Kevin Venzke stepjak at yahoo.fr
mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C1931864740.14928463.1559418507456%40mail.yahoo.com%3E
Sat Jun 1 12:48:27 PDT 2019

Hi Forest,

I had two ideas.

Idea 1:

1. If there is a CW using all rankings, elect the CW.
2. Otherwise flatten/discard all disapproved rankings.
3. Use any method that would elect C in scenario 2. (Approval,
   Bucklin, MinMax(WV).)

So scenario 1 has no CW. The disapproved C>A rankings are dropped. A
wins any method.
In scenario 2 there is no CW but nothing is dropped, so use a method
that picks C.
In both versions of scenario 3 there is a CW, B.

If step 3 is Approval then of course step 2 is unnecessary.

In place of step 1 you could find and apply the majority-strength
solid coalitions (using all rankings)
to disqualify A, instead of acting based on B being a CW. I'm not sure
if there's another elegant way
to identify the majority coalition.

Idea 2:

1. Using all rankings, find the strength of everyone's worst WV
   defeat. (A CW scores 0.)
2. Say that candidate X has a "double beatpath" to Y if X has a
   standard beatpath to Y regardless
   of whether the disapproved rankings are counted. (I don't know if it
   needs to be the same beatpath,
   but it shouldn't come into play with these scenarios.)
3. Disqualify from winning any candidate who is not in the Schwartz
   set calculated using double
   beatpaths. In other words, for every candidate Y where there exists a
   candidate X such that X has a
   double beatpath to Y and Y does not have a double beatpath to X, then
   Y is disqualified.
4. Elect the remaining candidate with the mildest WV defeat calculated
   earlier.

So in scenario 1, A always has a beatpath to the other candidates, no
matter whether disapproved
rankings are counted. The other candidates only have a beatpath to A
when the C>A win exists. So
A has a double beatpath to B and C, and they have no path back. This
leaves A as the only candidate
not disqualified.

In scenario 2, the defeat scores from weakest to strongest are B>C,
A>B, C>A. Every candidate has
a beatpath to every other candidate no matter whether the
(nonexistent) disapproved rankings are
counted. So no candidate is disqualified. C has the best defeat score
and wins.

In scenario 3, the first version: B has no losses. C's loss to B is
weaker than both of A's losses. B
beats C pairwise no matter what, so B has a double beatpath to C.
However C has no such beatpath
to A, nor has A one to B, nor has B one to A. The resulting Schwartz
set disqualifies only C. (C needs
to return B's double beatpath but can't, and neither A nor B has a
double beatpath to the other.)
Between A and B, B's score (as CW) is 0, so he wins.

Scenario 3, second version: B again has no losses, and also has double
beatpaths to both of A and
C, neither of whom have double beatpaths back. So A and C are
disqualified and B wins.

I must note that this is actually a Condorcet method, since a CW could
never get disqualified and
would always have the best worst defeat. That observation would
simplify the explanation of
scenario 3.

I needed the defeat strength rule because I had no way to give the win
to B over A in scenario 3
version 1. But I guess if it's a Condorcet rule in any case, we can
just add that as a rule, and greatly
simplify it to the point where it's going to look very much like idea

1. I guess all my ideas lead me to
   the same place with this question.

Oh well, I think the ideas are interesting enough to post.

Kevin

pcc.edu> a écrit :

consequence of these constraints is that in all three profiles below
the cycle >A>B>C>A will obtain.

but I don't want to prejudice your creative efforts with too many ideas.

defend itself against a "chicken" attack (truncation of B) from the C
faction.

game of Chicken is not going to work for them, the sincere CW is elected.

against the A faction's potential truncation attack.

most obvious one is Smith\Approval where the voters have

approval) with default approval as top rank only. The other

almost always electing from Smith.

Kevin Venzke stepjak at yahoo.fr
mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C1931864740.14928463.1559418507456%40mail.yahoo.com%3E
Sat Jun 1 12:48:27 PDT 2019

Hi Forest,

I had two ideas.

Idea 1:

1. If there is a CW using all rankings, elect the CW.
2. Otherwise flatten/discard all disapproved rankings.
3. Use any method that would elect C in scenario 2. (Approval,
   Bucklin, MinMax(WV).)

So scenario 1 has no CW. The disapproved C>A rankings are dropped. A
wins any method.
In scenario 2 there is no CW but nothing is dropped, so use a method
that picks C.
In both versions of scenario 3 there is a CW, B.

If step 3 is Approval then of course step 2 is unnecessary.

In place of step 1 you could find and apply the majority-strength
solid coalitions (using all rankings)
to disqualify A, instead of acting based on B being a CW. I'm not sure
if there's another elegant way
to identify the majority coalition.

Idea 2:

1. Using all rankings, find the strength of everyone's worst WV
   defeat. (A CW scores 0.)
2. Say that candidate X has a "double beatpath" to Y if X has a
   standard beatpath to Y regardless
   of whether the disapproved rankings are counted. (I don't know if it
   needs to be the same beatpath,
   but it shouldn't come into play with these scenarios.)
3. Disqualify from winning any candidate who is not in the Schwartz
   set calculated using double
   beatpaths. In other words, for every candidate Y where there exists a
   candidate X such that X has a
   double beatpath to Y and Y does not have a double beatpath to X, then
   Y is disqualified.
4. Elect the remaining candidate with the mildest WV defeat calculated
   earlier.

So in scenario 1, A always has a beatpath to the other candidates, no
matter whether disapproved
rankings are counted. The other candidates only have a beatpath to A
when the C>A win exists. So
A has a double beatpath to B and C, and they have no path back. This
leaves A as the only candidate
not disqualified.

In scenario 2, the defeat scores from weakest to strongest are B>C,
A>B, C>A. Every candidate has
a beatpath to every other candidate no matter whether the
(nonexistent) disapproved rankings are
counted. So no candidate is disqualified. C has the best defeat score
and wins.

In scenario 3, the first version: B has no losses. C's loss to B is
weaker than both of A's losses. B
beats C pairwise no matter what, so B has a double beatpath to C.
However C has no such beatpath
to A, nor has A one to B, nor has B one to A. The resulting Schwartz
set disqualifies only C. (C needs
to return B's double beatpath but can't, and neither A nor B has a
double beatpath to the other.)
Between A and B, B's score (as CW) is 0, so he wins.

Scenario 3, second version: B again has no losses, and also has double
beatpaths to both of A and
C, neither of whom have double beatpaths back. So A and C are
disqualified and B wins.

I must note that this is actually a Condorcet method, since a CW could
never get disqualified and
would always have the best worst defeat. That observation would
simplify the explanation of
scenario 3.

I needed the defeat strength rule because I had no way to give the win
to B over A in scenario 3
version 1. But I guess if it's a Condorcet rule in any case, we can
just add that as a rule, and greatly
simplify it to the point where it's going to look very much like idea

1. I guess all my ideas lead me to
   the same place with this question.

Oh well, I think the ideas are interesting enough to post.

Kevin

pcc.edu> a écrit :

consequence of these constraints is that in all three profiles below
the cycle >A>B>C>A will obtain.

but I don't want to prejudice your creative efforts with too many ideas.

defend itself against a "chicken" attack (truncation of B) from the C
faction.

game of Chicken is not going to work for them, the sincere CW is elected.

against the A faction's potential truncation attack.

most obvious one is Smith\Approval where the voters have

approval) with default approval as top rank only. The other

almost always electing from Smith.

Hi Chris,

I've been short on time so I don't actually have much thought on any
of the methods, even my own.

I suppose Idea 2 is the same as Schwartz-limited MinMax(WV) if nobody
submits disapproved rankings. I'm not sure if it makes sense to reject
the method over that. Specifically should "positional dominance" have
the same meaning whether or not the method has approval in it? As a
comparison, I will go easy on these methods over failing MD, because
it happens when some of the majority don't approve their common candidate.

I would have liked to simplify Idea 2, but actually Forest's eventual
proposal wasn't all that simple either. As I wrote, if you add "elect
a CW if there is one" it can become much simpler, so that it isn't
really distinct from Idea 1. I actually tried pretty hard to present
three "Ideas" in that post, but kept having that problem.

I posted those ideas because I thought Forest posed an interesting
challenge, and I thought I perceived that he was trying to fix a
problem with CD. That said, I am not a fan of
Smith//Approval(explicit). If all these methods are basically the same
then I probably won't end up liking any of them. I don't think it's
ideal if burying X under Y (both disapproved) can only backfire when Y
is made the CW.

Kevin

Le mercredi 5 juin 2019 à 21:26:23 UTC−5, C.Benham
cbenham@adam.com.au a écrit :

Kevin,

I didn't comment earlier on your "idea 2".

If there no "disapproved rankings" (i.e. if the voters all approve the
candidates they rank above bottom),
then your suggested method is simply normal  Winning Votes, which I
don't like because the winner can
be uncovered and positionally dominant or pairwise-beaten and
positionally dominated by a single other
candidate.

On top of that I don't think it really fills the bill as "simple". 
Approval Margins (using Sort or Smith//MinMax
or equivalent or almost equivalent algorithm) would be no more complex
and in my opinion would be better.

I would also prefer the still more simple Smith//Approval.

What did you think of my suggestion for a way to implement your idea 1?

Chris

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Why is that?  

Hi Chris,

Because I think if voters decide to attempt to prevent another
candidate from being CW, via insincerity, there should be risks to
doing that. Of course there is already some risk. But if you "knew"
that a given candidate had no chance of being CW then there would be
nothing to lose in using that candidate in a burial strategy.

For either a successful burial strategy, or one that backfires and
elects an arbitrary candidate, I think the possible complaints are
clear. Maybe someone would argue that a backfiring strategy proves the
method's incentives are just fine. But that wouldn't be how I see it.
I think if, in actual practice, it ever happens that voters calculate
that a strategy is worthwhile, and it completely backfires to the
point that everyone would like the results discarded, then that method
will probably get repealed.

arguably you are not even trying to elect the sincere CW.

Not an unfair statement. If you require voters to have that much
expressiveness then you can't use implicit.

To me, the motivation for three-slot C//A(implicit) is partly about
burial, partly about method simplicity, partly about ballot
simplicity. C//A(explicit) retains 1 of 3. (Arguably slightly less for
the Smith version.) Possibly it has its own merits, but they will
largely be different ones.

the reasons why Approval seems to be a lot less popular than IRV.

I have no inherent complaints about the ballot format of explicit
approval plus full ranking.

Kevin

Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham cbenham@adam.com.au
a écrit :

Kevin,

If the voters all choose to approve all the candidates they rank, then
yes.  (For a while I was wrongly assuming that Forest's suggested
default approval was for all ranked-above-bottom candidates, but then
I noticed that he specified that it was only for top voted candidates).

One of my tired examples:

25: A>B
26: B>C
23: C>A
26: C

Assuming all the ranked candidates are approved, C is by far the most
approved and the most top-voted candidate.
Normal Winning Votes (and your idea 2 in this example) elect B.

For me this this type of ballot avoids the Minimal Defense versus
Chicken Dilemma dilemma, rendering those criteria inapplicable.

48: A
27: B>C
25: C

The problem has been that we don't know whether the B>C voters are
thinking "I am ranking C because above all I don't want that evil A
to win" or  "My C>A preference isn't all that strong, and I think that
my favourite could well be the sincere CW, and if  C's supporters rank
B above A then B has a good chance to win. But if they if they create
a cycle by truncating I'm not having them steal it".

With the voters able to express explicit approval we no longer have to
guess which it is.

Why is that?  The post-election complaint (by any of the voters) would
be .. what?

If you don't allow voters to rank among their unapproved candidates
then arguably you are not even trying to elect the sincere CW.
Instead you are just modifying Approval to make it a lot more
Condorcet-ish.

A lot of voters like relatively expressive ballots. I think that is
one of the reasons why Approval seems to be a lot less popular than IRV.

Chris Benham

On 6/06/2019 5:34 pm, Kevin Venzke wrote:
Hi Chris,

I've been short on time so I don't actually have much thought on any
of the methods, even my own.

I suppose Idea 2 is the same as Schwartz-limited MinMax(WV) if nobody
submits disapproved rankings. I'm not sure if it makes sense to reject
the method over that. Specifically should "positional dominance" have
the same meaning whether or not the method has approval in it? As a
comparison, I will go easy on these methods over failing MD, because
it happens when some of the majority don't approve their common candidate.

I would have liked to simplify Idea 2, but actually Forest's eventual
proposal wasn't all that simple either. As I wrote, if you add "elect
a CW if there is one" it can become much simpler, so that it isn't
really distinct from Idea 1. I actually tried pretty hard to present
three "Ideas" in that post, but kept having that problem.

I posted those ideas because I thought Forest posed an interesting
challenge, and I thought I perceived that he was trying to fix a
problem with CD. That said, I am not a fan of
Smith//Approval(explicit). If all these methods are basically the same
then I probably won't end up liking any of them. I don't think it's
ideal if burying X under Y (both disapproved) can only backfire when Y
is made the CW.

Kevin

Le mercredi 5 juin 2019 à 21:26:23 UTC−5, C.Benham
cbenham@adam.com.au mailto:cbenham@adam.com.au a écrit :

Kevin,

I didn't comment earlier on your "idea 2".

If there no "disapproved rankings" (i.e. if the voters all approve the
candidates they rank above bottom),
then your suggested method is simply normal  Winning Votes, which I
don't like because the winner can
be uncovered and positionally dominant or pairwise-beaten and
positionally dominated by a single other
candidate.

On top of that I don't think it really fills the bill as "simple". 
Approval Margins (using Sort or Smith//MinMax
or equivalent or almost equivalent algorithm) would be no more complex
and in my opinion would be better.

I would also prefer the still more simple Smith//Approval.

What did you think of my suggestion for a way to implement your idea 1?

Chris

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Kevin,

So to be clear the possible "complaint" some voters might have (and you
think we should take seriously) is "We lied and the voting method
(instead of somehow reading our minds) believed us".

So therefore it is good to have a less expressive ballot because that
reduces the voter's opportunities to tell stupid lies and if the method
is simple enough then maybe also the temptation for them to do so.

To me that is absurd. If I agreed with that idea I would forget about the
Condorcet criterion and instead demand a method that meets
Later-no-Help,  such as  IRV or Bucklin or Approval.

But I've thought of a patch to address your issue.  We could have a rule
which says that if the winner's approval score is below some fixed
fraction of that of the most approved candidate, then a second-round
runoff is triggered between those two candidates.  What do you
think of that?  What do you think that fraction should be?

Chris

On 10/06/2019 9:57 am, Kevin Venzke wrote:

Hi Chris,

only backfire when Y is made the CW.

Because I think if voters decide to attempt to prevent another candidate
from being CW, via insincerity, there should be risks to doing that. Of
course there is already some risk. But if you "knew" that a given candidate
had no chance of being CW then there would be nothing to lose in using that
candidate in a burial strategy.

For either a successful burial strategy, or one that backfires and elects
an arbitrary candidate, I think the possible complaints are clear. Maybe
someone would argue that a backfiring strategy proves the method's
incentives are just fine. But that wouldn't be how I see it. I think if, in
actual practice, it ever happens that voters calculate that a strategy is
worthwhile, and it completely backfires to the point that everyone would
like the results discarded, then that method will probably get repealed.

arguably you are not even trying to elect the sincere CW.

Condorcet-ish.

Not an unfair statement. If you require voters to have that much
expressiveness then you can't use implicit.

To me, the motivation for three-slot C//A(implicit) is partly about
burial, partly about method simplicity, partly about ballot simplicity.
C//A(explicit) retains 1 of 3. (Arguably slightly less for the Smith
version.) Possibly it has its own merits, but they will largely be
different ones.

of the reasons why Approval seems to be a lot less popular than IRV.

I have no inherent complaints about the ballot format of explicit
approval plus full ranking.

Kevin

Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham cbenham@adam.com.au
cbenham@adam.com.au a écrit :

Kevin,

Specifically should "positional dominance" have the same meaning whether
or not the method has approval in it?

If the voters all choose to approve all the candidates they rank, then
yes.  (For a while I was wrongly assuming that Forest's suggested
default approval was for all ranked-above-bottom candidates, but then I
noticed that he specified that it was only for top voted candidates).

One of my tired examples:

25: A>B
26: B>C
23: C>A
26: C

Assuming all the ranked candidates are approved, C is by far the most
approved and the most top-voted candidate.
Normal Winning Votes (and your idea 2 in this example) elect B.

I will go easy on these methods over failing MD, because it happens when
some of the majority don't approve their common candidate.

For me this this type of ballot avoids the Minimal Defense versus Chicken
Dilemma dilemma, rendering those criteria inapplicable.

48: A
27: B>C
25: C

The problem has been that we don't know whether the B>C voters are
thinking "I am ranking C because above all I don't want that evil A
to win" or  "My C>A preference isn't all that strong, and I think that my
favourite could well be the sincere CW, and if  C's supporters rank
B above A then B has a good chance to win. But if they if they create a
cycle by truncating I'm not having them steal it".

With the voters able to express explicit approval we no longer have to
guess which it is.

I don't think it's ideal if burying X under Y (both disapproved) can only
backfire when Y is made the CW.

Why is that?  The post-election complaint (by any of the voters) would be
.. what?

If you don't allow voters to rank among their unapproved candidates then
arguably you are not even trying to elect the sincere CW.
Instead you are just modifying Approval to make it a lot more
Condorcet-ish.

A lot of voters like relatively expressive ballots. I think that is one of
the reasons why Approval seems to be a lot less popular than IRV.

Chris Benham

On 6/06/2019 5:34 pm, Kevin Venzke wrote:

Hi Chris,

I've been short on time so I don't actually have much thought on any of
the methods, even my own.

I suppose Idea 2 is the same as Schwartz-limited MinMax(WV) if nobody
submits disapproved rankings. I'm not sure if it makes sense to reject the
method over that. Specifically should "positional dominance" have the same
meaning whether or not the method has approval in it? As a comparison, I
will go easy on these methods over failing MD, because it happens when some
of the majority don't approve their common candidate.

I would have liked to simplify Idea 2, but actually Forest's eventual
proposal wasn't all that simple either. As I wrote, if you add "elect a CW
if there is one" it can become much simpler, so that it isn't really
distinct from Idea 1. I actually tried pretty hard to present three "Ideas"
in that post, but kept having that problem.

I posted those ideas because I thought Forest posed an interesting
challenge, and I thought I perceived that he was trying to fix a problem
with CD. That said, I am not a fan of Smith//Approval(explicit). If all
these methods are basically the same then I probably won't end up liking
any of them. I don't think it's ideal if burying X under Y (both
disapproved) can only backfire when Y is made the CW.

Kevin

Le mercredi 5 juin 2019 à 21:26:23 UTC−5, C.Benham cbenham@adam.com.au
cbenham@adam.com.au a écrit :

Kevin,

I didn't comment earlier on your "idea 2".

If there no "disapproved rankings" (i.e. if the voters all approve the
candidates they rank above bottom),
then your suggested method is simply normal  Winning Votes, which I don't
like because the winner can
be uncovered and positionally dominant or pairwise-beaten and positionally
dominated by a single other
candidate.

On top of that I don't think it really fills the bill as "simple".
Approval Margins (using Sort or Smith//MinMax
or equivalent or almost equivalent algorithm) would be no more complex and
in my opinion would be better.

I would also prefer the still more simple Smith//Approval.

What did you think of my suggestion for a way to implement your idea 1?

Chris

Kevin Venzke stepjak at yahoo.fr
<election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C1931864740.14928463.1559418507456%40mail.yahoo.com%3E>
Sat Jun 1 12:48:27 PDT 2019

Hi Forest,

I had two ideas.

Idea 1:

1. If there is a CW using all rankings, elect the CW.
2. Otherwise flatten/discard all disapproved rankings.
3. Use any method that would elect C in scenario 2. (Approval, Bucklin,
   MinMax(WV).)

So scenario 1 has no CW. The disapproved C>A rankings are dropped. A wins
any method.
In scenario 2 there is no CW but nothing is dropped, so use a method that
picks C.
In both versions of scenario 3 there is a CW, B.

If step 3 is Approval then of course step 2 is unnecessary.

In place of step 1 you could find and apply the majority-strength solid
coalitions (using all rankings)
to disqualify A, instead of acting based on B being a CW. I'm not sure if
there's another elegant way
to identify the majority coalition.

Idea 2:

1. Using all rankings, find the strength of everyone's worst WV defeat. (A
   CW scores 0.)
2. Say that candidate X has a "double beatpath" to Y if X has a standard
   beatpath to Y regardless
   of whether the disapproved rankings are counted. (I don't know if it needs
   to be the same beatpath,
   but it shouldn't come into play with these scenarios.)
3. Disqualify from winning any candidate who is not in the Schwartz set
   calculated using double
   beatpaths. In other words, for every candidate Y where there exists a
   candidate X such that X has a
   double beatpath to Y and Y does not have a double beatpath to X, then Y is
   disqualified.
4. Elect the remaining candidate with the mildest WV defeat calculated
   earlier.

So in scenario 1, A always has a beatpath to the other candidates, no
matter whether disapproved
rankings are counted. The other candidates only have a beatpath to A when
the C>A win exists. So
A has a double beatpath to B and C, and they have no path butt. This
leaves A as the only candidate
not disqualified.

In scenario 2, the defeat scores from weakest to strongest are B>C, A>B,
C>A. Every candidate has
a beatpath to every other candidate no matter whether the (nonexistent)
disapproved rankings are
counted. So no candidate is disqualified. C has the best defeat score and
wins.

In scenario 3, the first version: B has no losses. C's loss to B is weaker
than both of A's losses. B
beats C pairwise no matter what, so B has a double beatpath to C. However
C has no such beatpath
to A, nor has A one to B, nor has B one to A. The resulting Schwartz set
disqualifies only C. (C needs
to return B's double beatpath but can't, and neither A nor B has a double
beatpath to the other.)
Between A and B, B's score (as CW) is 0, so he wins.

Scenario 3, second version: B again has no losses, and also has double
beatpaths to both of A and
C, neither of whom have double beatpaths butt. So A and C are disqualified
and B wins.

I must note that this is actually a Condorcet method, since a CW could
never get disqualified and
would always have the best worst defeat. That observation would simplify
the explanation of
scenario 3.

I needed the defeat strength rule because I had no way to give the win to
B over A in scenario 3
version 1. But I guess if it's a Condorcet rule in any case, we can just
add that as a rule, and greatly
simplify it to the point where it's going to look very much like idea 1. I
guess all my ideas lead me to
the same place with this question.

Oh well, I think the ideas are interesting enough to post.

Kevin

pcc.edu> a écrit :

consequence of these constraints is that in all three profiles below the
cycle >A>B>C>A will obtain.

I don't want to prejudice your creative efforts with too many ideas.

itself against a "chicken" attack (truncation of B) from the C faction.

of Chicken is not going to work for them, the sincere CW is elected.

against the A faction's potential truncation attack.

obvious one is Smith\Approval where the voters have

with default approval as top rank only. The other

almost always electing from Smith.

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Why is that?  

Hi Chris,

Le dimanche 9 juin 2019 à 21:20:34 UTC−5, C.Benham
cbenham@adam.com.au a écrit :

you think we should take seriously) is "We lied

A burial strategy has two scenarios that could give rise to a
complaint. One is where burial succeeds. In that case the voters who
complain aren't the ones who buried. The other scenario is where
burial backfires. In that case it is, I guess, possible that actually
all voters were using burial. So you may argue that they don't have
a valid complaint. But implicit to my concerns is the premise that the
voters are behaving rationally under the incentives of the method. If
a method produces arbitrary results given rational voters then it will
be hard to retain it. I think if it happens even once it will be a
problem.

reduces the voter's opportunities to tell stupid

You're making it sound as though a simpler ballot just tricks people
into not lying. Expressiveness isn't the point. The reason three-slot
C//A (or implicit etc.) deters burial is that there is far more risk
in trying it. It is highly likely to backfire no matter what other
voters do. "Low expressiveness" of the ballot doesn't guarantee this
and isn't a prerequisite for it either.

rule which says that if the winner's approval

runoff is triggered between those two

I think there is some confusion here between what my issue is, and the
voter complaints you asked about. While I think voters will be unhappy
with a ruined election, ruining it is what reduces the burial
incentive. If the risk outweighs the benefit then people won't do it.
(That's an assumption.) This patch seems to remove the risk while
leaving the benefit unchanged. Burial will ultimately do nothing,
except to sometimes move the win from the CW to the AW. But that makes
the potential gain even clearer: If the voted CW turns out to not be
your candidate, you would have had a second chance at the win by
voting instead to deny CW status to that candidate. If the voted CW
is your candidate, then you're no worse off for using burial.

Kevin

On 10/06/2019 9:57 am, Kevin Venzke wrote:
Hi Chris,

Because I think if voters decide to attempt to prevent another
candidate from being CW, via insincerity, there should be risks to
doing that. Of course there is already some risk. But if you "knew"
that a given candidate had no chance of being CW then there would be
nothing to lose in using that candidate in a burial strategy.

For either a successful burial strategy, or one that backfires and
elects an arbitrary candidate, I think the possible complaints are
clear. Maybe someone would argue that a backfiring strategy proves the
method's incentives are just fine. But that wouldn't be how I see it.
I think if, in actual practice, it ever happens that voters calculate
that a strategy is worthwhile, and it completely backfires to the
point that everyone would like the results discarded, then that method
will probably get repealed.

are not even trying to elect the sincere CW.

Not an unfair statement. If you require voters to have that much
expressiveness then you can't use implicit.

To me, the motivation for three-slot C//A(implicit) is partly about
burial, partly about method simplicity, partly about ballot
simplicity. C//A(explicit) retains 1 of 3. (Arguably slightly less for
the Smith version.) Possibly it has its own merits, but they will
largely be different ones.

Approval seems to be a lot less popular than IRV.

I have no inherent complaints about the ballot format of explicit
approval plus full ranking.

Kevin

Le jeudi 6 juin 2019 à 21:03:19 UTC−5, C.Benham cbenham@adam.com.au
mailto:cbenham@adam.com.au a écrit :

Kevin,

If the voters all choose to approve all the candidates they rank, then
yes.  (For a while I was wrongly assuming that Forest's suggested
default approval was for all ranked-above-bottom candidates, but then
I noticed that he specified that it was only for top voted candidates).

One of my tired examples:

25: A>B
26: B>C
23: C>A
26: C

Assuming all the ranked candidates are approved, C is by far the most
approved and the most top-voted candidate.
Normal Winning Votes (and your idea 2 in this example) elect B.

For me this this type of ballot avoids the Minimal Defense versus
Chicken Dilemma dilemma, rendering those criteria inapplicable.

48: A
27: B>C
25: C

The problem has been that we don't know whether the B>C voters are
thinking "I am ranking C because above all I don't want that evil A
to win" or  "My C>A preference isn't all that strong, and I think that
my favourite could well be the sincere CW, and if  C's supporters rank
B above A then B has a good chance to win. But if they if they create
a cycle by truncating I'm not having them steal it".

With the voters able to express explicit approval we no longer have to
guess which it is.

Why is that?  The post-election complaint (by any of the voters) would
be .. what?

If you don't allow voters to rank among their unapproved candidates
then arguably you are not even trying to elect the sincere CW.
Instead you are just modifying Approval to make it a lot more
Condorcet-ish.

A lot of voters like relatively expressive ballots. I think that is
one of the reasons why Approval seems to be a lot less popular than IRV.

Chris Benham

On 6/06/2019 5:34 pm, Kevin Venzke wrote:
Hi Chris,

I've been short on time so I don't actually have much thought on any
of the methods, even my own.

I suppose Idea 2 is the same as Schwartz-limited MinMax(WV) if nobody
submits disapproved rankings. I'm not sure if it makes sense to reject
the method over that. Specifically should "positional dominance" have
the same meaning whether or not the method has approval in it? As a
comparison, I will go easy on these methods over failing MD, because
it happens when some of the majority don't approve their common candidate.

I would have liked to simplify Idea 2, but actually Forest's eventual
proposal wasn't all that simple either. As I wrote, if you add "elect
a CW if there is one" it can become much simpler, so that it isn't
really distinct from Idea 1. I actually tried pretty hard to present
three "Ideas" in that post, but kept having that problem.

I posted those ideas because I thought Forest posed an interesting
challenge, and I thought I perceived that he was trying to fix a
problem with CD. That said, I am not a fan of
Smith//Approval(explicit). If all these methods are basically the same
then I probably won't end up liking any of them. I don't think it's
ideal if burying X under Y (both disapproved) can only backfire when Y
is made the CW.

Kevin

Le mercredi 5 juin 2019 à 21:26:23 UTC−5, C.Benham
cbenham@adam.com.au mailto:cbenham@adam.com.au a écrit :

Kevin,

I didn't comment earlier on your "idea 2".

If there no "disapproved rankings" (i.e. if the voters all approve the
candidates they rank above bottom),
then your suggested method is simply normal  Winning Votes, which I
don't like because the winner can
be uncovered and positionally dominant or pairwise-beaten and
positionally dominated by a single other
candidate.

On top of that I don't think it really fills the bill as "simple". 
Approval Margins (using Sort or Smith//MinMax
or equivalent or almost equivalent algorithm) would be no more complex
and in my opinion would be better.

I would also prefer the still more simple Smith//Approval.

What did you think of my suggestion for a way to implement your idea 1?

Chris