Re: [EM] Quick and Clean Burial Resistant Smith
Forest, here is an example of how restricting to the Smith Set actually
leads to a failure of Q&CBRS.
This is a false-cycle strategy example from Colin Champion.
Sincere:
2: A > B > C > E > D
1: A > D > B > E > C
1: B > A > C > E > D
1: B > A > E > D > C
1: B > C > A > E > D
2: C > A > B > E > D
3: C > B > A > E > D
B is pairwise winner.
C voters create a cycle by insincerely elevating last place candidate D
over B. Last two blocks change to
2: C > D > A > B > E
3: C > D > B > A > E
With Ranked Approval, Approval (basic score) can be accumulated on the
diagonal, giving the pairwise array
[11. 5. 5. 6. 11.]
[ 6. 11. 6. 5. 11.]
[ 6. 5. 9. 9. 9.]
[ 5. 6. 2. 7. 6.]
[ 0. 0. 2. 5. 6.]
Smith set is {A,B,C,D}. D is least approved of Smith Set, but now defeats
B, leaving A and C. A has higher approval and is the winner.
If you eliminate E and recount to get a corrected basic score, you get a
pairwise array (basic score on diagonal) of
[8. 5. 5. 6.]
[6. 9. 6. 5.]
[6. 5. 9. 9.]
[5. 6. 2. 7.]
Same Smith set as before, of course, and D still has lowest approval, and
by defeating B, eliminates it. Remaining Smith candidates are A and C, as
before, but now C has higher basic score and wins.
So C's strategy of strategic burial to induce a cycle is now victorious.
On Fri, Jan 7, 2022 at 2:17 PM Ted Stern dodecatheon@gmail.com wrote:
[ISDA = Independence of Smith-dominated alternatives]
ISDA worthy criterion to satisfy. Unfortunately, you lose summability by
requiring a recount. Is there any way around having to eliminate non-Smith
candidates and recount?
I was going to suggest calling your method "Practical Ranked Approval", to
avoid having to include terms like Smith, Game-resistant, Burial, etc. But
requiring a recount might not be considered Practical. So the best you
could say would be Strategy-resistant Ranked Approval.
Thinking along the lines of practicality, I have been mulling how best to
keep pairwise arrays to a reasonable size for practical summability. If
pre-election polling is available, one could accumulate pairwise counts
explicitly for any candidate with more than, say, 2% approval, and lump
pairwise counts for other candidates under "Other". Compute the Smith Set.
If Other is in the Smith Set, then reduce the threshold and recount.
On Fri, Jan 7, 2022 at 1:57 PM Forest Simmons forest.simmons21@gmail.com
wrote:
Very true, and I would have said err on the side of VSE until Robert B-J
convinced me that sincere cycles are practically non-existent with an
occurrence of less than 0.5 percent.
He got that statistic from Fair Vote's analysis of over 400 elections,
and they have no particular reason to exaggerate that statistic. So suppose
they're right, then do we conclude that any old Condorcet method is as good
as another?
You know the answer to that, Kristofer, but I elaborate for the benefit
of the typical EM List reader:
No, because, as Kristofer pointed out, it depends on the "neighborhood."
Back in the fifties when I was a kid in rural/small town eastern
Washington state nobody locked their doors. In fact, they usually left
their keys in the ignition for convenience. But was that the
prudent/sustainable thing to do?
Nowadays sixty years later, in those same neighborhoods people have
learned by experience to adopt city slicker habits of door locking.
When 99.5 percent of election polls reveal the existence of sincere
Condorcet candidates, the election method with the greatest Condorcet
efficiency will come the closest to electing a CW 99.5 percent of the time.
But don't all Condorcet methods have equal Condorcet efficiency? Isn't
the very definition of "Condorcet method" a method that always elects the
Condorcet candidate when one exists?
That would be nice if there were such a method, but Gibbard-Satterwaithe
shows the impossibility of that ideal in any tough neiborhood.
Then what is the real definition of "Condorcet Method"?
It is a method that elects a ballot Condorcet candidate. In tough
neighborhoods there will often be sincere Condorcet candidates that are not
ballot Condorcet Candidates ... because they are ranked insincerely on the
ballots.
So how to ensure that sincere Condorcet candidates retain their Condorcet
status on the ballots?
Only methods that take this question seriously can have sustainable
Condorcet efficiency.
Let's do a thought experiment to compare the Condorcet efficiency of
Ranked Pairs, Benham, Schulze, and other Condorcet methods:
Suppose that sincere preferences are given...
40 A>C
35 B>C
25 C>A
Like 99.5 percent of electorates this one has a sincere Condorcet
candidate, namely C, which is preferred over A by a 60 percent majority,
and preferred over B by a 65 percent majority.
The question of Condorcet efficiency in this example is "Which Condorcet
methods are most likely to elect C ?"
But that depends on the neighborhood. In Grant County, Washington of the
fifties, any Condorcet method would elect C.
But which Condorcet method would robustly elect C even in Brooklyn, New
York?
That depends on which methods take the possibility of subversion
seriously... subversion of the sincere CW by intentional cycle creation.
Under Schulze, RP, River, MinMax, etc. candidate A would likely win
because the A faction could confidently bury A under B, creating an
insincere defeat cycle with weakest defeat being the 60 percent C over A
compared with the 75 percent B over C, and the 65 percent A over B.
All of these standard Condorcet methods are built on the assumption that
the smallest majority (60% C over A) is the one most likely to be "wrong".
So they elect A, unwittingly rewarding the A faction for subverting the
sincere CW.
But how about Q&D/C?
It would elect C because it is a ballot Condorcet method intolerant of
the kind of subversion that rewarded the A faction under Schulze, etc.
Since the subversion would just backfire, no faction would be dumb enough
to try it.
Let's look at how it would backfire were the A faction stupid enough to
attempt the burial of C under B:
The candidate with the lowest basic score would then be C, so B would win
as the only candidate pairwise undefeated by C.
So A's gambit would just change the winner from its second choice C to
its last choice B.
Do you think any major faction in Brooklyn would gamble on a sure loss
like that?
To be clear, what this example shows is that our Quick and Dirty/Clean
method has Condorcet efficiency superior to that of Schulze, etc.
And why is it more Condorcet efficient? Because it was designed on a
realistic game theoretic principle, rather than a statistical error
correcting technique designed mainly for filtering out inadvertent
"mistakes" in judgment (or minority opinion).
This example could be (and has been) multiplied indefinitely with the
same pattern of results:
Q&D/C is much more Condorcet efficient than Schulze et al in rough
neighborhoods, as well as 100 percent efficient in easy neighborhoods (like
any and every Condorcet method is).
So here's the best advice for Condorcet method design: focus on
frustrating cycle creators. Make sure that all attempts at cycle creation
backfire automatically. Beyond that accommodate any (possible but
vanishingly rare) sincere cycles by making sure the method always elects
simply, monotonically, and clone indepently from the ballot Smith set, as
does Q&D/C, a method that Pareto dominates all of the old Condorcet methods
on these criteria.
To put it bluntly, all of those older methods are pretty much passe ...
uniformly dominated by Q&D/C when it comes to single winner elections for
public office.
I'm sorry to talk so bluntly, but subtle words don't seem to register in
this context, especially among the self-styled movers and shakers [who
probably won't even read them anyway🤔]
On a technical note ... to make sure that Q&D/C is ISDA, use a version
that immediately restricts to Smith, or at least counts the "basic scores"
relative to the Smith Set candidates.
Forest
El vie., 7 de ene. de 2022 4:38 a. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:
On 07.01.2022 07:05, Forest Simmons wrote:
Most designers of Condorcet methods asume that the gentlemanly thing to
do is to give the votes a benefit of a doubt and assume that they must
have voted sincerely but cycles are a result of errores of judgement.
Because of these assumptions they attempt to filter out the erroneous
preferences statistically
.. the main heuristic is that larger majorities are less apt to hold
erroneous opinions than smaller ones ... hence cycles are broken by
annulling the defeats with the smallest majorities.
There is probably a tradeoff between strategic resistance and honest
VSE. The more you want one, the less you get the other, and at the
extremes you completely disregard one or the other.
So if we could construct methods to spec, the best approach would be to
somehow infer just how much strategy the method needs to resist, and
then maximize VSE in a suitable model (probably spatial) subject to this
constraint.
But we don't really know how strong the barrier has to be against
strategy. As I've mentioned before, I think it differs based on culture:
IIRC Ireland saw much less vote management under STV than did New York.
If we only have one shot, it's reasonable to err on the side of strategy
resistance. That's not to say that the honesty-favoring methods don't
have their place, though: Debian seems to do pretty well with Schulze,
for instance.
As for methods like Plurality and (probably) IRV -- well, they're just
Pareto-dominated. You can find methods with better VSE and the same
level of strategic resistance, or methods that handle strategy better
while providing the same VSE.
-km
Robert,
You opined ...
"Probably Schulze or RP is the best thing to do for those cases when there
is no Condorcet winner. But getting that into legislative language is
difficult, which is why I have advocated for BTR-STV."
Actually, neither RP nor Schulze has better Condorcet efficiency than
Smith//TopTwoRunOff, which is the simple method you should be aiming for.
Here's the typical example that I used earlier today:
40 A>C
35 B>C
25 C>A
The sincere CW is C, which any Condorcet method will elect in an ideal
neighborhood, but only a burial resistant method like Q&D/C will reliably
elect in a saavy, scrappy neighborhood.
All of the standard (head-in-the-sand) Universal Domain methods like RP,
Schulze, MinMax, etc. are more or less likely to elect A, depending on how
politically saavy/street smart the A faction is.
So those highly vaunted methods are no better than Condorcet completed
byTopTwoRunoff, which produces the exact same result as they do 100 percent
of the time in this context, but much more simply.
So TopTwoRunoff works just as well as Schulze for cycle resolution in this
context, yet it is by far the most adoptable proposal for Condorcet
completion.... because of its simplicity and familiarity.
Don't worry about the legislative language .. just copy the language from
existing jurisdictions where it is already in use ... with the simple tweak
of replacing the phrase, "In the event there is no absolute majority
candidate ..." ... with the phrase, "In the event there is no head-to-head
majority candidate ..."
There is no valid excuse for proposing Plurality as a Condorcet finisher
when this more adoptable proposal is there for the taking.
Plurality as a finisher would be a huge liability/embarrassment even if you
could get it adopted, which is doubtful.
Fair Vote people would rightly mock a Condorcet method that in principle
allows a Condorcet Loser to win.
How would we prevent that happening?
Of course we could say ... "In the event there is no majority head-to-head
winner, elect the FPTP winner, unless all Plurality counts fall short of 50
percent, in which case complete the Plurality finisher with a TopTwoRunOff
finisher, finisher."
That wouldn't even make sense, because there could never be a 50% plus
Plutality winner without already having a Condorcet Winner... since a 50
percent plus Plurality winner is automatically a Condorcet Winner.
I hate to be pedantic, but let's not squander our opportunity on an
atrocious proposal. If there were not a simpler, more adoptable proposal
readily available, I would say, "Go ahead, leave your keys in the car,
cross your fingers, and take your chances!"
In my humble, but expert opinion, there are only two tenable proposals for
Burlington, Vt. at this time ...
-
Condorcet completed by TopTwoRunoff when necessary... of course under a
more attractive name. -
TopTwoRunoff restricted to the "top cycle" or "Smith Set" ... even more
important to get a better name.
This second method is just as good as Schulze for public elections, so
don't pine for the day when the world is safe for Kemeny-Young, for Pete's
sake!
You should put the choice to the people who control the decision orocess.
After making clear the prestige of an ISDA upgrade at practically no extra
cost, let them decide between the two options.
Either choice will result in a respectable method that cannot be easily
gainsayed.
Good Luck!
-Forest
El vie., 7 de ene. de 2022 12:15 a. m., robert bristow-johnson <
rbj@audioimagination.com> escribió:
On 01/07/2022 1:05 AM Forest Simmons forest.simmons21@gmail.com wrote:
Most designers of Condorcet methods asume that the gentlemanly thing to
do is to give the votes a benefit of a doubt and assume that they must have
voted sincerely
I just think that, without some other information to suggest otherwise,
the marked ballot should be assumed to represent the voter's sincere
preferences.
but cycles are a result of errores of judgement.
A preference cycle would need a very close 3-way race and and somewhat
schizoid electorate. "If I can't have my favorite Bernie Sanders, then I'm
voting for T****."
Probably Schulze or RP is the best thing to do for those cases when there
is no Condorcet winner. But getting that into legislative language is
difficult, which is why I have advocated for BTR-STV.
Because of these assumptions they attempt to filter out the erroneous
preferences statistically
I just think that the method tries to make the best thing out of a
confusing situation that will rarely happen.
.. the main heuristic is that larger majorities are less apt to hold
erroneous opinions than smaller ones ... hence cycles are broken by
annulling the defeats with the smallest majorities.
That's one way to do it.
I used to think that way, too.
But seasoned election observers are of the opinion that the vast
majority (more than 90 percent) of public elections for political office
have a sincere Condorcet candidate, and that when there is a defeat cycle,
it is more likely to be the result of intentional subversion of the
Condorcet candidate than of erroneous voter judgment.
The thing is more like 99.5% have Condorcet winner. Right now, at least
with the 440 RCV elections that FairVote says they analyzed, that all had
Condorcet winners and all but one succeeded at electing the Condorcet
winner.
I just sorta wanna get any Condorcet method. The simpler language the
better. I think cycles will be rare. If we elect the plurality winner in
case of a cycle, that might be an indication of preference. It's not
Schulze. It might not elect the bestest candidate that disincentivizes
certain tactical voting. But if simple language get a Condorcet method
understood, it has a better chance of maybe someday getting legislated.
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for list
info
On 1/7/2022 4:27 PM, Forest Simmons wrote:
Actually, neither RP nor Schulze has better Condorcet efficiency than
Smith//TopTwoRunOff, which is the simple method you should be aiming for.
To anyone, I have some questions (that might also be in the minds of a
few lurkers).
How are the "top two" candidates determined according to the
Smith//TopTwoRunoff method?
Or, where is Smith//TopTwoRunoff described? (I didn't find it in
Electowiki.)
Since the topic is simplicity, how can ballots be hand counted to
determine the Smith set?
Yes I know that pairwise counting can be done by having each person at a
table keep track of only one pair of candidates -- as each ballot is
passed from person to person. But how can those pairwise vote counts be
simply(!) converted into the Smith set -- for any set of ballots?
As a related question, how does "//" differ from "/"? In other words,
is Smith/TopTwoRunoff different from Smith//TopTwoRunoff, and if so, how?
Thanks!
Richard Fobes
On 1/7/2022 4:27 PM, Forest Simmons wrote:
Robert,
You opined ...
"Probably Schulze or RP is the best thing to do for those cases when
there is no Condorcet winner. But getting that into legislative
language is difficult, which is why I have advocated for BTR-STV."
Actually, neither RP nor Schulze has better Condorcet efficiency than
Smith//TopTwoRunOff, which is the simple method you should be aiming for.
Here's the typical example that I used earlier today:
40 A>C
35 B>C
25 C>A
The sincere CW is C, which any Condorcet method will elect in an ideal
neighborhood, but only a burial resistant method like Q&D/C will
reliably elect in a saavy, scrappy neighborhood.
All of the standard (head-in-the-sand) Universal Domain methods like RP,
Schulze, MinMax, etc. are more or less likely to elect A, depending on
how politically saavy/street smart the A faction is.
So those highly vaunted methods are no better than Condorcet completed
byTopTwoRunoff, which produces the exact same result as they do 100
percent of the time in this context, but much more simply.
So TopTwoRunoff works just as well as Schulze for cycle resolution in
this context, yet it is by far the most adoptable proposal for Condorcet
completion.... because of its simplicity and familiarity.
Don't worry about the legislative language .. just copy the language
from existing jurisdictions where it is already in use ... with the
simple tweak of replacing the phrase, "In the event there is no absolute
majority candidate ..." ... with the phrase, "In the event there is no
head-to-head majority candidate ..."
There is no valid excuse for proposing Plurality as a Condorcet finisher
when this more adoptable proposal is there for the taking.
Plurality as a finisher would be a huge liability/embarrassment even if
you could get it adopted, which is doubtful.
Fair Vote people would rightly mock a Condorcet method that in principle
allows a Condorcet Loser to win.
How would we prevent that happening?
Of course we could say ... "In the event there is no majority
head-to-head winner, elect the FPTP winner, unless all Plurality counts
fall short of 50 percent, in which case complete the Plurality finisher
with a TopTwoRunOff finisher, finisher."
That wouldn't even make sense, because there could never be a 50% plus
Plutality winner without already having a Condorcet Winner... since a 50
percent plus Plurality winner is automatically a Condorcet Winner.
I hate to be pedantic, but let's not squander our opportunity on an
atrocious proposal. If there were not a simpler, more adoptable proposal
readily available, I would say, "Go ahead, leave your keys in the car,
cross your fingers, and take your chances!"
In my humble, but expert opinion, there are only two tenable proposals
for Burlington, Vt. at this time ...
-
Condorcet completed by TopTwoRunoff when necessary... of course under
a more attractive name. -
TopTwoRunoff restricted to the "top cycle" or "Smith Set" ... even
more important to get a better name.
This second method is just as good as Schulze for public elections, so
don't pine for the day when the world is safe for Kemeny-Young, for
Pete's sake!
You should put the choice to the people who control the decision
orocess. After making clear the prestige of an ISDA upgrade at
practically no extra cost, let them decide between the two options.
Either choice will result in a respectable method that cannot be easily
gainsayed.
Good Luck!
-Forest
On 08.01.2022 02:42, Richard, the VoteFair guy wrote:
On 1/7/2022 4:27 PM, Forest Simmons wrote:
Actually, neither RP nor Schulze has better Condorcet efficiency than
Smith//TopTwoRunOff, which is the simple method you should be aiming for.
To anyone, I have some questions (that might also be in the minds of a
few lurkers).
How are the "top two" candidates determined according to the
Smith//TopTwoRunoff method?
Or, where is Smith//TopTwoRunoff described? (I didn't find it in
Electowiki.)
I'm not Forest, but I think it would go like this:
- First determine the Smith set. If there's a CW, you're done.
- Otherwise eliminate everybody who's not in the Smith set.
- Count the number of first preferences after elimination.
- Let X be the first preference winner, and Y the runner-up.
- Of the two, elect the candidate who beats the other pairwise.
Smith,TTR is slightly easier and gives you summability at the cost of
ISDA. However, it would probably produce worse results (e.g. consider if
the Smith set all have plurality count zero, being hidden behind
polarizing candidates who are not in the Smith set).
Since the topic is simplicity, how can ballots be hand counted to
determine the Smith set?
I would imagine you could do it like this: First find the candidate who
beats the most other candidates pairwise. Choose one at random if
there's a tie. Then repeatedly add someone who beats anyone in the
current set until no such candidate exists. What you end up with is the
Smith set.
It's perhaps a bit labor intensive, though. You'd most likely need to
calculate the Condorcet matrix.
Yes I know that pairwise counting can be done by having each person at a
table keep track of only one pair of candidates -- as each ballot is
passed from person to person. But how can those pairwise vote counts be
simply(!) converted into the Smith set -- for any set of ballots?
As a related question, how does "//" differ from "/"? In other words,
is Smith/TopTwoRunoff different from Smith//TopTwoRunoff, and if so, how?
There's to my knowledge no difference, it's just a matter of notation.
-km
Hi Forest,
Le vendredi 7 janvier 2022, 15:57:27 UTC−6, Forest Simmons forest.simmons21@gmail.com a écrit :
Very true, and I would have said err on the side of VSE until Robert B-J
convinced me that sincere cycles are practically non-existent with an occurrence
of less than 0.5 percent.
Â
He got that statistic from Fair Vote's analysis of over 400 elections, and they
have no particular reason to exaggerate that statistic. So suppose they're
right, then do we conclude that any old Condorcet method is as good as another?
I would think that I wouldn't trust a study of IRV elections to talk about voted
CWs across all methods, for the same reason I wouldn't trust a study of FPP
elections to tell me that most elections will have a voted majority favorite
across all methods. The incentives aren't the same.
IRV has no truncation strategy. (In Burlington, we see truncation anyway; how
much more would we see if the method could actually reward truncation?) If there
is usually a sincere CW (which I think is likely), then it's easy to imagine
that more complete rankings might lead to finding that CW.
IRV also has among the highest compromise incentive, which I believe translates
directly to nomination disincentive. Meaning, those 400 elections probably
could have had more candidates nominated under a different method. Particularly
if these were not very viable candidates, I think this could definitely lower
the rate of seeing a voted CW.
If we enact a Condorcet method and find that, indeed, there is almost always a
voted Condorcet winner, I would be inclined to wonder if there is something
wrong. Because given a couple of assumptions:
- Voters feel inclined to truncate the candidates they feel they are trying to
defeat, or that they don't care to worry about for whatever reason. - Candidates feel free to enter the race even if they can't win, and their
supporters feel free to vote for them despite this possibility.
Then, this should create an environment where voted cycles are certainly
possible. In particular, cases where a less viable candidate manages to get a
pairwise win over a more viable candidate, due to considerable abstentions of
voters who either were not interested in that contest, or perceived it as unsafe
to support the lesser evil between the two.
Kevin
Thanks for the valuable perspective and insights!
El sáb., 8 de ene. de 2022 2:07 p. m., Kevin Venzke stepjak@yahoo.fr
escribió:
Hi Forest,
Le vendredi 7 janvier 2022, 15:57:27 UTC−6, Forest Simmons <
forest.simmons21@gmail.com> a écrit :
Very true, and I would have said err on the side of VSE until Robert B-J
convinced me that sincere cycles are practically non-existent with an
occurrence
of less than 0.5 percent.
He got that statistic from Fair Vote's analysis of over 400 elections,
and they
have no particular reason to exaggerate that statistic. So suppose
they're
right, then do we conclude that any old Condorcet method is as good as
another?
I would think that I wouldn't trust a study of IRV elections to talk about
voted
CWs across all methods, for the same reason I wouldn't trust a study of FPP
elections to tell me that most elections will have a voted majority
favorite
across all methods. The incentives aren't the same.
IRV has no truncation strategy. (In Burlington, we see truncation anyway;
how
much more would we see if the method could actually reward truncation?) If
there
is usually a sincere CW (which I think is likely), then it's easy to
imagine
that more complete rankings might lead to finding that CW.
IRV also has among the highest compromise incentive, which I believe
translates
directly to nomination disincentive. Meaning, those 400 elections probably
could have had more candidates nominated under a different method.
Particularly
if these were not very viable candidates, I think this could definitely
lower
the rate of seeing a voted CW.
If we enact a Condorcet method and find that, indeed, there is almost
always a
voted Condorcet winner, I would be inclined to wonder if there is something
wrong. Because given a couple of assumptions:
- Voters feel inclined to truncate the candidates they feel they are
trying to
defeat, or that they don't care to worry about for whatever reason. - Candidates feel free to enter the race even if they can't win, and their
supporters feel free to vote for them despite this possibility.
Then, this should create an environment where voted cycles are certainly
possible. In particular, cases where a less viable candidate manages to
get a
pairwise win over a more viable candidate, due to considerable abstentions
of
voters who either were not interested in that contest, or perceived it as
unsafe
to support the lesser evil between the two.
Kevin
Hi Forest,
Le vendredi 7 janvier 2022, 18:28:06 UTC−6, Forest Simmons forest.simmons21@gmail.com a écrit :
[Robert] opined ...
"Probably Schulze or RP is the best thing to do for those cases when there is
no Condorcet winner. But getting that into legislative language is difficult,
which is why I have advocated for BTR-STV."
Â
Actually, neither RP nor Schulze has better Condorcet efficiency than
Smith//TopTwoRunOff, which is the simple method you should be aiming for.
Of course the Condorcet efficiency is the same, however the compromise incentive
(or other incentives) won't be, across various methods.
What hurts my heart is if we will say "let's adopt Condorcet, so people don't
have to always vote for the lesser evil, and weak candidates won't spoil races,
etc." and then we leave so much of this promise on the table unused.
I just ran some 4-candidate 5-bloc no-ER random sims. I don't do exhaustive
searches so take these numbers as suggestive only (not even minimums/maximums).
Compromise incentive detected in what % of elections sans majority favorite:
3.0% best achieved by an experimental method
4.0% River, Schulze(WV), MAM
4.4% MinMax(WV)
4.6% BTP
10.2% MinMax(margins)
12.0% Bucklin
13.2% Condorcet//Approval (implicit)
14.6% FPCC (an extension of Stensholt BPW)
15.3% Condorcet//King of the Hill
17.2% TACC (implicit)
17.8% Condorcet//FPP
18.1% Condorcet//IRV and my extension of Kristofer's Linear method (tie)
18.3% BTR-IRV
26.5% IRV
40.4% FPP
To be fair, I am running the same ballots through every method, which may not
be realistic. These numbers can also differ if you generate scenarios based on
an underlying issue space. But aside from these points, I can't help but notice
that a lot of these "strategy-resistant" Condorcet methods are getting beat by
Bucklin.
Of course, Bucklin's Condorcet efficiency is really poor, and the truncation
incentive is horrendous. But what's the goal of Condorcet efficiency, is it an
end in itself? Personally I'm not comfortable thinking of it that way (maybe
because it's defined on the cast ballots only, which seems insufficiently
grounded in the underlying preferences which are what really matter).
I haven't tried to do an extensive study of the burial games possible under
Condorcet//FPP. But measuring similarity of results with three candidates, the
three most similar methods are BTR-IRV (literally the same method), Kristofer's
Linear method, and a bit further away, Condorcet//IRV.
I have a hunch that if you put your "strategy-resistant Condorcet" hat on and
evaluate C//FPP, you will find it to be "good."
Incidentally, if you want a Condorcet method where burial never looks attractive
in the first place (before even considering strategic responses to burial), the
best methods I have are Stensholt's (SV and BPW slash FPCC), C//IRV, and C//KOTH.
None are monotone though.
Kevin
On 08.01.2022 23:37, Kevin Venzke wrote:
I have a hunch that if you put your "strategy-resistant Condorcet" hat on and
evaluate C//FPP, you will find it to be "good."
In my Monte Carlo (non-exhaustive) simulations, there are generally
three types of methods as far as strategy resistance goes: the type
that's susceptible >90% of the time whatever the number of candidates,
the type that's ~30% but increases with number of candidates to very
high levels with lots of candidates, and the type that's low and doesn't
increase.
A method is susceptible to strategy in a particular election if the
honest winner is A but voters who prefer some other B to A can conspire
to get B elected by changing their ballots.
C//FPP is the first type. MAM, Schulze, minmax, etc are of the second
type, and Smith-IRV, Benham, and fpA-fpC are of the third type.
Each election is a one-shot game (first some candidate wins, then
factions get to try to make other candidates win); there's no defensive
strategy. So it probably resembles your "never looks attractive in the
first place" setting.
-km
On Sat, Jan 8, 2022 at 5:21 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 08.01.2022 23:37, Kevin Venzke wrote:
I have a hunch that if you put your "strategy-resistant Condorcet" hat
on and
evaluate C//FPP, you will find it to be "good."
In my Monte Carlo (non-exhaustive) simulations, there are generally
three types of methods as far as strategy resistance goes: the type
that's susceptible >90% of the time whatever the number of candidates,
the type that's ~30% but increases with number of candidates to very
high levels with lots of candidates, and the type that's low and doesn't
increase.
A method is susceptible to strategy in a particular election if the
honest winner is A but voters who prefer some other B to A can conspire
to get B elected by changing their ballots.
C//FPP is the first type. MAM, Schulze, minmax, etc are of the second
type, and Smith-IRV, Benham, and fpA-fpC are of the third type.
Wow. What type is Ranked Pairs? Is Ranked Pairs is part of the "etc"? Is
there an intuitive explanation why Smith-IRV and Benham are more resistant
to strategy? I'm trying to find Behman's method on the electowiki but I'm
not finding it. I was sure I had seen it there before. Does it have an
alternate name?
Cheers,
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
On Sat, Jan 8, 2022 at 5:58 PM Daniel Carrera dcarrera@gmail.com wrote:
I'm trying to find Behman's method on the electowiki but I'm not finding
it. I was sure I had seen it there before. Does it have an alternate name?
My bad. https://electowiki.org/wiki/Benham%27s_method
I was typing it wrong.
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University