Strategy-free criterion
Hi CLC,
Something I will have to post about at some point is what a game-changer it
is if we take it as an assumption that elections will have two frontrunners
and all voters use frontrunner truncation strategy. Arbitrary-looking majority
rules prove very useful in maximizing performance.
I think there's a big issue with assuming two frontrunners because A) in that case,
it's just a majority vote between them and B) you can have situations where
multiple candidates have strongly correlated scores, e.g. if they're all from the
same party.
It seems like you think I meant that a method identifies the frontrunners. It could
try, but that isn't inherent to what I'm saying. I'm talking about an assumption
about the environment methods will run in. And I don't propose any assumptions
about how the perceived frontrunners are chosen.
This is why I previously suggested that, ideally, a system should satisfy both
zero-info honesty and LNHe+FBC. This seems like the maximally-honest combination
of properties, because it handles low-information elections honestly, and
high-information elections "as sincerely as possible" (i.e. no order-reversal,
which is enough to guarantee the Condorcet winner is visible from the ballots).
I am curious what your definition of "visible from the ballots" is. It's possible
to generate scenarios where the sincere CW is one of two frontrunners and yet still
loses under practically all methods, because they lose necessary support (from
truncation) from supporters of the other frontrunner while most of the CW's
supporters actually prefer a different candidate to the CW.
STAR works off of a very similar principle. The hope is the first stage will find
two similar frontrunners, and then the second stage is strategyproof (since it's a
majority vote). This combination fails both criteria in theory, but might satisfy
them in practice. That's especially true if you combine it with other improvements:
countbacks, a master lever for straight-ticket voting, and skipping the runoff if
the top-two finishers are from different parties could maximize the chances of
STAR working as it should.
I think the best hope for a system that formally satisfies both criteria is
probably somewhere in the generalized median family of voting methods.
That would surprise me, but who knows.
Kevin
votingmethods.net
Kevin,
Who in 49/24/27 ranks a candidate below the less-liked frontrunner?
No-one, which is why any method that meets SD and Plurality must elect B.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win.
"Truncates" X means vote no-one below X.
If this property doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above the preferred frontrunner.
But here you talk about "ranked other candidates above" which has
nothing to do with truncation.
That sounds more like failure of Non-Drastic Defense (which says that if
more than half the voters vote X above Y and X no lower than equal-top
then Y can't win.)
In such a setting I find that MAMPO is usually not as good as MDDA or RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
That's great. Does that mean that you find failure of Mono-add-Plump
acceptable?
Chris B.
On 9/06/2024 8:09 am, Kevin Venzke wrote:
Hi Chris,
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner.
Instead of "above the preferred frontrunner" don't you mean below the
less-liked frontrunner?
I don't mean that, and I am not sure how "below the less-liked frontrunner" would
apply? Who in 49/24/27 ranks a candidate below the less-liked frontrunner?
The classic example used by people who like Winning Votes and Approval
to flout those method's compliance with MD (versus the MD failures of
Margins and IRV):
49 A (sincere might be A>B)
24 B (sincere might be B>C)
27 C>B (sincere)
A>C 49-27 (=23) C>B 27-24 (=3) B>A 51-49 (=2)
By Margins A's defeat is the weakest and MinMax (and methods that are
equivalent to it with only 3 candidates, such as Ranked Pairs and
Schulze) using margins elects A.
But Minimal Defense says "not A" because more than half the voters voted
B above A and A not above equal-bottom. MD has no problem with the 27
C>B voters who ranked a candidate above their preferred (presumably
perceived) "frontrunner."
What I'm saying is that if a method fails MD in this scenario, the likely issue
is that the C>B voters ranked C above B, and if they didn't do that, then A
could've been defeated. In this scenario, that is fairly obvious, but it's true
in general, that MD failures are almost always instances of a majority (or part of
one) facing compromise incentive.
In practice you can liken MD / SDSC to a weak form of the strong FBC, and liken SFC
to a weak form of Later-no-harm.
Incidentally I agree with what CLC seems to suggest, that you don't have to discuss
burial to find merit in MD. There are methods with no burial incentive that satisfy
MD and it is certainly not meaningless in those contexts, because it addresses
compromise.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Inventing those methods was some achievement as a thought experiment to
demonstrate that certain criteria are mutually compatible.
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on its
electowiki page.
I can hardly advocate MDDA now due to the Plurality failure. However, it performs
very well in my truncation simulation, as does a method with very similar results,
which I call RMPA (River Majority Pass Approval). However, RMPA doesn't actually
satisfy FBC, so I can't list it in the same breath as the other two.
In RMPA we go down the list of candidates in order of descending implicit approval,
and process each candidate's full majority pairwise wins River-style (using the
"bins" conception, I would suggest). There is no need to sort the propositions; it's
enough to treat each candidate's wins in a batch with arbitrary order. Elect the
owner of the "bin" that the approval winner ends up in.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3
ballots that plump for X, the majority threshold rises to 52 and so C's
majority-strength defeat goes away and C wins again by being the most approved
candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method
would also fail Irrelevant Ballots Independence. It may be far less bad.
Something I will have to post about at some point is what a game-changer it is if we
take it as an assumption that elections will have two frontrunners and all voters
use frontrunner truncation strategy. Arbitrary-looking majority rules prove very
useful in maximizing performance.
In such a setting I find that MAMPO is usually not as good as MDDA or RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
It's a different approach from what I usually use, to say "let's just assume voters
act in this way regardless of what the method is." We may not be standing on firm
ground there. But I find it a bit intuitive to think voters will mainly truncate
worse frontrunners. Compromise incentive isn't even completely ignored: By having
voters refuse to compromise, methods that depend on it this to work well (such as
FPP) are penalized in the analysis.
Kevin
votingmethods.net
CLC,
I assume no-one posts a ballot "intending to be irrelevant" (and
whether they do or not I don't see as relevant).
Normally I wouldn't expect irrelevant ballots to be literally "empty",
just containing no information about any of the remotely viable information.
An equal-ranking isn’t a way to express indifference (or else
equal-ranks would never happen); it’s a way of pleading the fifth
What?
Learning that a voter refuses to say whether they prefer Bob or Bill
provides an important piece of information.
Which is?
Learning a voter has cast a completely blank ballot is an extreme
case, where the ballot provides a very important piece of information:
it means the voter expects a participation failure, because a nonempty
ballot will hurt them.
But an empty one might "help" them ?? Hilarious.
A rational response to this is to raise the threshold for a defeat,
because setting the bar for a defeat closer to 50% prevents cycles
(and therefore participation failures). In other words, these ballots
are /very/ relevant.
Of course, you anonymous STAR Voting advocate.
Chris B.
On 7/06/2024 1:33 am, Closed Limelike Curves wrote:
Yeah, MAMPO seems like it might behave more sensibly there.
IIB doesn’t make sense to me outside of positional voting systems
(which trivially satisfy it). If an empty ballot was genuinely
intended to be irrelevant, the voter wouldn’t have cast it in the
first place. An equal-ranking isn’t a way to express indifference (or
else equal-ranks would never happen); it’s a way of pleading the
fifth. Learning that a voter refuses to say whether they prefer Bob or
Bill provides an important piece of information.
Learning a voter has cast a completely blank ballot is an extreme
case, where the ballot provides a very important piece of information:
it means the voter expects a participation failure, because a nonempty
ballot will hurt them.
A rational response to this is to raise the threshold for a defeat,
because setting the bar for a defeat closer to 50% prevents cycles
(and therefore participation failures). In other words, these ballots
are /very/ relevant.
On Thu, Jun 6, 2024 at 7:40 AM Chris Benham cbenhamau@yahoo.com.au
wrote:
Kevin,
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Inventing those methods was some achievement as a thought
experiment to demonstrate that certain criteria are mutually
compatible.
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on
its electowiki page.
https://electowiki.org/wiki/Majority_Defeat_Disqualification_Approval
Procedure
The voter submits a ranking of the candidates. The candidates
explicitly ranked are considered/approved/by that voter.
A candidate is/dominated/if more than half of the voters rank
some other candidate strictly above him.
All dominated candidates are eliminated, unless this would
eliminate all the candidates.
Of remaining candidates, the one approved by the most voters is
elected.
Criteria
*MDDA*satisfies theFavorite Betrayal criterion
<https://electowiki.org/wiki/Favorite_Betrayal_criterion>,Strategy-Free
criterion <https://electowiki.org/wiki/Strategy-Free_criterion>,
theStrong Defensive Strategy criterion
<https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion>(andMinimal
Defense criterion
<https://electowiki.org/wiki/Minimal_Defense_criterion>),
andmonotonicity <https://electowiki.org/wiki/Monotonicity_criterion>.
It failsClone-Winner
<https://electowiki.org/wiki/Strategic_nomination>, thePlurality
criterion <https://electowiki.org/wiki/Plurality_criterion>,
theGeneralized Strategy-Free criterion
<https://electowiki.org/wiki/Generalized_Strategy-Free_criterion>,
theCondorcet criterion
<https://electowiki.org/wiki/Condorcet_criterion>, theSmith
criterion <https://electowiki.org/wiki/Smith_set>,Participation
<https://electowiki.org/wiki/Participation_criterion>,
theMajority criterion for solid coalitions
<https://electowiki.org/wiki/Majority_criterion>,
andLater-no-harm
<https://electowiki.org/wiki/Later-no-harm_criterion>.
25: A>B
26: B>C
23: C>A
04: C
78 ballots (majority threshold = 40)
B>C 51-27, C>A 53-25, A>B 48-26. Implicit Approval scores: C 53, B 51, A 48.
All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.
Say we now add 22 ballots that all plump (i.e. bullet vote) for C:
25: A>B
26: B>C
23: C>A
26: C
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 48-26. Implicit Approval scores: C 75, B 51, A 48.
Now only B is without a "majority-strength defeat", so the winner changes from C to B.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method would also fail Irrelevant Ballots Independence. It may be far less bad.
https://electowiki.org/wiki/Majority_Approval,_Minimum_Pairwise_Opposition
Procedure
The voter submits a ranking of the candidates. The candidates
explicitly ranked are considered/approved/by that voter.
The/score/for candidate/X/against candidate/Y/is equal to the
number of voters ranking/X/above/Y/. The/max score/of
candidate/X/is the largest score of any other candidate against/X/.
If nobody is approved by more than half of the voters, then the
candidate approved by the most voters is elected.
Otherwise, the candidate with the lowest max score, who is
approved by more than half of the voters, is elected.
Chris B.
On 2/06/2024 7:23 am, Kevin Venzke wrote:
Hi all,
When I test for SFC compliance the rule on cast votes is that if there is no
majority over A, and A has a majority over B, then B can't win.
This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
in terms of a graph of majority-strength defeats, it would say that if A has a
majority over B and B doesn't have a majority over anyone, then B can't win.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner. So MD is mostly about compromise incentive.
SFC is probably going to be about truncation. When a method fails it, most likely
it's because the majority gave the election away to a less liked compromise choice.
For example:
20 C>A>B
35 A>B
5 B
40 D
Here B is the implicit approval winner, but by SFC B should not win, because it
means it was not safe for the A voters to rank B.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Kevin
votingmethods.net <http://votingmethods.net>
Hi Chris,
Kevin,
Who in 49/24/27 ranks a candidate below the less-liked frontrunner?
No-one, which is why any method that meets SD and Plurality must elect B.
MD basically says that if there are two frontrunners and everyone truncates
their
less liked frontrunner, then the worse frontrunner won't win.
"Truncates" X means vote no-one below X.
In that case I mean "truncate above X but below the other frontrunner."
If this property doesn't hold, it means the majority has done something to stop
the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner.
But here you talk about "ranked other candidates above" which has
nothing to do with truncation.
Truncation is what MD requires for it to work, but the problem it's usually
addressing is compromise. Every method that violates MD in 49/24/27 violates it
because of C being ranked above B. Betray C and there is no more issue. That's
bad, and MD wants to offer a way to fix it.
If MD fails to work because voters fail to truncate, that's not a violation of MD.
That sounds more like failure of Non-Drastic Defense (which says that if
more than half the voters vote X above Y and X no lower than equal-top
then Y can't win.)
NDD is a weaker form of MD that does less to counter compromise.
In such a setting I find that MAMPO is usually not as good as MDDA or RMPA, but
all of them outperform all Condorcet methods at sincere Condorcet efficiency.
That's great. Does that mean that you find failure of Mono-add-Plump acceptable?
Compared to Plurality criterion failures, sure.
I don't really want to prejudge methods based on criteria that might primarily be
important for marketability reasons. I say "primarily" not "purely."
Hypothetically if there were a movement promoting MDDA, and in this world MDDA
doesn't violate the Plurality criterion, then Mono-add-plump failures wouldn't stop
me from supporting that movement.
And really, if I found that the whole world was actually OK with Plurality
failures, I might relax my stance on that as well. Because the marketability aspect
of Plurality failures is a big part of my allergy to them. Maybe I would study
under what conditions MDDA would have high risk of violating Plurality, and see if
I could live with it.
Kevin
votingmethods.net
Kevin,
"Does that mean that you find failure of Mono-add-Plump acceptable?"
Compared to Plurality criterion failures, sure.
No, that is very very weird and wrong. A failure of Mono-add-Plump is
completely absurd and outrageous and a failure destroys the credibility
of the winner, whereas a failure of the Plurality criterion is merely
very embarrassing and hard to sell.
Also giving away Plurality can "buy" something sort-of worth having. For
example MinMax Margins is not an absurd method and has a "maximal set"
of Woodall properties. It fails Plurality but meets Condorcet and I
think Mono-add-Top and Later-no-Harm.
But I refuse to believe that we need to give up Mono-add-Plump (or
Mono-append) compliance to get anything remotely worth having. (And if
I'm wrong about that I wouldn't accept the bargain.)
Something I will have to post about at some point is what a
game-changer it is if we
take it as an assumption that elections will have two frontrunners and
all voters
use frontrunner truncation strategy. Arbitrary-looking majority rules
prove very
useful in maximizing performance.
In such a setting I find that MAMPO is usually not as good as MDDA or
RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
A near-universal assumption among Condorcetists is that if (assuming the
voters are free to rank enough candidates) there is a voted CW then that
must be the sincere CW and everything is perfect.
You imply that your aim is to elect the "sincere CW" (if there is one).
I think we should be trying to elect a candidate with no lower Social
Utility than the highest SU voted Smith set member.
The person who coined SFC (and supports MD) also coined the Chicken
Dilemma criterion, which is directly incompatible with MD.
https://electowiki.org/wiki/Chicken_dilemma
I am in sympathy with both criteria so one of my standards is that a
rankings-only method must meet one or the other.
Chris B.
On 11/06/2024 9:30 pm, Kevin Venzke wrote:
Hi Chris,
Kevin,
Who in 49/24/27 ranks a candidate below the less-liked frontrunner?
No-one, which is why any method that meets SD and Plurality must elect B.
MD basically says that if there are two frontrunners and everyone truncates
their
less liked frontrunner, then the worse frontrunner won't win.
"Truncates" X means vote no-one below X.
In that case I mean "truncate above X but below the other frontrunner."
If this property doesn't hold, it means the majority has done something to stop
the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner.
But here you talk about "ranked other candidates above" which has
nothing to do with truncation.
Truncation is what MD requires for it to work, but the problem it's usually
addressing is compromise. Every method that violates MD in 49/24/27 violates it
because of C being ranked above B. Betray C and there is no more issue. That's
bad, and MD wants to offer a way to fix it.
If MD fails to work because voters fail to truncate, that's not a violation of MD.
That sounds more like failure of Non-Drastic Defense (which says that if
more than half the voters vote X above Y and X no lower than equal-top
then Y can't win.)
NDD is a weaker form of MD that does less to counter compromise.
In such a setting I find that MAMPO is usually not as good as MDDA or RMPA, but
all of them outperform all Condorcet methods at sincere Condorcet efficiency.
That's great. Does that mean that you find failure of Mono-add-Plump acceptable?
Compared to Plurality criterion failures, sure.
I don't really want to prejudge methods based on criteria that might primarily be
important for marketability reasons. I say "primarily" not "purely."
Hypothetically if there were a movement promoting MDDA, and in this world MDDA
doesn't violate the Plurality criterion, then Mono-add-plump failures wouldn't stop
me from supporting that movement.
And really, if I found that the whole world was actually OK with Plurality
failures, I might relax my stance on that as well. Because the marketability aspect
of Plurality failures is a big part of my allergy to them. Maybe I would study
under what conditions MDDA would have high risk of violating Plurality, and see if
I could live with it.
Kevin
votingmethods.net
Hi Chris,
I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a rule
at the start:
- Disqualify all candidates with sub-majority approval if possible.
- Disqualify all candidates with a majority pairwise defeat if possible.
- Elect the most approved remaining candidate.
This now matches MAMPO's four properties: FBC, MD, SFC, and Plurality.
Experimentally, my challenge in proving this is that I'm having a hard time
randomly generating any scenarios at all where the two MDDAs differ. But we know
MDDA v1 violates Plurality (even if random scenarios won't produce it for me), and
MDDA v2 pretty clearly doesn't.
(Why not do this before? I guess I thought MAMPO was more elegant, and I could not
foresee that I would have simulations where MDDA outperforms MAMPO.)
On to the reply...
"Does that mean that you find failure of Mono-add-Plump acceptable?"
Compared to Plurality criterion failures, sure.
No, that is very very weird and wrong. A failure of Mono-add-Plump is
completely absurd and outrageous and a failure destroys the credibility
of the winner, whereas a failure of the Plurality criterion is merely
very embarrassing and hard to sell.
I'm not sure I follow, that a winner barred by Plurality has more credibility than
a winner who won under the rules but is challenged by a second candidate who
regrets how his supporters filled out their ballots. Candidates who win despite
being barred by Plurality usually seem to have won not due to their own merit.
Also giving away Plurality can "buy" something sort-of worth having. For
example MinMax Margins is not an absurd method and has a "maximal set"
of Woodall properties. It fails Plurality but meets Condorcet and I
think Mono-add-Top and Later-no-Harm.
I would've gone with MMPO as the example, but OK. As a Condorcet method,
MinMax(margins) doesn't satisfy LNHarm.
But I refuse to believe that we need to give up Mono-add-Plump (or
Mono-append) compliance to get anything remotely worth having.
I don't know whether you're right about that or not. Just because I've gotten
interesting results from MDDA doesn't mean they could only come from MDDA. I have
also seen some impressive performance from DAC in some situations, and I don't know
right now what accounts for that. I usually just say "DAC is like Bucklin" but this
is seemingly not quite right.
(And if I'm wrong about that I wouldn't accept the bargain.)
That's fine, if many people feel that way then that will be decisive. I feel there
are a number of criteria like this that are "absurd to fail" according to the
intuition of some number of people. To me it's not very interesting because it
doesn't lead to a clear metric that could be tested. I wouldn't want to say a
method is "good" just because no one can call it absurd.
Something I will have to post about at some point is what a
game-changer it is if we
take it as an assumption that elections will have two frontrunners and
all voters
use frontrunner truncation strategy. Arbitrary-looking majority rules
prove very
useful in maximizing performance.
In such a setting I find that MAMPO is usually not as good as MDDA or
RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
A near-universal assumption among Condorcetists is that if (assuming the
voters are free to rank enough candidates) there is a voted CW then that
must be the sincere CW and everything is perfect.
Sure, if that's all you have, that's all you can do. The only way you can arrive at
a suspicion that other methods could outperform Condorcet at sincere Condorcet is
with a model that started with sincere preferences (somehow generated) and
translated them (somehow) into voted preferences.
You imply that your aim is to elect the "sincere CW" (if there is one).
I think we should be trying to elect a candidate with no lower Social
Utility than the highest SU voted Smith set member.
Sincere CW and SU as goals are tricky to disentangle I think. You can mess around
with the voter distribution and force methods to behave differently wrt SU, but I
don't have an intuition yet about the nature of the change in some methods'
performance. In 2D spatial simulations I find that there is usually a sincere CW,
incidentally.
My thought on your goal is that if we say that we know the SU (due to some model of
behavior that we're using to test scenarios), why wouldn't we just prioritize that?
The makeup of the voted Smith set would just be an artifact of strategy. But maybe
you would say that electing outside Smith would look unacceptable. Fair enough.
The person who coined SFC (and supports MD) also coined the Chicken
Dilemma criterion, which is directly incompatible with MD.
https://electowiki.org/wiki/Chicken_dilemma
I am in sympathy with both criteria so one of my standards is that a
rankings-only method must meet one or the other.
I don't like the CD criterion because of the three incentives it creates, only one
of them is positive. And even if that were not true, it seems rash to resolve
elections according to the speculation that any pairwise majority over the first
preference winner "ought" to have been accompanied by a mutual majority.
Kevin
votingmethods.net
Kevin,
I don't like the CD criterion because of the three incentives it creates, only one
of them is positive.
What are they?
I'm not sure I follow, that a winner barred by Plurality has more credibility than
a winner who won under the rules but is challenged by a second candidate who
regrets how his supporters filled out their ballots.
I didn't mean to make it a big competition, because I don't accept
failure of either. "Plumpers" for X didn't exactly "fill out" their
ballots, they had no interest in any other candidate, so they showed up
and plumped for X.
It would be readily apparent from the post-election ballot profile that
if some or all of them had stayed home then X would have won. It's the
simplest and most egregious version of Participation failure. There is
no excuse for any algorithm to be confused by such pure and simple
information.
Sometimes methods that fail Plurality meet Later-no-Harm and may have a
(at least zero-info) random-fill incentive. So then failures of
Plurality would be very rare, and the occasional complaint would usually
be answerable by the retort:
"Well suckers, you didn't make your (full) contribution to GIGO!" :)
I am intolerant of methods that fail Irrelevant Ballot Independence
(although I recognise that putting up with its failure might be able to
buy something) so I'm suspicious of methods that have arbitrary
thresholds (relating to some fraction of the "total votes") as an
essential part of their definitions.
I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a rule
at the start:
- Disqualify all candidates with sub-majority approval if possible.
- Disqualify all candidates with a majority pairwise defeat if possible.
- Elect the most approved remaining candidate.
Given that you are using implicit approval (ranking), I struggle to see
how rule 1 can make any difference. Can the most approved candidate
without a "majority pairwise defeat" really have sub-majority approval
while some other candidate doesn't?
As a Condorcet method, MinMax(margins) doesn't satisfy LNHarm.
Yes, my mistake. I forget what name Woodall used for MMM. I think he
said it meets Condorcet, Mono-add-Top and "Symmetric Completion" (which
happily means in the zero-info case there is neither truncation or
random-fill incentive).
I know that MMM is equivalent to "elect the X who needs the fewest extra
X-plumping ballots to become the CW." Obviously that meets
Mono-add-Top, which strikes me as almost implying LNHarm.
I wouldn't want to say a method is "good" just because no one can call it absurd.
I think it is a promising start, especially if we are aware of (and
honest about) which criteria are compatible with others.
I think a "votes only" definition of SFC is
- If X has a majority strength pairwise win over Y, and it is possible
to complete the truncated ballots in a way that makes X the CW, then Y
can't win.*
Do you agree? A version that goes without the "majority" bit:
If X pairwise beats Y, and it is possible to complete the truncated
ballots in a way that makes X (but not Y) the CW, then Y can't win.
I prefer the second.
Chris B.
On 13/06/2024 7:16 pm, Kevin Venzke wrote:
Hi Chris,
I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a rule
at the start:
- Disqualify all candidates with sub-majority approval if possible.
- Disqualify all candidates with a majority pairwise defeat if possible.
- Elect the most approved remaining candidate.
This now matches MAMPO's four properties: FBC, MD, SFC, and Plurality.
Experimentally, my challenge in proving this is that I'm having a hard time
randomly generating any scenarios at all where the two MDDAs differ. But we know
MDDA v1 violates Plurality (even if random scenarios won't produce it for me), and
MDDA v2 pretty clearly doesn't.
(Why not do this before? I guess I thought MAMPO was more elegant, and I could not
foresee that I would have simulations where MDDA outperforms MAMPO.)
On to the reply...
"Does that mean that you find failure of Mono-add-Plump acceptable?"
Compared to Plurality criterion failures, sure.
No, that is very very weird and wrong. A failure of Mono-add-Plump is
completely absurd and outrageous and a failure destroys the credibility
of the winner, whereas a failure of the Plurality criterion is merely
very embarrassing and hard to sell.
I'm not sure I follow, that a winner barred by Plurality has more credibility than
a winner who won under the rules but is challenged by a second candidate who
regrets how his supporters filled out their ballots. Candidates who win despite
being barred by Plurality usually seem to have won not due to their own merit.
Also giving away Plurality can "buy" something sort-of worth having. For
example MinMax Margins is not an absurd method and has a "maximal set"
of Woodall properties. It fails Plurality but meets Condorcet and I
think Mono-add-Top and Later-no-Harm.
I would've gone with MMPO as the example, but OK. As a Condorcet method,
MinMax(margins) doesn't satisfy LNHarm.
But I refuse to believe that we need to give up Mono-add-Plump (or
Mono-append) compliance to get anything remotely worth having.
I don't know whether you're right about that or not. Just because I've gotten
interesting results from MDDA doesn't mean they could only come from MDDA. I have
also seen some impressive performance from DAC in some situations, and I don't know
right now what accounts for that. I usually just say "DAC is like Bucklin" but this
is seemingly not quite right.
(And if I'm wrong about that I wouldn't accept the bargain.)
That's fine, if many people feel that way then that will be decisive. I feel there
are a number of criteria like this that are "absurd to fail" according to the
intuition of some number of people. To me it's not very interesting because it
doesn't lead to a clear metric that could be tested. I wouldn't want to say a
method is "good" just because no one can call it absurd.
Something I will have to post about at some point is what a
game-changer it is if we
take it as an assumption that elections will have two frontrunners and
all voters
use frontrunner truncation strategy. Arbitrary-looking majority rules
prove very
useful in maximizing performance.
In such a setting I find that MAMPO is usually not as good as MDDA or
RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
A near-universal assumption among Condorcetists is that if (assuming the
voters are free to rank enough candidates) there is a voted CW then that
must be the sincere CW and everything is perfect.
Sure, if that's all you have, that's all you can do. The only way you can arrive at
a suspicion that other methods could outperform Condorcet at sincere Condorcet is
with a model that started with sincere preferences (somehow generated) and
translated them (somehow) into voted preferences.
You imply that your aim is to elect the "sincere CW" (if there is one).
I think we should be trying to elect a candidate with no lower Social
Utility than the highest SU voted Smith set member.
Sincere CW and SU as goals are tricky to disentangle I think. You can mess around
with the voter distribution and force methods to behave differently wrt SU, but I
don't have an intuition yet about the nature of the change in some methods'
performance. In 2D spatial simulations I find that there is usually a sincere CW,
incidentally.
My thought on your goal is that if we say that we know the SU (due to some model of
behavior that we're using to test scenarios), why wouldn't we just prioritize that?
The makeup of the voted Smith set would just be an artifact of strategy. But maybe
you would say that electing outside Smith would look unacceptable. Fair enough.
The person who coined SFC (and supports MD) also coined the Chicken
Dilemma criterion, which is directly incompatible with MD.
https://electowiki.org/wiki/Chicken_dilemma
I am in sympathy with both criteria so one of my standards is that a
rankings-only method must meet one or the other.
I don't like the CD criterion because of the three incentives it creates, only one
of them is positive. And even if that were not true, it seems rash to resolve
elections according to the speculation that any pairwise majority over the first
preference winner "ought" to have been accompanied by a mutual majority.
Kevin
votingmethods.net
Hi Chris,
Kevin,
I don't like the CD criterion because of the three incentives it creates, only
one of them is positive.
What are they?
The disunited majority has three options to avoid the criterion's wrath:
- The "defecting" faction can add another preference, if they have it or are
willing to lie that they have it. - The "defected-against" faction can compromise and try to give the other
candidate a majority of first preferences. - One of the candidates can simply drop out of the race, as it will be apparent
that the method poses such risks.
On an additional note, it's strange to me that CD crit allows one faction to defect
but not the other. If both factions optimistically think they are the larger one,
they will all assume CD applies to the other voters and not themselves. It seems to
me that a "real" CD criterion would take no nonsense from anyone.
I'm not sure I follow, that a winner barred by Plurality has more credibility than
a winner who won under the rules but is challenged by a second candidate who
regrets how his supporters filled out their ballots.
I didn't mean to make it a big competition, because I don't accept
failure of either. "Plumpers" for X didn't exactly "fill out" their
ballots, they had no interest in any other candidate, so they showed up
and plumped for X.
It would be readily apparent from the post-election ballot profile that
if some or all of them had stayed home then X would have won. It's the
simplest and most egregious version of Participation failure. There is
no excuse for any algorithm to be confused by such pure and simple
information.
Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking. I understand that you see a difference in
severity, but for myself I don't see where to draw the line.
Sometimes methods that fail Plurality meet Later-no-Harm and may have a
(at least zero-info) random-fill incentive. So then failures of
Plurality would be very rare, and the occasional complaint would usually
be answerable by the retort:
"Well suckers, you didn't make your (full) contribution to GIGO!" :)
I am intolerant of methods that fail Irrelevant Ballot Independence
(although I recognise that putting up with its failure might be able to
buy something) so I'm suspicious of methods that have arbitrary
thresholds (relating to some fraction of the "total votes") as an
essential part of their definitions.
Well, in an environment where the concept of "median voter" is likely to be
meaningful, pairwise majorities are basically the only suggestion you can get about
what side the median voter is on. I don't think the premise of IIB is necessarily
sound, because introducing IBs can remove information we previously thought we had
about the median voter.
I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a
rule at the start:
- Disqualify all candidates with sub-majority approval if possible.
- Disqualify all candidates with a majority pairwise defeat if possible.
- Elect the most approved remaining candidate.
Given that you are using implicit approval (ranking), I struggle to see
how rule 1 can make any difference. Can the most approved candidate
without a "majority pairwise defeat" really have sub-majority approval
while some other candidate doesn't?
Yes, actually Woodall showed it in 2005:
20 a>b
5 b>a
24 b>c
24 c>a
9 d>a>b
9 d>b>c
9 d>c>a
D wins in original MDDA. The new version is an A-B tie.
As a Condorcet method, MinMax(margins) doesn't satisfy LNHarm.
Yes, my mistake. I forget what name Woodall used for MMM. I think he
said it meets Condorcet, Mono-add-Top and "Symmetric Completion" (which
happily means in the zero-info case there is neither truncation or
random-fill incentive).
I know that MMM is equivalent to "elect the X who needs the fewest extra
X-plumping ballots to become the CW." Obviously that meets
Mono-add-Top, which strikes me as almost implying LNHarm.
That's an interesting comparison, but note that DAC satisfies Participation
(implying Mono-add-top), and DAC is definitely not good according to Later-no-harm.
I wouldn't want to say a method is "good" just because no one can call it absurd.
I think it is a promising start, especially if we are aware of (and
honest about) which criteria are compatible with others.
I think a "votes only" definition of SFC is
- If X has a majority strength pairwise win over Y, and it is possible
to complete the truncated ballots in a way that makes X the CW, then Y
can't win.*
Do you agree?
That sounds about right.
A version that goes without the "majority" bit:
If X pairwise beats Y, and it is possible to complete the truncated
ballots in a way that makes X (but not Y) the CW, then Y can't win.
I prefer the second.
They're both hard to test because they are asking us to search for ways of actually
completing the presented ballots. And it's not totally clear why it's helpful for
there to be a sort of loophole here.
This is probably clear to you, but if it's possible to complete the ballots so that
X is the CW, but it's not possible to do the same for Y, then the normal intuition
is that Y probably does have a majority loss to somebody. But it might not be to X.
An interesting idea. I'm not really sure how to look into it, or find scenarios
where we can see a contrast.
Kevin
votingmethods.net
Kevin,
The disunited majority has three options to avoid the [Chicken Dilemma] criterion's wrath:
-
The "defecting" faction can add another preference, if they have it or are
willing to lie that they have it. -
The "defected-against" faction can compromise and try to give the other
candidate a majority of first preferences. -
One of the candidates can simply drop out of the race, as it will be apparent
that the method poses such risks.
You said that you thought one of these is positive. Which one?
I am still thinking about a much fuller reply.
Chris
I am curious what your definition of "visible from the ballots" is. It's
possible
to generate scenarios where the sincere CW is one of two frontrunners and
yet still
loses under practically all methods, because they lose necessary support
(from
truncation) from supporters of the other frontrunner while most of the CW's
supporters actually prefer a different candidate to the CW.
Am I missing something about the CW under approval? I was under the
impression that, if everyone is following the polls and knows everyone
else's voting intentions, the majority-preferred candidate will win because
people will adjust their approval threshold until the CW is the only
candidate with >50% approval.
That would surprise me, but who knows.
Huh, why would it surprise you?
On Sun, Jun 9, 2024 at 11:57 AM Kevin Venzke stepjak@yahoo.fr wrote:
Hi CLC,
Something I will have to post about at some point is what a
game-changer it
is if we take it as an assumption that elections will have two
frontrunners
and all voters use frontrunner truncation strategy. Arbitrary-looking
majority
rules prove very useful in maximizing performance.
I think there's a big issue with assuming two frontrunners because A) in
that case,
it's just a majority vote between them and B) you can have situations
where
multiple candidates have strongly correlated scores, e.g. if they're all
from the
same party.
It seems like you think I meant that a method identifies the frontrunners.
It could
try, but that isn't inherent to what I'm saying. I'm talking about an
assumption
about the environment methods will run in. And I don't propose any
assumptions
about how the perceived frontrunners are chosen.
This is why I previously suggested that, ideally, a system should
satisfy both
zero-info honesty and LNHe+FBC. This seems like the maximally-honest
combination
of properties, because it handles low-information elections honestly, and
high-information elections "as sincerely as possible" (i.e. no
order-reversal,
which is enough to guarantee the Condorcet winner is visible from the
ballots).
I am curious what your definition of "visible from the ballots" is. It's
possible
to generate scenarios where the sincere CW is one of two frontrunners and
yet still
loses under practically all methods, because they lose necessary support
(from
truncation) from supporters of the other frontrunner while most of the CW's
supporters actually prefer a different candidate to the CW.
STAR works off of a very similar principle. The hope is the first stage
will find
two similar frontrunners, and then the second stage is strategyproof
(since it's a
majority vote). This combination fails both criteria in theory, but
might satisfy
them in practice. That's especially true if you combine it with other
improvements:
countbacks, a master lever for straight-ticket voting, and skipping the
runoff if
the top-two finishers are from different parties could maximize the
chances of
STAR working as it should.
I think the best hope for a system that formally satisfies both criteria
is
probably somewhere in the generalized median family of voting methods.
That would surprise me, but who knows.
Kevin
votingmethods.net