Strategy-free criterion
Hi Chris,
Chris Benham cbenhamau@yahoo.com.au a écrit :
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.
#1 includes a truncation disincentive so I'm willing to call it positive. You could
also see a random-fill incentive there I suppose. And when a voter deliberately
gives a specific lower preference that they don't actually have, we usually call
that burial... A kind of "defensive burial" in this case.
Kevin
votingmethods.net
Hi CLC,
Closed Limelike Curves closed.limelike.curves@gmail.com a écrit :
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.
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.
If the polls are accurate I think that theory could work. What I'm saying is that if
two frontrunners are chosen arbitrarily, but one of them is the CW, that isn't a
sufficient condition for the CW to win.
Here's a contrived example, starting with the sincere preferences:
38: Yellow>Blue>Red
37: Red>Blue>Yellow
15: Blue>Red>Yellow
7: Yellow>Red>Blue
2: Red>Yellow>Blue
1: Blue>Yellow>Red
Blue is sincere CW, and Yellow is the best opposition to Blue (barely). With Blue
and Yellow as perceived frontrunners, these ballots are possible (truncating midway
between frontrunners):
45: Yellow
37: Red>Blue
15: Blue>Red
2: Red>Yellow
1: Blue
This returns Red as the voted CW and implicit approval winner.
Since Blue and Red both end up with majority approval, it's possible you will say
that the polls shouldn't have ended up with a Blue/Yellow match-up, but a Blue/Red
one. By my math (here omitted) that would give Blue majority approval and uniquely
so. (Interestingly Blue would not be the voted CW; Yellow would always have
sub-majority wins over the other two.) An odd thing about this outcome is that
Blue/Red look like they are from the same party and the 45% who favor Yellow don't
bullet vote at all. That makes me skeptical that a Blue/Red match-up would actually
happen in such a clean way.
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.
Huh, why would it surprise you?
I assumed you were talking about median rating or something like that.
The outcomes of our election methods can (almost as a rule) be dictated by a
coordinated majority (or a group of more numerous voters) so I expect a "zero-info
honesty" method to have some kind of inherent tether to this reality, as though the
coordination is done for the voters already, behind the scenes.
Kevin
votingmethods.net
Corrections:
Kevin Venzke stepjak@yahoo.fr a écrit :
Hi Chris,
Chris Benham cbenhamau@yahoo.com.au a écrit :
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.
#1 includes a truncation disincentive so I'm willing to call it positive. You could
also see a random-fill incentive there I suppose. And when a voter deliberately
gives a specific lower preference that they don't actually have, we usually call
that burial... A kind of "defensive burial" in this case.
Actually, given how CD is actually defined (and not how I might define it),
characterizing this as random-fill or burial is wrong, because voters adding an
additional preference are conceding the election to that preference. It's not
too plausible that their preferred candidate will actually win.
So, #1 is indeed positive and has nothing to do with lying.
The caveat of course is that if the voters targeted by incentive #1 actually don't
have a second preference, then CD imposes a sub-optimal MD-defying outcome for no
benefit at all.
Kevin
votingmethods.net
Kevin,
On Mono-add-Plump as a weak version of Participation:
Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking.
What sort of "trouble"? I don't see how your conclusion follows from
your premise. Why do "almost all proposals fail Participation"? It
isn't because there is anything inherently wrong with "that kind of
thinking". It is because it just happens that Participation is very
expensive (in terms of other desirable criterion compliances, such as
Condorcet). But in that way Mono-add-Plump is very very cheap (if not
free), and some of us are currently "in trouble" due to disregarding
"this kind of thinking".
Suppose a mini-bus with a driver is contracted to pick up a group of
people and take then on a trip to one of X, Y or Z after polling the
passengers on their ranking-preferences among these alternative
destinations. After the bus is nearly full it is mistakenly assumed that
there will be no more passengers and the driver applies some algorithm
to the rankings of those present and announces that winning alternative
is X.
Then it is learned that there are two more passengers to come to fill up
the bus. They do so and the driver says to them "I've polled all the
other passengers and at the moment the winning destination is X. Where
would you like to go?" and they reply "X is our first preference and Y
wouldn't be too bad and we are very glad we aren't gong to Z".
The driver replies "You prefer Y to Z? In that case the new winning
alternative is Y". Now if these two voters (and perhaps others whose
first preference was X) were enlightened election-method experts, they
might think "Obviously this fellow's election-method algorithm fails
Participation (and presumably Later-no-Harm). Perhaps it meets
Condorcet, which we know is incompatible with both Participation and
Later-no-Harm. Perhaps before we showed up there was a top cycle and our
Y>Z preferences turned Y into the Condorcet winner.
But we know that Condorcet is also incompatible with Later-no-Help so us
revealing our second preferences could have just as likely helped us, so
I suppose we were just unlucky."
Or if they were not experts but charitably minded they might think "I
suppose it is possible that this fellow made an honest mistake due to
him being thick and us confusing him with too much information".
Now replay this scenario except this time the new passengers just say
"Great! We just really want to go to X and we don't know or care about
any other destination." And then the driver says "In that case the
winning alternative changes from X to Y".
The response could only be that the destination-decider (supposedly
purely based on the passengers' stated preferences) is insane (or
malevolent, in any case illegitimate) and that Y is obviously an
illegitimate winner.
Did you notice a very different vibe from the first case, which was a
failure of Participation and Mono-add-Top but not Mono-add-Plump?
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump. Your new MDDA 2 method fails the example I gave:
25 A>B
26 B>C
23 C>A
04 C
(78 ballots, majority threshold = 40)
Implicit approval scores: C 53, B 51, A 48. No candidate is
disqualified due to sub-majority approval.
B>C 51-27, C>A 53-25, A>B 48-26. All candidates have a
"majority" strength defeat, so it "isn't possible" to disqualify any
candidate on that basis. So, according to the rules of MDDA 2, we elect
the most approved candidate, C.
Now say we add 22 ballots that plump for C to give:
25 A>B
26 B>C
23 C>A
26 C
(100 ballots, majority threshold = 51)
Implicit approval scores: C 75, B 51, A 48. Now A has sub-majority
approval and so is disqualified.
B>C 51-49, C>A 75-25, A>B 48-26. Now C and A have
majority-strength defeats and B doesn't, so (according to the rules of
MDDA 2), A (again) and C are disqualified leaving B as the new winner.
The contention that C is the right winner when there were just 78
ballots but when we add 22 ballots that plump (bullet vote) for C the
right winner is no longer C is .... completely crazy.
Well, in an environment where the concept of "median voter" is likely to be meaningful,...
What "environment" is that? And why is that the environment the one we
should primarily focus on? I think that is the sort of thinking that
leads some people to support Median Ratings methods, which we know are
garbage because they fail Dominant Candidate and Irrelevant Ballots
Independence, and the voters have a strong incentive to just submit
approval ballots (giving the same result as Approval). And it has led
you to the absurdity of suggesting a method that fails Mono-add-Plump.
I think for the purposes of properly analysing single-winner election
methods and inspiring the invention of new ones, we can and should do
without criteria that refer to irrelevant ballots dependent "majority"
thresholds or pairwise defeats. Those have almost no positive point
aside from marketing.
My suggestion for something as close as possible to Minimal Defense:
If the number of ballots that vote X above bottom and Y no higher than
equal-bottom is greater than Y's maximum pairwise support, then Y can't
win.
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
That already inspires a simple method suggestion: DDI,MMM: Elect the
candidate not disqualified by Double-Defeat (Implicit) that is highest
ordered by MinMax(Margins).
What do you think of that? And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
Chris B.
On 16/06/2024 6:56 am, Kevin Venzke wrote:
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
I assumed you were talking about median rating or something like that.
Yeah, that would be one possible guess. (Linear medians also might work).
The outcomes of our election methods can (almost as a rule) be dictated by a
coordinated majority (or a group of more numerous voters) so I expect a
"zero-info
honesty" method to have some kind of inherent tether to this reality, as
though the
coordination is done for the voters already, behind the scenes.
Well, the two examples of proven zero-information honesty I know about are
quadratic voting and Borda count. I'm not actually aware of any proofs for
the Condorcet cases, but I suspect most Condorcet methods work here.
Later-no-help is incompatible with Condorcet, so I'm not sure if those
methods can stand up to fully-informed voting.
On Wed, Jun 19, 2024 at 3:12 AM Kevin Venzke stepjak@yahoo.fr wrote:
Hi CLC,
Closed Limelike Curves closed.limelike.curves@gmail.com a écrit :
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.
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.
If the polls are accurate I think that theory could work. What I'm saying
is that if
two frontrunners are chosen arbitrarily, but one of them is the CW, that
isn't a
sufficient condition for the CW to win.
Here's a contrived example, starting with the sincere preferences:
38: Yellow>Blue>Red
37: Red>Blue>Yellow
15: Blue>Red>Yellow
7: Yellow>Red>Blue
2: Red>Yellow>Blue
1: Blue>Yellow>Red
Blue is sincere CW, and Yellow is the best opposition to Blue (barely).
With Blue
and Yellow as perceived frontrunners, these ballots are possible
(truncating midway
between frontrunners):
45: Yellow
37: Red>Blue
15: Blue>Red
2: Red>Yellow
1: Blue
This returns Red as the voted CW and implicit approval winner.
Since Blue and Red both end up with majority approval, it's possible you
will say
that the polls shouldn't have ended up with a Blue/Yellow match-up, but a
Blue/Red
one. By my math (here omitted) that would give Blue majority approval and
uniquely
so. (Interestingly Blue would not be the voted CW; Yellow would always have
sub-majority wins over the other two.) An odd thing about this outcome is
that
Blue/Red look like they are from the same party and the 45% who favor
Yellow don't
bullet vote at all. That makes me skeptical that a Blue/Red match-up would
actually
happen in such a clean way.
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.
Huh, why would it surprise you?
I assumed you were talking about median rating or something like that.
The outcomes of our election methods can (almost as a rule) be dictated by
a
coordinated majority (or a group of more numerous voters) so I expect a
"zero-info
honesty" method to have some kind of inherent tether to this reality, as
though the
coordination is done for the voters already, behind the scenes.
Kevin
votingmethods.net
Hi Chris,
On Mono-add-Plump as a weak version of Participation:
Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking.
What sort of "trouble"? I don't see how your conclusion follows from
your premise. Why do "almost all proposals fail Participation"? It
isn't because there is anything inherently wrong with "that kind of
thinking". It is because it just happens that Participation is very
expensive (in terms of other desirable criterion compliances, such as
Condorcet). But in that way Mono-add-Plump is very very cheap (if not
free), and some of us are currently "in trouble" due to disregarding
"this kind of thinking".
What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider, and we aren't
necessarily getting anything of value except that fewer people can call the method
absurd. What I call inherently of value would be things like sincere Condorcet
efficiency or reduced strategic incentives.
Suppose a mini-bus with a driver is contracted to pick up a group of
people and take then on a trip to one of X, Y or Z after polling the
passengers on their ranking-preferences among these alternative
destinations. After the bus is nearly full it is mistakenly assumed that
there will be no more passengers and the driver applies some algorithm
to the rankings of those present and announces that winning alternative
is X.
Then it is learned that there are two more passengers to come to fill up
the bus. They do so and the driver says to them "I've polled all the
other passengers and at the moment the winning destination is X. Where
would you like to go?" and they reply "X is our first preference and Y
wouldn't be too bad and we are very glad we aren't gong to Z".
The driver replies "You prefer Y to Z? In that case the new winning
alternative is Y". Now if these two voters (and perhaps others whose
first preference was X) were enlightened election-method experts, they
might think "Obviously this fellow's election-method algorithm fails
Participation (and presumably Later-no-Harm). Perhaps it meets
Condorcet, which we know is incompatible with both Participation and
Later-no-Harm. Perhaps before we showed up there was a top cycle and our
Y>Z preferences turned Y into the Condorcet winner.
But we know that Condorcet is also incompatible with Later-no-Help so us
revealing our second preferences could have just as likely helped us, so
I suppose we were just unlucky."
Or if they were not experts but charitably minded they might think "I
suppose it is possible that this fellow made an honest mistake due to
him being thick and us confusing him with too much information".
Now replay this scenario except this time the new passengers just say
"Great! We just really want to go to X and we don't know or care about
any other destination." And then the driver says "In that case the
winning alternative changes from X to Y".
The response could only be that the destination-decider (supposedly
purely based on the passengers' stated preferences) is insane (or
malevolent, in any case illegitimate) and that Y is obviously an
illegitimate winner.
Did you notice a very different vibe from the first case, which was a
failure of Participation and Mono-add-Top but not Mono-add-Plump?
The difference in vibe is quite similar to your own difference in vibe when you
compare these situations.
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there. And that's
fine, that is their right.
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
But given their compatibility, isn't that a strange thing to say?
Your new MDDA 2 method fails the example I gave:
25 A>B
26 B>C
23 C>A
04 C
(78 ballots, majority threshold = 40)
Implicit approval scores: C 53, B 51, A 48. No candidate is
disqualified due to sub-majority approval.
B>C 51-27, C>A 53-25, A>B 48-26. All candidates have a
"majority" strength defeat, so it "isn't possible" to disqualify any
candidate on that basis. So, according to the rules of MDDA 2, we elect
the most approved candidate, C.
Now say we add 22 ballots that plump for C to give:
25 A>B
26 B>C
23 C>A
26 C
(100 ballots, majority threshold = 51)
Implicit approval scores: C 75, B 51, A 48. Now A has sub-majority
approval and so is disqualified.
B>C 51-49, C>A 75-25, A>B 48-26. Now C and A have
majority-strength defeats and B doesn't, so (according to the rules of
MDDA 2), A (again) and C are disqualified leaving B as the new winner.
The contention that C is the right winner when there were just 78
ballots but when we add 22 ballots that plump (bullet vote) for C the
right winner is no longer C is .... completely crazy.
The voters' behavior had a side effect of strengthening B. All sorts of monotonicity
failures take such an appearance.
And again, there could be differences in severity, e.g. what percent of voters think
a given phenomenon is absurd. But I don't find that very interesting because it
doesn't tell us about the merits of the method. It's basically marketability.
Well, in an environment where the concept of "median voter" is likely
to be meaningful,...
What "environment" is that? And why is that the environment the one we
should primarily focus on?
One where voter and candidate preferences can be explained by an underlying issue
space. In this case if you could project everyone onto a plane or spectrum it would
be a bit easy to find the median voter and their preferred candidate.
I think this usually describes public elections, but it probably wouldn't cover a
vote on what color is the best, or a vote on what cuisine to have delivered. So I
think we should probably have IIB for those cases.
I think that is the sort of thinking that
leads some people to support Median Ratings methods, which we know are
garbage because they fail Dominant Candidate and Irrelevant Ballots
Independence, and the voters have a strong incentive to just submit
approval ballots (giving the same result as Approval). And it has led
you to the absurdity of suggesting a method that fails Mono-add-Plump.
Not at all, median rating methods aren't motivated by the notion of a single median
voter. There are multiple median voters on different posed questions, and that's
true on a pairwise matrix as well.
I think for the purposes of properly analysing single-winner election
methods and inspiring the invention of new ones, we can and should do
without criteria that refer to irrelevant ballots dependent "majority"
thresholds or pairwise defeats. Those have almost no positive point
aside from marketing.
You're saying that criteria directly specifying "majority" and not something else
is what lacks positive points aside from marketing? That could be true.
My suggestion for something as close as possible to Minimal Defense:
If the number of ballots that vote X above bottom and Y no higher than
equal-bottom is greater than Y's maximum pairwise support, then Y can't
win.
I don't hate that. I don't know what you gain from using "max pairwise support"
instead of "votes in total."
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
That already inspires a simple method suggestion: DDI,MMM: Elect the
candidate not disqualified by Double-Defeat (Implicit) that is highest
ordered by MinMax(Margins).
What do you think of that?
I don't like it but it might be fine.
And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).
You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.
In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.
Kevin
votingmethods.net
Hi CLC,
The outcomes of our election methods can (almost as a rule) be dictated by a
coordinated majority (or a group of more numerous voters) so I expect a "zero-info
honesty" method to have some kind of inherent tether to this reality, as though the
coordination is done for the voters already, behind the scenes.
Well, the two examples of proven zero-information honesty I know about are quadratic
voting and Borda count. I'm not actually aware of any proofs for the Condorcet
cases, but I suspect most Condorcet methods work here.
In some cases proofs seem a little trivial. Why wouldn't IRV have zero-info honesty
for example?
Kevin
votingmethods.net
Kevin,
What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider,...
And that's bad because that list is so boringly short.
...and we aren't necessarily getting anything of value except that fewer people can call the method absurd.
So to you nothing actually is absurd, and if other people mistakenly
think otherwise then that is just a marketing problem. Got it.
What I call inherently of value would be things like sincere Condorcet efficiency or reduced strategic incentives.
I can understand voted Smith-set fundamentalism, and that is expensive
enough. But if there is a top cycle I don't share the mind-set "Probably
there is a sincere CW (concealed by strategic truncation or
order-reversal) and our top priority should be to infer or guess who
that is and elect him/her." There may well be no sincere CW or a higher
SU candidate. So quite nice, but mainly just a marketing benefit.
Of course I agree with the value of "reduced strategic incentives".
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there.
They "won't" because it isn't even possible to imagine any "other
considerations".
In reference to my example showing MDDA 2 failing Mono-add-Plump:
The voters' behavior had a side effect of strengthening B.
No, it just had the "side effect" of exposing the method's perverse
stupidity.
All sorts of monotonicity failures take such an appearance.
None anything like as starkly. And without some excuse we avoid them.
IRV used to be ridiculed for failing mono-raise (then just called
"Monotonicity"), but we know that it isn't possible to fix that without
losing other criterion compliances that some people like.
But again, I can't believe that we have to put up with failure of
Mono-add-Plump in order to get anything desirable.
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
But given their compatibility, isn't that a strange thing to say?
Not really. The criterion can have nothing to say against candidate X
in some ballot profile but then if we modify that profile by just adding
ballots the plump for X it can decide that X is no longer acceptable.
That is what I meant by the "concept". The two criteria are compatible
because there are other candidates and GMC doesn't say that X has to win
in the original profile. Purely strengthening X (by stuffing extra
X-plumping ballots into the ballot box) can, according to the criterion.
change X from a candidate that is not disqualified into one that is.
That makes the criterion silly and unacceptable.
Because of mutual criteria incompatibilities, we can sometimes make a
case for a (at least in some way) silly method. But there is no need or
excuse for a silly criterion.
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
I see. Then substitute the Strong Defensive Strategy Criterion for SFC.
If a Condorcet candidate exists, and if a majority prefers this
candidate to another candidate, then the other candidate should not
win if that majority votes sincerely and no other voter falsifies any
preferences.
I think that is very similar to the Generalised Majority Criterion,
enough for me to reject it on the same grounds. And even if I didn't
have that criticism, I don't see why it's something we should care much
about. It looks like something contrived just to serve as ammunition
against Hare and Margins. (And possibly the similar GMC was contrived
just to help promote the Schulze method.)
Putting back my "celebrated" example from December 2008:
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.
As I also wrote then:
As I hope some may have guessed from the spectacular failure of Mono-add-Plump, the GMC
concept is grossly unfair to truncators. And Winning Votes (as a GMC complying method) is
unfair to truncators.
Say the 26C "we're just here to elect C and don't care about any other candidate" voters use a
random-fill strategy, each tossing a fair coin to decide between voting C>B or C>A; then even if as
few as 4 of them vote C>A they will elect C. Their chance making C the decisive winner is 99.9956%
(according to an online calculator).
I have some sympathy with the idea of giving up something so as to counter order-reversing buriers,
but not with the idea that electing a CW is obviously so wonderful that when there is no voted CW
we must guess that there is a "sincere CW" and if we can infer that that can only (assuming no voters
are order-reversing) be X then we must elect X.
All that also applies to MDDA 2 and SFC. Take the case where of the original 26 C plumbers, 4 vote C>A and the rest vote C>B.
25: A>B
26: B>C
27: C>A
22: C>B
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 52-48. Implicit Approval scores: C 75, B 51, A 52.
No candidate has sub-majority approval and no candidate has a majority-strength defeat so the MDDA 2 winner is the most approved candidate, C.
Chris B.
On 21/06/2024 9:32 pm, Kevin Venzke wrote:
Hi Chris,
On Mono-add-Plump as a weak version of Participation:
Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking.
What sort of "trouble"? I don't see how your conclusion follows from
your premise. Why do "almost all proposals fail Participation"? It
isn't because there is anything inherently wrong with "that kind of
thinking". It is because it just happens that Participation is very
expensive (in terms of other desirable criterion compliances, such as
Condorcet). But in that way Mono-add-Plump is very very cheap (if not
free), and some of us are currently "in trouble" due to disregarding
"this kind of thinking".
What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider, and we aren't
necessarily getting anything of value except that fewer people can call the method
absurd. What I call inherently of value would be things like sincere Condorcet
efficiency or reduced strategic incentives.
Suppose a mini-bus with a driver is contracted to pick up a group of
people and take then on a trip to one of X, Y or Z after polling the
passengers on their ranking-preferences among these alternative
destinations. After the bus is nearly full it is mistakenly assumed that
there will be no more passengers and the driver applies some algorithm
to the rankings of those present and announces that winning alternative
is X.
Then it is learned that there are two more passengers to come to fill up
the bus. They do so and the driver says to them "I've polled all the
other passengers and at the moment the winning destination is X. Where
would you like to go?" and they reply "X is our first preference and Y
wouldn't be too bad and we are very glad we aren't gong to Z".
The driver replies "You prefer Y to Z? In that case the new winning
alternative is Y". Now if these two voters (and perhaps others whose
first preference was X) were enlightened election-method experts, they
might think "Obviously this fellow's election-method algorithm fails
Participation (and presumably Later-no-Harm). Perhaps it meets
Condorcet, which we know is incompatible with both Participation and
Later-no-Harm. Perhaps before we showed up there was a top cycle and our
Y>Z preferences turned Y into the Condorcet winner.
But we know that Condorcet is also incompatible with Later-no-Help so us
revealing our second preferences could have just as likely helped us, so
I suppose we were just unlucky."
Or if they were not experts but charitably minded they might think "I
suppose it is possible that this fellow made an honest mistake due to
him being thick and us confusing him with too much information".
Now replay this scenario except this time the new passengers just say
"Great! We just really want to go to X and we don't know or care about
any other destination." And then the driver says "In that case the
winning alternative changes from X to Y".
The response could only be that the destination-decider (supposedly
purely based on the passengers' stated preferences) is insane (or
malevolent, in any case illegitimate) and that Y is obviously an
illegitimate winner.
Did you notice a very different vibe from the first case, which was a
failure of Participation and Mono-add-Top but not Mono-add-Plump?
The difference in vibe is quite similar to your own difference in vibe when you
compare these situations.
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there. And that's
fine, that is their right.
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
But given their compatibility, isn't that a strange thing to say?
Your new MDDA 2 method fails the example I gave:
25 A>B
26 B>C
23 C>A
04 C
(78 ballots, majority threshold = 40)
Implicit approval scores: C 53, B 51, A 48. No candidate is
disqualified due to sub-majority approval.
B>C 51-27, C>A 53-25, A>B 48-26. All candidates have a
"majority" strength defeat, so it "isn't possible" to disqualify any
candidate on that basis. So, according to the rules of MDDA 2, we elect
the most approved candidate, C.
Now say we add 22 ballots that plump for C to give:
25 A>B
26 B>C
23 C>A
26 C
(100 ballots, majority threshold = 51)
Implicit approval scores: C 75, B 51, A 48. Now A has sub-majority
approval and so is disqualified.
B>C 51-49, C>A 75-25, A>B 48-26. Now C and A have
majority-strength defeats and B doesn't, so (according to the rules of
MDDA 2), A (again) and C are disqualified leaving B as the new winner.
The contention that C is the right winner when there were just 78
ballots but when we add 22 ballots that plump (bullet vote) for C the
right winner is no longer C is .... completely crazy.
The voters' behavior had a side effect of strengthening B. All sorts of monotonicity
failures take such an appearance.
And again, there could be differences in severity, e.g. what percent of voters think
a given phenomenon is absurd. But I don't find that very interesting because it
doesn't tell us about the merits of the method. It's basically marketability.
Well, in an environment where the concept of "median voter" is likely
to be meaningful,...
What "environment" is that? And why is that the environment the one we
should primarily focus on?
One where voter and candidate preferences can be explained by an underlying issue
space. In this case if you could project everyone onto a plane or spectrum it would
be a bit easy to find the median voter and their preferred candidate.
I think this usually describes public elections, but it probably wouldn't cover a
vote on what color is the best, or a vote on what cuisine to have delivered. So I
think we should probably have IIB for those cases.
I think that is the sort of thinking that
leads some people to support Median Ratings methods, which we know are
garbage because they fail Dominant Candidate and Irrelevant Ballots
Independence, and the voters have a strong incentive to just submit
approval ballots (giving the same result as Approval). And it has led
you to the absurdity of suggesting a method that fails Mono-add-Plump.
Not at all, median rating methods aren't motivated by the notion of a single median
voter. There are multiple median voters on different posed questions, and that's
true on a pairwise matrix as well.
I think for the purposes of properly analysing single-winner election
methods and inspiring the invention of new ones, we can and should do
without criteria that refer to irrelevant ballots dependent "majority"
thresholds or pairwise defeats. Those have almost no positive point
aside from marketing.
You're saying that criteria directly specifying "majority" and not something else
is what lacks positive points aside from marketing? That could be true.
My suggestion for something as close as possible to Minimal Defense:
If the number of ballots that vote X above bottom and Y no higher than
equal-bottom is greater than Y's maximum pairwise support, then Y can't
win.
I don't hate that. I don't know what you gain from using "max pairwise support"
instead of "votes in total."
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
That already inspires a simple method suggestion: DDI,MMM: Elect the
candidate not disqualified by Double-Defeat (Implicit) that is highest
ordered by MinMax(Margins).
What do you think of that?
I don't like it but it might be fine.
And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).
You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.
In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.
Kevin
votingmethods.net
On Fri, Jun 21, 2024 at 17:22 Chris Benham cbenhamau@yahoo.com.au .
I can understand voted Smith-set fundamentalism, and that is expensive
enough.
It a avoids the possible embarrassment of electing a Condorcet loser, with
the likely resulting repeal. Maybe some additional desired criteria are
gained too.
RP(wv) & Schulze do even better, with their clone-independence, & probably
various other criterion-gains.
But if there is a top cycle I don't share the mind-set "Probably there is a
sincere CW (concealed by strategic truncation or order-reversal) and our
top priority should be to infer or guess who that is and elect him/her."
There may well be no sincere CW or a higher SU candidate. So quite nice,
but mainly just a marketing benefit.
No. Available evidence, including thousands of CIVS polls, indicates that
sincerely-voted top-cycles are rare. It isn’t speculation. It’s experience.
Because any top-cycle is almost surely strategic, & because allowing
offensive strategy to defeat a sincere CW (with the consequent
defensive-strategy-need) results in big problematic defensive-strategy-need…
…& because it doesn’t make a whole hell of a lot of difference who wins in
a sincerely-voted circular-tie…
…then yes, what matters is, as well as possible, preventing
offensive-strategy from talking the win away from a sincere-CW.
The wv Condorcet methods excellently achieve that….resulting in a fully
strategy-free method
…by which I mean, a method with which no defensive-strategy is needed.
…the achievement of the Condorcet ideal.
…&, in general, the ideal goal of voting system reform.
The best wv Condorcet methods that I’ve heard of are:
RP(wv)
Schulze
MinMax(wv)
Smith//MinMax(wv)
RP(wv) Schulze meet the most criteria.
Those methods achieve the ideal by two properties.
-
Minimal-Defence Criterion compliance
-
Autodeterence
Of course I agree with the value of "reduced strategic incentives".
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there.
They "won't" because it isn't even possible to imagine any "other
considerations".
In reference to my example showing MDDA 2 failing Mono-add-Plump:
The voters' behavior had a side effect of strengthening B.
No, it just had the "side effect" of exposing the method's perverse
stupidity.
All sorts of monotonicity failures take such an appearance.
None anything like as starkly. And without some excuse we avoid them. IRV
used to be ridiculed for failing mono-raise (then just called
"Monotonicity"), but we know that it isn't possible to fix that without
losing other criterion compliances that some people like.
But again, I can't believe that we have to put up with failure of
Mono-add-Plump in order to get anything desirable.
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
But given their compatibility, isn't that a strange thing to say?
Not really. The criterion can have nothing to say against candidate X in
some ballot profile but then if we modify that profile by just adding
ballots the plump for X it can decide that X is no longer acceptable. That
is what I meant by the "concept". The two criteria are compatible because
there are other candidates and GMC doesn't say that X has to win in the
original profile. Purely strengthening X (by stuffing extra X-plumping
ballots into the ballot box) can, according to the criterion. change X from
a candidate that is not disqualified into one that is. That makes the
criterion silly and unacceptable.
Because of mutual criteria incompatibilities, we can sometimes make a case
for a (at least in some way) silly method. But there is no need or excuse
for a silly criterion.
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
I see. Then substitute the Strong Defensive Strategy Criterion for SFC.
https://electowiki.org/wiki/Strategy-free_criterion
If a Condorcet candidate exists, and if a majority prefers this candidate
to another candidate, then the other candidate should not win if that
majority votes sincerely and no other voter falsifies any preferences.
I think that is very similar to the Generalised Majority Criterion, enough
for me to reject it on the same grounds. And even if I didn't have that
criticism, I don't see why it's something we should care much about. It
looks like something contrived just to serve as ammunition against Hare and
Margins. (And possibly the similar GMC was contrived just to help promote
the Schulze method.)
Putting back my "celebrated" example from December 2008:
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.
As I also wrote then:
As I hope some may have guessed from the spectacular failure of Mono-add-Plump, the GMC
concept is grossly unfair to truncators. And Winning Votes (as a GMC complying method) is
unfair to truncators.
Say the 26C "we're just here to elect C and don't care about any other candidate" voters use a
random-fill strategy, each tossing a fair coin to decide between voting C>B or C>A; then even if as
few as 4 of them vote C>A they will elect C. Their chance making C the decisive winner is 99.9956%
(according to an online calculator).
I have some sympathy with the idea of giving up something so as to counter order-reversing buriers,
but not with the idea that electing a CW is obviously so wonderful that when there is no voted CW
we must guess that there is a "sincere CW" and if we can infer that that can only (assuming no voters
are order-reversing) be X then we must elect X.
All that also applies to MDDA 2 and SFC. Take the case where of the
original 26 C plumbers, 4 vote C>A and the rest vote C>B. 25: A>B 26: B>C
27: C>A 22: C>B 100 ballots (majority threshold = 51) B>C 51-49, C>A
75-25, A>B 52-48. Implicit Approval scores: C 75, B 51, A 52. No
candidate has sub-majority approval and no candidate has a
majority-strength defeat so the MDDA 2 winner is the most approved
candidate, C. Chris B.
On 21/06/2024 9:32 pm, Kevin Venzke wrote:
Hi Chris,
On Mono-add-Plump as a weak version of Participation:
Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking.
What sort of "trouble"? I don't see how your conclusion follows from
your premise. Why do "almost all proposals fail Participation"? It
isn't because there is anything inherently wrong with "that kind of
thinking". It is because it just happens that Participation is very
expensive (in terms of other desirable criterion compliances, such as
Condorcet). But in that way Mono-add-Plump is very very cheap (if not
free), and some of us are currently "in trouble" due to disregarding
"this kind of thinking".
What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider, and we aren't
necessarily getting anything of value except that fewer people can call the method
absurd. What I call inherently of value would be things like sincere Condorcet
efficiency or reduced strategic incentives.
Suppose a mini-bus with a driver is contracted to pick up a group of
people and take then on a trip to one of X, Y or Z after polling the
passengers on their ranking-preferences among these alternative
destinations. After the bus is nearly full it is mistakenly assumed that
there will be no more passengers and the driver applies some algorithm
to the rankings of those present and announces that winning alternative
is X.
Then it is learned that there are two more passengers to come to fill up
the bus. They do so and the driver says to them "I've polled all the
other passengers and at the moment the winning destination is X. Where
would you like to go?" and they reply "X is our first preference and Y
wouldn't be too bad and we are very glad we aren't gong to Z".
The driver replies "You prefer Y to Z? In that case the new winning
alternative is Y". Now if these two voters (and perhaps others whose
first preference was X) were enlightened election-method experts, they
might think "Obviously this fellow's election-method algorithm fails
Participation (and presumably Later-no-Harm). Perhaps it meets
Condorcet, which we know is incompatible with both Participation and
Later-no-Harm. Perhaps before we showed up there was a top cycle and our
Y>Z preferences turned Y into the Condorcet winner.
But we know that Condorcet is also incompatible with Later-no-Help so us
revealing our second preferences could have just as likely helped us, so
I suppose we were just unlucky."
Or if they were not experts but charitably minded they might think "I
suppose it is possible that this fellow made an honest mistake due to
him being thick and us confusing him with too much information".
Now replay this scenario except this time the new passengers just say
"Great! We just really want to go to X and we don't know or care about
any other destination." And then the driver says "In that case the
winning alternative changes from X to Y".
The response could only be that the destination-decider (supposedly
purely based on the passengers' stated preferences) is insane (or
malevolent, in any case illegitimate) and that Y is obviously an
illegitimate winner.
Did you notice a very different vibe from the first case, which was a
failure of Participation and Mono-add-Top but not Mono-add-Plump?
The difference in vibe is quite similar to your own difference in vibe when you
compare these situations.
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there. And that's
fine, that is their right.
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
But given their compatibility, isn't that a strange thing to say?
Your new MDDA 2 method fails the example I gave:
25 A>B
26 B>C
23 C>A
04 C
(78 ballots, majority threshold = 40)
Implicit approval scores: C 53, B 51, A 48. No candidate is
disqualified due to sub-majority approval.
B>C 51-27, C>A 53-25, A>B 48-26. All candidates have a
"majority" strength defeat, so it "isn't possible" to disqualify any
candidate on that basis. So, according to the rules of MDDA 2, we elect
the most approved candidate, C.
Now say we add 22 ballots that plump for C to give:
25 A>B
26 B>C
23 C>A
26 C
(100 ballots, majority threshold = 51)
Implicit approval scores: C 75, B 51, A 48. Now A has sub-majority
approval and so is disqualified.
B>C 51-49, C>A 75-25, A>B 48-26. Now C and A have
majority-strength defeats and B doesn't, so (according to the rules of
MDDA 2), A (again) and C are disqualified leaving B as the new winner.
The contention that C is the right winner when there were just 78
ballots but when we add 22 ballots that plump (bullet vote) for C the
right winner is no longer C is .... completely crazy.
The voters' behavior had a side effect of strengthening B. All sorts of monotonicity
failures take such an appearance.
And again, there could be differences in severity, e.g. what percent of voters think
a given phenomenon is absurd. But I don't find that very interesting because it
doesn't tell us about the merits of the method. It's basically marketability.
Well, in an environment where the concept of "median voter" is likely
to be meaningful,...
What "environment" is that? And why is that the environment the one we
should primarily focus on?
One where voter and candidate preferences can be explained by an underlying issue
space. In this case if you could project everyone onto a plane or spectrum it would
be a bit easy to find the median voter and their preferred candidate.
I think this usually describes public elections, but it probably wouldn't cover a
vote on what color is the best, or a vote on what cuisine to have delivered. So I
think we should probably have IIB for those cases.
I think that is the sort of thinking that
leads some people to support Median Ratings methods, which we know are
garbage because they fail Dominant Candidate and Irrelevant Ballots
Independence, and the voters have a strong incentive to just submit
approval ballots (giving the same result as Approval). And it has led
you to the absurdity of suggesting a method that fails Mono-add-Plump.
Not at all, median rating methods aren't motivated by the notion of a single median
voter. There are multiple median voters on different posed questions, and that's
true on a pairwise matrix as well.
I think for the purposes of properly analysing single-winner election
methods and inspiring the invention of new ones, we can and should do
without criteria that refer to irrelevant ballots dependent "majority"
thresholds or pairwise defeats. Those have almost no positive point
aside from marketing.
You're saying that criteria directly specifying "majority" and not something else
is what lacks positive points aside from marketing? That could be true.
My suggestion for something as close as possible to Minimal Defense:
If the number of ballots that vote X above bottom and Y no higher than
equal-bottom is greater than Y's maximum pairwise support, then Y can't
win.
I don't hate that. I don't know what you gain from using "max pairwise support"
instead of "votes in total."
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
That already inspires a simple method suggestion: DDI,MMM: Elect the
candidate not disqualified by Double-Defeat (Implicit) that is highest
ordered by MinMax(Margins).
What do you think of that?
I don't like it but it might be fine.
And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).
You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.
In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.
Kevinvotingmethods.net
Kevin,
Something I didn't address in my previous email:
And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).
You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.
In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.
In these mass public elections the chance that an individual voter's
ballot will be pivotal is negligible. I would think that if the method
is making some attempt to minimise the number of "wasted votes", then
many voters would want to be able to express their full sincere ranking
and also would at least not mind giving their sincere or semi-sincere
approval cutoff. For example in a Hare (aka IRV) election (with
unrestricted strict ranking from the top) I can't imagine it ever
crossing my mind to vote insincerely (and I never have).
Also I think the method needs to have some justification on the
assumption that the voters are sincere. So if voters complain "Why
aren't I allowed to rank among the candidates I don't approve?" and "How
do we know that the voted CW is really the CW if we have been forced to
truncate our rankings?", we need some answer that isn't just about
"deterring burial". We could say "Well this is more simple, and it's
not strictly a Condorcet method but rather an Approval-Condorcet hybrid
that is trying to produce a high SU winner" but I expect that a lot of
voters would not be fully satisfied with that answer. (I wouldn't be.)
I have become firmer in my support for Double Defeat (explicit) methods
and my favourite of these is Margins-Sorted Approval. Those method allow
voters to rank however many candidates they wish and also give a
approval cutoff, and no candidate that is pairwise-beaten by a more
approved candidate is allowed to win. Much of the time this is by itself
decisive.
I think those of us who are extra hung-up about frustrating Burial
should look more closely at Double Defeat, Hare. I suspect that it has
most of the Condorcet efficiency of an actual Condorcet method while
retaining most of the Burial resistance of Hare, while possibly tending
to give higher SU winners than both.
Chris B.
On 21/06/2024 9:32 pm, Kevin Venzke wrote:
Hi Chris,
On Mono-add-Plump as a weak version of Participation:
Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking.
What sort of "trouble"? I don't see how your conclusion follows from
your premise. Why do "almost all proposals fail Participation"? It
isn't because there is anything inherently wrong with "that kind of
thinking". It is because it just happens that Participation is very
expensive (in terms of other desirable criterion compliances, such as
Condorcet). But in that way Mono-add-Plump is very very cheap (if not
free), and some of us are currently "in trouble" due to disregarding
"this kind of thinking".
What I'm saying is that if we pursue criteria in the vein of Participation (or
monotonicity), we cut down the list of methods we can consider, and we aren't
necessarily getting anything of value except that fewer people can call the method
absurd. What I call inherently of value would be things like sincere Condorcet
efficiency or reduced strategic incentives.
Suppose a mini-bus with a driver is contracted to pick up a group of
people and take then on a trip to one of X, Y or Z after polling the
passengers on their ranking-preferences among these alternative
destinations. After the bus is nearly full it is mistakenly assumed that
there will be no more passengers and the driver applies some algorithm
to the rankings of those present and announces that winning alternative
is X.
Then it is learned that there are two more passengers to come to fill up
the bus. They do so and the driver says to them "I've polled all the
other passengers and at the moment the winning destination is X. Where
would you like to go?" and they reply "X is our first preference and Y
wouldn't be too bad and we are very glad we aren't gong to Z".
The driver replies "You prefer Y to Z? In that case the new winning
alternative is Y". Now if these two voters (and perhaps others whose
first preference was X) were enlightened election-method experts, they
might think "Obviously this fellow's election-method algorithm fails
Participation (and presumably Later-no-Harm). Perhaps it meets
Condorcet, which we know is incompatible with both Participation and
Later-no-Harm. Perhaps before we showed up there was a top cycle and our
Y>Z preferences turned Y into the Condorcet winner.
But we know that Condorcet is also incompatible with Later-no-Help so us
revealing our second preferences could have just as likely helped us, so
I suppose we were just unlucky."
Or if they were not experts but charitably minded they might think "I
suppose it is possible that this fellow made an honest mistake due to
him being thick and us confusing him with too much information".
Now replay this scenario except this time the new passengers just say
"Great! We just really want to go to X and we don't know or care about
any other destination." And then the driver says "In that case the
winning alternative changes from X to Y".
The response could only be that the destination-decider (supposedly
purely based on the passengers' stated preferences) is insane (or
malevolent, in any case illegitimate) and that Y is obviously an
illegitimate winner.
Did you notice a very different vibe from the first case, which was a
failure of Participation and Mono-add-Top but not Mono-add-Plump?
The difference in vibe is quite similar to your own difference in vibe when you
compare these situations.
In one case, some voters are willing to say "I guess there were other considerations
in play; we were unlucky" but in the other case they won't go there. And that's
fine, that is their right.
In December 2008 on EM I argued that Schulze's Generalised Majority
Criterion is a mistaken standard because the concept is vulnerable to
Mono-add-Plump.
But given their compatibility, isn't that a strange thing to say?
Your new MDDA 2 method fails the example I gave:
25 A>B
26 B>C
23 C>A
04 C
(78 ballots, majority threshold = 40)
Implicit approval scores: C 53, B 51, A 48. No candidate is
disqualified due to sub-majority approval.
B>C 51-27, C>A 53-25, A>B 48-26. All candidates have a
"majority" strength defeat, so it "isn't possible" to disqualify any
candidate on that basis. So, according to the rules of MDDA 2, we elect
the most approved candidate, C.
Now say we add 22 ballots that plump for C to give:
25 A>B
26 B>C
23 C>A
26 C
(100 ballots, majority threshold = 51)
Implicit approval scores: C 75, B 51, A 48. Now A has sub-majority
approval and so is disqualified.
B>C 51-49, C>A 75-25, A>B 48-26. Now C and A have
majority-strength defeats and B doesn't, so (according to the rules of
MDDA 2), A (again) and C are disqualified leaving B as the new winner.
The contention that C is the right winner when there were just 78
ballots but when we add 22 ballots that plump (bullet vote) for C the
right winner is no longer C is .... completely crazy.
The voters' behavior had a side effect of strengthening B. All sorts of monotonicity
failures take such an appearance.
And again, there could be differences in severity, e.g. what percent of voters think
a given phenomenon is absurd. But I don't find that very interesting because it
doesn't tell us about the merits of the method. It's basically marketability.
Well, in an environment where the concept of "median voter" is likely
to be meaningful,...
What "environment" is that? And why is that the environment the one we
should primarily focus on?
One where voter and candidate preferences can be explained by an underlying issue
space. In this case if you could project everyone onto a plane or spectrum it would
be a bit easy to find the median voter and their preferred candidate.
I think this usually describes public elections, but it probably wouldn't cover a
vote on what color is the best, or a vote on what cuisine to have delivered. So I
think we should probably have IIB for those cases.
I think that is the sort of thinking that
leads some people to support Median Ratings methods, which we know are
garbage because they fail Dominant Candidate and Irrelevant Ballots
Independence, and the voters have a strong incentive to just submit
approval ballots (giving the same result as Approval). And it has led
you to the absurdity of suggesting a method that fails Mono-add-Plump.
Not at all, median rating methods aren't motivated by the notion of a single median
voter. There are multiple median voters on different posed questions, and that's
true on a pairwise matrix as well.
I think for the purposes of properly analysing single-winner election
methods and inspiring the invention of new ones, we can and should do
without criteria that refer to irrelevant ballots dependent "majority"
thresholds or pairwise defeats. Those have almost no positive point
aside from marketing.
You're saying that criteria directly specifying "majority" and not something else
is what lacks positive points aside from marketing? That could be true.
My suggestion for something as close as possible to Minimal Defense:
If the number of ballots that vote X above bottom and Y no higher than
equal-bottom is greater than Y's maximum pairwise support, then Y can't
win.
I don't hate that. I don't know what you gain from using "max pairwise support"
instead of "votes in total."
I propose Double Defeat (Implicit) as something that can substitute for
the votes-only versions of Minimal Defense and SFC and also Plurality.
Interpreting ranking (or ranking above equal bottom) as approval, no
candidate that is pairwise-beaten by a more approved candidate is
allowed to win.
It's interesting but it doesn't cover SFC. In an SFC failure scenario the
disqualified candidate might very well have more approval than the candidate who
disqualifies them. The concern is that supporters of the latter gave the election
away.
That already inspires a simple method suggestion: DDI,MMM: Elect the
candidate not disqualified by Double-Defeat (Implicit) that is highest
ordered by MinMax(Margins).
What do you think of that?
I don't like it but it might be fine.
And what is wrong with your "Improved
Condorcet Approval" method ? I think it would be good using
unrestricted ranking ballots with an explicit approval cutoff.
ICA or C//A (implicit) are not bad. They don't satisfy SFC. In my recent simulations
on frontrunner truncation strategy, C//A is among the best Condorcet methods. In
random elections I am disturbed that ICA and C//A are worse than WV methods at
strong FBC (i.e. what I call compromise incentive).
You've asked me many times about C//A(explicit) and I still think it's bad. The
entire notion of C//A(implicit) being good at deterring burial is based on the
fact that if you use burial to prevent there from being a Condorcet winner, then in
the "cycle resolution" you cannot prefer any candidate to the one you raised
insincerely.
In C//A(explicit), burial only backfires if it actually creates a fake CW. Creating
a fake cycle is never bad for your favorite.
Kevin
votingmethods.net