more strength to high ratings .. so IRV gives more
strength to high rankings ... which (in both cases) is a big incentive for
insincerely ranking compromise over favorite ... the important urgency of
first place rankings and ratings (and their role in subverting sincere
voting) cannot be ignored.
That urgency wouldn't be there if the IRV big lie were true ..."go ahead
and rank your favorite first ... if it doesn't win, your vote will transfer
to your second choice."
RCIPE is an important corrective ... but other, more streamlined IPE
variants are much more efficient, transparent, and practical... if only the
public could understand that reality.
In score voting that compromise urgency makes score strategically
equivalent to Approval ... strategically it would be just as good to do
STAR with RCV ballots and approval cutoffs ... and have the runoff between
the top two approval candidates.
In that case there would be zero incentive for insincere rankings.
In fact, any runoff method that picks the two finalists with a provisional
set of ballots (approval, score, grade, judgment, RCV, whatever) and
reserves a fresh set of RCV ballots for choosing between the two finalists
... gives zero incentive for insincere rankings on the final ballots.
Any voters that want to abstain from that messy, provisional, strategical
ballot should be able to do so, imho.
What do you think about the VPB Vote for a Published Ballot option?
It might get more participation from voters put off by the inconvenience of
copying those recommendations onto a ballot in the voting booth.
In summary, graphics that show many thousands of simulations for
multiple methods are useful among informed voters.
Such graphics are also useful for us, the experts. It reveals the
extent to which a method is better than other methods.
In other words, just looking at specific cases to identify failure
possibilities is of limited use. In contrast, quantitative graphics
that allow failure rates to be compared with familiar methods are quite
useful.
Not as "proofs" but as supporting evidence for claims about being "better."
And such graphics answer the question "Is this 'better' method worth the
extra effort it takes to understand it and calculate it?" If there is
only a small gain, most people will say "no it's not worth the extra
complication."
Forest, I've enjoyed your speculations about better methods. It would
be interesting to see graphics that show specific failure rates -- such
as IIA, clone independence, burial resistance, chicken resistance, etc.
That's exactly what we need. Kevin and Kristofer have created some top
notch graphics along those lines to satisfy our curiosities ... but
somebody needs to digest them and adapt them for public consumption.
Such graphic comparisons will reveal whether your improvements are big
improvements or tiny improvements, and which methods excel at which
characteristics.
Then it will become easier to find a balance between mathematically
ideal and "good enough" for use in real elections.
Richard Fobes
The VoteFair guy
Election-Methods mailing list - see https://electorama.com/em for list
info
After many thought experiments I'm leaning towards the following Worst
Loser Elimination version:
Elect the pairwise undefeated candidate if there is one ... otherwise ...
until there is an undefeated candidate ... among the uneliminated
candidates, eliminate the candidate whose maximum pairwise support is the
smallest ... after first eliminating any candidates it defeats pairwise.
One thing I like about this version is that it only needs as input the
pairwise support information ... unlike elimination methods that depend on
Top or Bottom ballot counts, it is applicable to tournaments.
To me, that is the true spirit of Universal Domain methods ... binary
choices based on ordinal information .. no inference of strength that is
based on how high or low in the rankings ... a subtle influence that
subverts the purity of binary comparisons as a basis for voting.
I'm not against methods that do make use of expressions of intensity of
preference ... only methods that pretend not to, but actuually do.
The pairwise information is efficiently precinct summable with one pass
through the ballots. The practical importance of this feature is hard to
over estimate.
Example1
x: A>B>C (Sincere is A>C>B)
y: B>C>A
z: C>A>B
Assume (y+z)>x>max(y,z), so the A faction is the largest, but not a
majority of the electorate.
The maximum pairwise support for C is its support against A by the B and C
factions ... the winning votes of the defeat of A by C: y+z= n-x, where
n=x+y+z.
The max pairwise supports of the other two candidates A and B are n-y and
n-z, respectively, which are both larger than n-x ... the smallest value
of max pairwise support ... making C the candidate to eliminate (after
eliminating the candidate defeated by it).
So in the context of this kind of three faction cycle with complete
ballots, the candidate that defeats the favorite of the largest faction is
the first one eliminated ... after first eliminating the candidate it
defeats.
How does this discourage burial?
The candidate on the losing end of the weakest wv defeat is the one with
the greatest hope of successfully burying its victor... and when it is the
favorite of the largest faction, it has the greatest hope of coming out on
top of the cycle resulting from that burial.
Example 2
48 C
28 A>B
24 B (sincere B>A)
Evidently a Chicken defection by the B faction ... putting the Sincere CW
into a cycle in which its max pairwise support is 28 votes against C. The
respective max supports of B and C in this cycle are 52 and 48, both larger
than 28.
So A is eliminated after the candidate it defeats ... the defector B.
In example 1 the MinMaxPS candidate took down with it the candidate
responsible for its burial.
In example 2 the MinMaxPS candidate took down with it the defecting
candidate that put it into a cycle.
In both cases the MinMaxPS candidate was the Sincere CW.
In both cases the manipulating candidate had high hopes of winning the
cycle it created by its manipulation ... because almost all Condorcet
efficient methods break cycles at weakest wv defeat in the beatcycle chain.
Our method also eliminates that defeat ... but both winner and loser of
that defeat ... making the manipulator's gambit fail, instead of rewarding
the loser of the weakest wv defeat like naive Condorcet methods do ...
which thereby reward the manipulator responsible for creating the cycle.
So this method takes very precise aim at taking down Chicken Defectors and
Buriers that hope to defeat the Sincere CW by creating a cycle in which it
(the Sincere CW) has become the weakest link.
Our method counters that strategy by taking out the entire weakest link ...
both winner and loser, unlike RP, CSSD, River, MinMax(wv), etc.
Can the general public appreciate this?
How do we help them see?
Through a wide variety of examples where ordinary Condorcet fails to elect
the Sincere CW while rewarding the cycle creator?
But also we need to make clear that burial of the Sincere CW is no problem
for IRV .... only because IRV is not a Condorct method ... it's not even
expected to elect the CW in the first place .... instead of burying the CW
it eliminates it by the Squeeze effect ... a much more common problem than
Burial ... one that is only overcome by serious insincere compromise ...
which belies the IRV promise of sincere voting safety.
The squeeze effect happens with sincere votes. Burial cannot happen with
sincere ballots. The Squeeze distortion of the democratic will, will be
more common than Burial ... as long as voters vote sincerely ... which
ordinary voters tend to do when not urged to vote lesser evil above their
favorite.
So don't throw out the Condorcet baby with the burial bath water. Keep
Condorcet ... but make sure it is Burial and Chicken resistant Condorcet
... not vulnerable to the most tempting insincere manipulations.
If that required some elaborate multiple pass version of Condorcet ... like
Smith//IRV, BTR-IRV, RCIPE, etc ... or even anything as elaborate as Ranked
Pairs ... then it might not be worth it.
But voters like (and practically demand) elimination methods ... like ours
... with the same simplicity as MinMax the simplest well known Condorcet
method (but not Burial resistant or Landau efficient).
Let's formulate MinMax(wv) as an elimination method to facilitate the
comparison:
Until there is a candidate that is undefeated among the uneliminated
candidates, eliminate the candidate whose Max Pairwise Support is minimal.
Here's our manipulation resistant version:
Until there is an candidate that is undefeated among the uneliminated
candidates, eliminate the candidate whose Max Pairwise Support is minimal,
after first eliminating any candidates defeated by it.
-Forest
On Sun, Feb 26, 2023, 9:47 PM Forest Simmons forest.simmons21@gmail.com
wrote:
The Symmetric Gross Loser notion of nominal "worst" seems to work well for
burial resistance ... but it is not very chicken resistant.
Here's a better one ... one I mentioned before .... where the nominally
worst candidate is the loser of the strongest defeat... where defeat
strength is gauged by the number of ballots on which the victor outranks
the loser plus the bottom count of the loser... we abbreviate this gauge as
wv+lbc... winning votes plus losing bottom count.
Remember that a candidate's bottom count is the number of ballots on which
it outranks nobody.
So the method is to elect the CW if there is one ... otherwise ...
Until there is an unbeaten candidate among the remaining candidates,
eliminate the nominally worst candidate after first eliminating the
candidates it beats pairwise (if any).
The nominally worst candidate is
the loser of the single strongest defeat, gauged by av+lbc ... winning
votes plus losing bottom count.
This method seems very promising for both burial and chicken resistance
according to initial hand counts of some standard test cases.
Simulations will tell.
Here's my question: do simulations carry any weight with the public? Or do
they just care about choice of buzz words and phrases like democracy;
majority rule, etc?
-Forest
On Sun, Feb 26, 2023, 3:57 PM Forest Simmons forest.simmons21@gmail.com
wrote:
Here's the cleanest notion of "worst" in this contex:
The "nominally worst" candidate is the Symmetric Gross Loser (SGL)
defined as the pairwise loser between the candidate with the greatest
pairwise opposition and the least pairwise support.
I am suggesting specializing our "worst-loser" elimination method to the
following:
While there is more than one remaining candidate, from among them
eliminate the current Symmetric Gross Loser SGL after first eliminating
every candidate (if any) pairwise defeated by this SGL.
Elect the last candidate to be left standing (or eliminated).
This is the version I would like to see tested.
-Forest
On Sun, Feb 26, 2023, 11:45 AM Forest Simmons forest.simmons21@gmail.com
wrote:
Correction below ...
On Sun, Feb 26, 2023, 10:58 AM Forest Simmons <
forest.simmons21@gmail.com> wrote:
In the context of elimination methods (like IRV, Coombs, Baldwin, rtc,
as well as all of our "worst-elimination" methods) the temptation for a
faction to bury (insincerely lower on their ballots relative to one or more
other candidates) a candidate C in order to help some candidate A win
instead of C ... this temptation arises when C defeats A pairwise, but the
A supporters, by lowering C, get C eliminated at some earlier elimination
step so A and C are not competing head to head.
Note that this burial ploy will not work wih IRV elimination, because
lowering C on a ballot where A is already preferred over C will not
decrease C's first place support ... so it cannot get C eliminated earlier
... since IRV elimination prioritizes low first place support.
Coombs elimination, on the other hand prioritizes high last place
counts for early elimination, so the burial ploy has a good chance of
succeeding under Coombs.
Note that the feature that gives IRV immunity to burial is the same
feature that makes it vulnerable to the Squeeze Effect.
So is it possible to have immunity to burial and squeeze in the same
method?
Yes, our "worst-elimination" methods have immunity to both... immunity
to squeeze because of Condorcet efficiency and immunity to burial because
in the above ploy, to eliminate C earlier (whether by burial or some other
means) must backfire as long as the ballot change preserves C's pairwise
win over A.
It does preserve C's pairwise win over A in the case of burial ...
because A was already ranked ahead of C by the buriers before the burial.
So how does this fact make C's elimination before A backfire?
Because according to our method...when C reaches "worst" status .... it
is eliminated only "after any and every candidate defeated by it [including
A] is eliminated"
In other words, if and when C reaches "worst" status (with or without
the push downward from A supporters), it takes down A with it. So it
doesn't matter if our nominal standard of worst is "fewest first" or "most
last" or anything else ... if it speeds up C's demise, it also speeds up
the demise of any candidate that C defeats pairwise.
In the three candidate case ... C is the sincere CW, and wins if C is
eliminated, sothe other candidate B is the sincere Condorcet Loser.
The A faction buries C under B, which creates a beat cycle ABCA.
A thinks this cycle gives it a chance at winning ... which it would
under most elimination methods.
But not under ours, because, on the one hand A cannot win unless B or C
is "worst" ... and ...
If B is worst it takes A down with it because B defeats A in the cycle
... then B defeats C.
Whoops... A defeats B.
So the burial can succeed if it is enough to make B beat C, but not
enough to make C nominally "worse" than B ... a delicate, hence risky
balance.
Which nominal standards of "worst" make this balance most precarious if
not impossible?
On the other hand, if C is worst, it takes A down with it, leaving B as
winner.
So burial of the A faction's second choice results in the election of
their anti-favorite B ... a complete backfire of the burial gambit!
I hope that.explanation clarifies the main reason for the clearing out
of the candidates defeated by the pivot candidate, i.e. the nominally
"worst" candidate, at each elimination stage ... see there really is a
"method to our madness".
You may remember I once proposed a Quick & Dirty method that simply
said elect the "best" candidate that pairwise defeats the "worst" Smith
candidate.
That's a shortcut rule of thumb that will elect the same candidate as
our "worst-elimination" methods do whenever there are no more than three
Smith members ... but the short cut is not Landau efficient ... so I don't
recommend it.
The main defect of the shortcut is that it requires some knowledge of
Smith ... which our "worst-elimination" methods do not require.
So even though Q&D is shorter ... it is neither quite as good nor quite
as simple.
If you have any question about any other method that you would like to
compare with its nearest "worst-elimination" method ... it could interest
other readers of the EM list, too.
Remember "worst" is a nominal, tentative judgment that can hardly go
wrong ... since the direct pairwise comparisons trump the tentative
judgments if there is any disagreement.
Good sources for "worst" candidates are losers of other methods.
Also losing candidates in strong pairwise defeats ... for any decent
gauge of defeat strength.
Enjoy!
Forest
On Sun, Feb 26, 2023, 8:37 AM Forest Simmons <
forest.simmons21@gmail.com> wrote:
The ElectoScope aka Yee Diagram makes clear both the problem with and
the solution to the Center Squeeze phenomenon ... elimination methods that
judge "worst" by size of the Voronoi regions ten to suffer from the defect.
But the cure is easy and sure ... no eliminations of undefeated
candidates.
All Condorcet Efficient methods have the same Yee Diagram ... the win
region for a candidate is its entire Voronoi polygon, no matter how small.
Next ... burial ...
On Fri, Feb 24, 2023, 3:49 PM Forest Simmons <
forest.simmons21@gmail.com> wrote:
Why can't we just have majority rule? Why all the fiss?
Many a student of my "Math for Liberal Arts" class asked me that
question during the decades I taught the Community College course by that
name.
That's the reason Joe Malkovich's contribution to the textbook was
so important ... his examples of ballot profiles for which no two of
several different majority rule methods agreed on who should be elected.
Most if not all of these methods start out with the phrase..."Elect
the majority winner if there is one, otherwise cull out the weakest
(meaning democratically weakest) candidates one by one until there is a
majority winner among the remaining."
But there is no agreement on what constitutes "democratically weak'
... and it makes a big difference!
So what can we do?
One thing we have tried without much success is to suggest that the
next best thing, lacking a first preference majority winner ... is to elect
the candidate unbeaten by any majority comparison with another candidate.
But just as there is no guaranteed outright majority winner ...
neither is there any guarantee of the existence of a pairwise unbeaten
candidate.
It turns out that the best we can guarantee along these lines is the
existence of at least one candidate that can pairwise beat in two steps
every candidate that he cannot defeat in one step (by a majority of the
participating voters).
Such a candidate is said to be "uncovered." We're going to need a
better word than that if we want to get anybody on board with this minimum
guaranteeable standard of "majority rule."
Let's say a candidate is "democratically strong" if it has a beatpath
to every other candidate ... and is "very strong majority pairwise" if it
has a beatpath of one or two steps to each of the other candidates ... each
step being a pairwise victory by a majority of the participating voters ...
meaning voters expressing a preference.
Then the "Strong Majority Pairwise Criterion" (SMPC) is satisfied
only by methods that always elect uncovered candidates.
Contrast that with the weaker, relatively impotent Condorcet
Criterion which is satisfied by any method that elects an unbeaten
candidate "when such a candidate exists" ... the copout escape clause in
quotes letting the method off the hook whenever things start to get
interesting.
Another way to express compliance with this SMPC criterion is "Landau
Efficient."
Every method under the "Worst-Elimination" umbrella is seamlessly
Landau Efficient ... it effortlessly (and without fanfare) satisfies the
SMPC ... no matter what nominal standard of worst is instantiated into the
umbrella template.
Who can name even one commonly known election method that is Landau
efficient?
What's more ... no matter the nominal "worst" criterion, the method
will be more or less burial resistant ... as I will explain presently.
I suggest that proposals for any method under this umbrella, include
verbiage to the effect ...
"When there is no majority winner or any candidate that a majority of
the participating voters rank ahead of each of the other candidates ...
cull out one-by-one the nominally "worst" candidates as well as any
democratically weaker candidates (as determined by majority ballot
preferences) until there is a majority winner among the remaining
candidates."
This umbrella is so robust that the choice of nominal "worst" is not
overly critical. The main thing is to keep it simple enough that (1)
voters can easily understand and relate to it, and (2) it can be
efficiently and transparently tallied by precinct without multiple passes
through the ballots.
Complicated "worst" criteria are the ones that tend to introduce
crowding and teaming distortions ... smallest Borda score is a example of
this kind of "worst" criterion ... pun intended.
Anti-vote splitting can be easily ensured (in general) by allowing
equal-top whole counting, and multiple truncations in large elections.
In the continuation I will explain why this method tends to backfire
on buriers.
At some point those who have power to advocate for one method over
another need to understand them beyond the surface heuristics that appeal
to the impatient public.
Among other things enlightened defenders of electoral democracy need
to understand the "squeeze effect" and "burial ploys" ...
To be continued ...
-Forest
Elimination methods may have a policy mandate but they do not have a scientific or knowledge mandate. They violate conservation of (preference) information. Elimination independent of scale of preference is precisely the fault, found over two centuries ago, by Pierre-Simon Laplace, according to JFS Ross, with Condorcet pairing elimination of candidates. It does not take into account the relative importance of higher to lower preferences. Why Laplace sided with Borda amounted to his opening the way to rational counts of preference ranges. Of which Gregory supplied the definitive statistical method to next preferences, of weighting in arithmetic proportion.
It is doubtful whether the Condorcet Winner (or conversely Loser) applies to more than single winner elections, the least democratic, lacking multi-member range of representation. This perhaps may be demonstrated by the consideration that individual candidates hold an over-lapping group or "party" of opinions. Voters support for parties themselves become less and less partisan with more particular choices of parties in proportionally elected multi-member constituencies. So, it may be the CW becomes less and less an absolute individual choice, within the wider context of personal proportional representation, in multi-member constituencies.
Regards,
Richard Lung.
On 1 Mar 2023, at 2:47 am, Forest Simmons forest.simmons21@gmail.com wrote:
After many thought experiments I'm leaning towards the following Worst Loser Elimination version:
Elect the pairwise undefeated candidate if there is one ... otherwise ...
until there is an undefeated candidate ... among the uneliminated candidates, eliminate the candidate whose maximum pairwise support is the smallest ... after first eliminating any candidates it defeats pairwise.
One thing I like about this version is that it only needs as input the pairwise support information ... unlike elimination methods that depend on Top or Bottom ballot counts, it is applicable to tournaments.
To me, that is the true spirit of Universal Domain methods ... binary choices based on ordinal information .. no inference of strength that is based on how high or low in the rankings ... a subtle influence that subverts the purity of binary comparisons as a basis for voting.
I'm not against methods that do make use of expressions of intensity of preference ... only methods that pretend not to, but actuually do.
The pairwise information is efficiently precinct summable with one pass through the ballots. The practical importance of this feature is hard to over estimate.
Example1
x: A>B>C (Sincere is A>C>B)
y: B>C>A
z: C>A>B
Assume (y+z)>x>max(y,z), so the A faction is the largest, but not a majority of the electorate.
The maximum pairwise support for C is its support against A by the B and C factions ... the winning votes of the defeat of A by C: y+z= n-x, where n=x+y+z.
The max pairwise supports of the other two candidates A and B are n-y and n-z, respectively, which are both larger than n-x ... the smallest value of max pairwise support ... making C the candidate to eliminate (after eliminating the candidate defeated by it).
So in the context of this kind of three faction cycle with complete ballots, the candidate that defeats the favorite of the largest faction is the first one eliminated ... after first eliminating the candidate it defeats.
How does this discourage burial?
The candidate on the losing end of the weakest wv defeat is the one with the greatest hope of successfully burying its victor... and when it is the favorite of the largest faction, it has the greatest hope of coming out on top of the cycle resulting from that burial.
Example 2
48 C
28 A>B
24 B (sincere B>A)
Evidently a Chicken defection by the B faction ... putting the Sincere CW into a cycle in which its max pairwise support is 28 votes against C. The respective max supports of B and C in this cycle are 52 and 48, both larger than 28.
So A is eliminated after the candidate it defeats ... the defector B.
In example 1 the MinMaxPS candidate took down with it the candidate responsible for its burial.
In example 2 the MinMaxPS candidate took down with it the defecting candidate that put it into a cycle.
In both cases the MinMaxPS candidate was the Sincere CW.
In both cases the manipulating candidate had high hopes of winning the cycle it created by its manipulation ... because almost all Condorcet efficient methods break cycles at weakest wv defeat in the beatcycle chain.
Our method also eliminates that defeat ... but both winner and loser of that defeat ... making the manipulator's gambit fail, instead of rewarding the loser of the weakest wv defeat like naive Condorcet methods do ... which thereby reward the manipulator responsible for creating the cycle.
So this method takes very precise aim at taking down Chicken Defectors and Buriers that hope to defeat the Sincere CW by creating a cycle in which it (the Sincere CW) has become the weakest link.
Our method counters that strategy by taking out the entire weakest link ... both winner and loser, unlike RP, CSSD, River, MinMax(wv), etc.
Can the general public appreciate this?
How do we help them see?
Through a wide variety of examples where ordinary Condorcet fails to elect the Sincere CW while rewarding the cycle creator?
But also we need to make clear that burial of the Sincere CW is no problem for IRV .... only because IRV is not a Condorct method ... it's not even expected to elect the CW in the first place .... instead of burying the CW it eliminates it by the Squeeze effect ... a much more common problem than Burial ... one that is only overcome by serious insincere compromise ... which belies the IRV promise of sincere voting safety.
The squeeze effect happens with sincere votes. Burial cannot happen with sincere ballots. The Squeeze distortion of the democratic will, will be more common than Burial ... as long as voters vote sincerely ... which ordinary voters tend to do when not urged to vote lesser evil above their favorite.
So don't throw out the Condorcet baby with the burial bath water. Keep Condorcet ... but make sure it is Burial and Chicken resistant Condorcet ... not vulnerable to the most tempting insincere manipulations.
If that required some elaborate multiple pass version of Condorcet ... like Smith//IRV, BTR-IRV, RCIPE, etc ... or even anything as elaborate as Ranked Pairs ... then it might not be worth it.
But voters like (and practically demand) elimination methods ... like ours ... with the same simplicity as MinMax the simplest well known Condorcet method (but not Burial resistant or Landau efficient).
Let's formulate MinMax(wv) as an elimination method to facilitate the comparison:
Until there is a candidate that is undefeated among the uneliminated candidates, eliminate the candidate whose Max Pairwise Support is minimal.
Here's our manipulation resistant version:
Until there is an candidate that is undefeated among the uneliminated candidates, eliminate the candidate whose Max Pairwise Support is minimal, after first eliminating any candidates defeated by it.
-Forest
On Sun, Feb 26, 2023, 9:47 PM Forest Simmons forest.simmons21@gmail.com wrote:
The Symmetric Gross Loser notion of nominal "worst" seems to work well for burial resistance ... but it is not very chicken resistant.
Here's a better one ... one I mentioned before .... where the nominally worst candidate is the loser of the strongest defeat... where defeat strength is gauged by the number of ballots on which the victor outranks the loser plus the bottom count of the loser... we abbreviate this gauge as wv+lbc... winning votes plus losing bottom count.
Remember that a candidate's bottom count is the number of ballots on which it outranks nobody.
So the method is to elect the CW if there is one ... otherwise ...
Until there is an unbeaten candidate among the remaining candidates, eliminate the nominally worst candidate after first eliminating the candidates it beats pairwise (if any).
The nominally worst candidate is
the loser of the single strongest defeat, gauged by av+lbc ... winning votes plus losing bottom count.
This method seems very promising for both burial and chicken resistance according to initial hand counts of some standard test cases.
Simulations will tell.
Here's my question: do simulations carry any weight with the public? Or do they just care about choice of buzz words and phrases like democracy; majority rule, etc?
-Forest
On Sun, Feb 26, 2023, 3:57 PM Forest Simmons forest.simmons21@gmail.com wrote:
Here's the cleanest notion of "worst" in this contex:
The "nominally worst" candidate is the Symmetric Gross Loser (SGL) defined as the pairwise loser between the candidate with the greatest pairwise opposition and the least pairwise support.
I am suggesting specializing our "worst-loser" elimination method to the following:
While there is more than one remaining candidate, from among them eliminate the current Symmetric Gross Loser SGL after first eliminating every candidate (if any) pairwise defeated by this SGL.
Elect the last candidate to be left standing (or eliminated).
This is the version I would like to see tested.
-Forest
On Sun, Feb 26, 2023, 11:45 AM Forest Simmons forest.simmons21@gmail.com wrote:
Correction below ...
On Sun, Feb 26, 2023, 10:58 AM Forest Simmons forest.simmons21@gmail.com wrote:
In the context of elimination methods (like IRV, Coombs, Baldwin, rtc, as well as all of our "worst-elimination" methods) the temptation for a faction to bury (insincerely lower on their ballots relative to one or more other candidates) a candidate C in order to help some candidate A win instead of C ... this temptation arises when C defeats A pairwise, but the A supporters, by lowering C, get C eliminated at some earlier elimination step so A and C are not competing head to head.
Note that this burial ploy will not work wih IRV elimination, because lowering C on a ballot where A is already preferred over C will not decrease C's first place support ... so it cannot get C eliminated earlier ... since IRV elimination prioritizes low first place support.
Coombs elimination, on the other hand prioritizes high last place counts for early elimination, so the burial ploy has a good chance of succeeding under Coombs.
Note that the feature that gives IRV immunity to burial is the same feature that makes it vulnerable to the Squeeze Effect.
So is it possible to have immunity to burial and squeeze in the same method?
Yes, our "worst-elimination" methods have immunity to both... immunity to squeeze because of Condorcet efficiency and immunity to burial because in the above ploy, to eliminate C earlier (whether by burial or some other means) must backfire as long as the ballot change preserves C's pairwise win over A.
It does preserve C's pairwise win over A in the case of burial ... because A was already ranked ahead of C by the buriers before the burial.
So how does this fact make C's elimination before A backfire?
Because according to our method...when C reaches "worst" status .... it is eliminated only "after any and every candidate defeated by it [including A] is eliminated"
In other words, if and when C reaches "worst" status (with or without the push downward from A supporters), it takes down A with it. So it doesn't matter if our nominal standard of worst is "fewest first" or "most last" or anything else ... if it speeds up C's demise, it also speeds up the demise of any candidate that C defeats pairwise.
In the three candidate case ... C is the sincere CW, and wins if C is eliminated, sothe other candidate B is the sincere Condorcet Loser.
The A faction buries C under B, which creates a beat cycle ABCA.
A thinks this cycle gives it a chance at winning ... which it would under most elimination methods.
But not under ours, because, on the one hand A cannot win unless B or C is "worst" ... and ...
If B is worst it takes A down with it because B defeats A in the cycle ... then B defeats C.
Whoops... A defeats B.
So the burial can succeed if it is enough to make B beat C, but not enough to make C nominally "worse" than B ... a delicate, hence risky balance.
Which nominal standards of "worst" make this balance most precarious if not impossible?
On the other hand, if C is worst, it takes A down with it, leaving B as winner.
So burial of the A faction's second choice results in the election of their anti-favorite B ... a complete backfire of the burial gambit!
I hope that.explanation clarifies the main reason for the clearing out of the candidates defeated by the pivot candidate, i.e. the nominally "worst" candidate, at each elimination stage ... see there really is a "method to our madness".
You may remember I once proposed a Quick & Dirty method that simply said elect the "best" candidate that pairwise defeats the "worst" Smith candidate.
That's a shortcut rule of thumb that will elect the same candidate as our "worst-elimination" methods do whenever there are no more than three Smith members ... but the short cut is not Landau efficient ... so I don't recommend it.
The main defect of the shortcut is that it requires some knowledge of Smith ... which our "worst-elimination" methods do not require.
So even though Q&D is shorter ... it is neither quite as good nor quite as simple.
If you have any question about any other method that you would like to compare with its nearest "worst-elimination" method ... it could interest other readers of the EM list, too.
Remember "worst" is a nominal, tentative judgment that can hardly go wrong ... since the direct pairwise comparisons trump the tentative judgments if there is any disagreement.
Good sources for "worst" candidates are losers of other methods.
Also losing candidates in strong pairwise defeats ... for any decent gauge of defeat strength.
Enjoy!
Forest
On Sun, Feb 26, 2023, 8:37 AM Forest Simmons forest.simmons21@gmail.com wrote:
The ElectoScope aka Yee Diagram makes clear both the problem with and the solution to the Center Squeeze phenomenon ... elimination methods that judge "worst" by size of the Voronoi regions ten to suffer from the defect.
But the cure is easy and sure ... no eliminations of undefeated candidates.
All Condorcet Efficient methods have the same Yee Diagram ... the win region for a candidate is its entire Voronoi polygon, no matter how small.
Next ... burial ...
On Fri, Feb 24, 2023, 3:49 PM Forest Simmons forest.simmons21@gmail.com wrote:
Why can't we just have majority rule? Why all the fiss?
Many a student of my "Math for Liberal Arts" class asked me that question during the decades I taught the Community College course by that name.
That's the reason Joe Malkovich's contribution to the textbook was so important ... his examples of ballot profiles for which no two of several different majority rule methods agreed on who should be elected.
Most if not all of these methods start out with the phrase..."Elect the majority winner if there is one, otherwise cull out the weakest (meaning democratically weakest) candidates one by one until there is a majority winner among the remaining."
But there is no agreement on what constitutes "democratically weak' ... and it makes a big difference!
So what can we do?
One thing we have tried without much success is to suggest that the next best thing, lacking a first preference majority winner ... is to elect the candidate unbeaten by any majority comparison with another candidate.
But just as there is no guaranteed outright majority winner ... neither is there any guarantee of the existence of a pairwise unbeaten candidate.
It turns out that the best we can guarantee along these lines is the existence of at least one candidate that can pairwise beat in two steps every candidate that he cannot defeat in one step (by a majority of the participating voters).
Such a candidate is said to be "uncovered." We're going to need a better word than that if we want to get anybody on board with this minimum guaranteeable standard of "majority rule."
Let's say a candidate is "democratically strong" if it has a beatpath to every other candidate ... and is "very strong majority pairwise" if it has a beatpath of one or two steps to each of the other candidates ... each step being a pairwise victory by a majority of the participating voters ... meaning voters expressing a preference.
Then the "Strong Majority Pairwise Criterion" (SMPC) is satisfied only by methods that always elect uncovered candidates.
Contrast that with the weaker, relatively impotent Condorcet Criterion which is satisfied by any method that elects an unbeaten candidate "when such a candidate exists" ... the copout escape clause in quotes letting the method off the hook whenever things start to get interesting.
Another way to express compliance with this SMPC criterion is "Landau Efficient."
Every method under the "Worst-Elimination" umbrella is seamlessly Landau Efficient ... it effortlessly (and without fanfare) satisfies the SMPC ... no matter what nominal standard of worst is instantiated into the umbrella template.
Who can name even one commonly known election method that is Landau efficient?
What's more ... no matter the nominal "worst" criterion, the method will be more or less burial resistant ... as I will explain presently.
I suggest that proposals for any method under this umbrella, include verbiage to the effect ...
"When there is no majority winner or any candidate that a majority of the participating voters rank ahead of each of the other candidates ... cull out one-by-one the nominally "worst" candidates as well as any democratically weaker candidates (as determined by majority ballot preferences) until there is a majority winner among the remaining candidates."
This umbrella is so robust that the choice of nominal "worst" is not overly critical. The main thing is to keep it simple enough that (1) voters can easily understand and relate to it, and (2) it can be efficiently and transparently tallied by precinct without multiple passes through the ballots.
Complicated "worst" criteria are the ones that tend to introduce crowding and teaming distortions ... smallest Borda score is a example of this kind of "worst" criterion ... pun intended.
Anti-vote splitting can be easily ensured (in general) by allowing equal-top whole counting, and multiple truncations in large elections.
In the continuation I will explain why this method tends to backfire on buriers.
At some point those who have power to advocate for one method over another need to understand them beyond the surface heuristics that appeal to the impatient public.
Among other things enlightened defenders of electoral democracy need to understand the "squeeze effect" and "burial ploys" ...
To be continued ...
-Forest
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