[EM] What are some simple methods that accomplish the following conditions?

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[EM] What are some simple methods that accomplish the following conditions?

C.Benham
Kevin,

As something fairly simple I think I like this version of your "Idea 1":

1. If there is a CW using all rankings, elect the CW.

2. Otherwise flatten/discard all disapproved rankings.

3. If there is a "CW" based on the remaining rankings (i.e. the rankings among approved plus approved over not approved)
then elect that candidate.

4. Otherwise elect the most approved candidate.

That strikes me as something not too hard to explain or sell.

Chris Benham

Kevin Venzke [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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[EM] What are some simple methods that accomplish the following conditions?

C.Benham

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 [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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Re: [EM] What are some simple methods that accomplish the following conditions?

Kevin Venzke
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 <[hidden email]> 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 [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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Re: [EM] What are some simple methods that accomplish the following conditions?

C.Benham

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 [hidden email] 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 [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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Re: [EM] What are some simple methods that accomplish the following conditions?

Kevin Venzke
Hi Chris,

>>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?  

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.

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

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.

>
>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.  

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.

>
>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.

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 <[hidden email]> 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 [hidden email] 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 [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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Re: [EM] What are some simple methods that accomplish the following conditions?

C.Benham

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,

>>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?  

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.

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

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.

>
>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.  

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.

>
>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.

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 [hidden email] 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 [hidden email] 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 [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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Re: [EM] What are some simple methods that accomplish the following conditions?

John
I've suggested larger electoral systems for this.

If you use Single Transferable Vote for a nonpartisan blanket Primary Election to get down to somewhere between 5 and 9 (I think 7 may be better than 5), then Tideman's Alternative as a Condorcet system, you get a pretty reliable result.

Consider the two-party oligarchy problem:  30% of voters vote D, 24% vote C, the parties are {A,B} and {C,D}.  If A>B>C>D for an {A} voter, then C is your Condorcet winner:

30%:  D>C>B>A
24%: C>D>B>A
46%:  {A,B}>C>D

24% + 46% consider C>D.  There's no marginal utility for C voters to vote D>C as a way to band together and prevent a loss.

Now, the 30% can vote D>A>C>B, under the theory that A is the Condorcet loser.  A few outcomes:

1.  An A vs. C pair where A defeats C creates a full cycle (A>C>{D,B}, D>A, Smith set is all candidates).  We're looking at 23% give or take for each of A and B, so the cycle will break in the runoff iteration, and C still wins even with all 30% voting D>C.
2.  If 32% and 22% instead of 30% and 24% for {C,D} voters, then this huge 32% plurality can indeed defeat C.  If just 4% of C voters defect and decide that D is f*$%ing crazy and their vote is C>B>D>A (because A is worse, to them)—and this is highly-likely, as we all well know and have seen in real elections—then D voters just elected B, who is worse from their perspective.

This tampering doesn't likely elect D, but rather pushes the winner farther toward A.  The distortion from the other side also doesn't work, although it might be possible for 21% A>B>C>D voters to rank A>D>B>C and elect D (also a worse outcome).

Pretty much only D and A have any utility voting as such.  C and B voters would be best off voting honestly, e.g. C>D>B or C>B>D.  Changing your first choice is always weakening your first choice.

With a span of 7, you have {A,B,C,D,E,F,G} at roughly 14% of the vote.  The impact of these groups and the usefulness or utility of tactical voting falls away, so these failures simply stop happening.  Don't use group voting tickets.

This proportional NPBP, Condorcet Election has a few other interesting properties, notably due to vote impact.

Imagine of the 7, {C,D,E} being centered around {D} (the natural Condorcet candidate), D defeats all other candidates, while E defeats all candidates except D.  E loses to D by 10%.  If E can get out 10% more voters—out of the whole election, not just 10% more E voters—then E can win.  That's pretty heavy.

Likewise, social media propaganda has to make some major shifts.  It can't change the winner to A or G or even E.  The change in ballots is immense and complex and nonsense.  This system resists such propaganda.

On the other hand, CHANGING a vote is two votes.  If D offends A voters who vote A>B>C>D>E, then A voters will change their vote to A>B>C>E>D.  That's -1 D, +1 E—it's 2 votes.  Just a 5% movement here will switch the winner from D to the substantially-similar E, even though the only people who switched their votes were fringe voters who are nowhere near the base for D and E.

This is more-sensitive with 7 candidates.  It does require voters to rank so many candidates, and voters typically rank to six in practice (according to Fair Vote).  If they tend to rank to three, then e.g. B>C>D and F>E>D votes form the edges, and we have likely enough of those (A and G voters are 2/7, then half of B and F voters makes 3/7, leaving 71% of voters who likely explicitly rank the Condorcet candidate) to accurately locate the Condorcet candidate.  I worry about 9 or 11 or 15 because it'll break.

Think in terms of larger electoral systems.  Think in terms of how many candidates and the distribution of first-choice voters, and in terms of engineering an election cycle to create the conditions which protect your election from such failures.  You will not find one voting rule to rule them all:  when 9 people show up from one party, 5 show up from another, 3 small parties send a candidate, and you have 2 independents, any single-winner method will bluntly fail.  You need a primary election.

On Sun, Jun 9, 2019 at 10:20 PM C.Benham <[hidden email]> wrote:

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,

>>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?  

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.

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

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.

>
>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.  

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.

>
>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.

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 [hidden email] 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 [hidden email] 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 [hidden email]
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

>Le jeudi 30 mai 2019 à 17:32:42 UTC−5, Forest Simmons <fsimmons at pcc.edu> a écrit :
>
>In the example profiles below 100 = P+Q+R, and  50>P>Q>R>0.  One consequence of these constraints is that in all three profiles below the cycle >A>B>C>A will obtain.
>
>I am interested in simple methods that always ...
>
>(1) elect candidate A given the following profile:
>
>P: A
>Q: B>>C
>R: C,
>and
>(2) elect candidate C given
>P: A
>Q: B>C>>
>R: C,
>and
>(3) elect candidate B given

>
>P: A
>Q: B>>C  (or B>C)
>R: C>>B. (or C>B)
>
>I have two such methods in mind, and I'll tell you one of them below, but I don't want to prejudice your creative efforts with too many ideas.
>
>Here's the rationale for the requirements:
>
>Condition (1) is needed so that when the sincere preferences are

>
>P: A
>Q: B>C
>R: C>B,
>the B faction (by merely disapproving C without truncation) can defend itself against a "chicken" attack (truncation of B) from the C faction.
>
>Condition (3) is needed so that when the C faction realizes that the game of Chicken is not going to work for them, the sincere CW is elected.
>
>Condition (2) is needed so that when  sincere preferences are

>
>P: A>C
>Q: B>C
>R: C>A,
>then the C faction (by proactively truncating A) can defend the CW against the A faction's potential truncation attack.
>
>Like I said, I have a couple of fairly simple methods in mind. The most obvious one is Smith\\Approval where the voters have
>control over their own approval cutoffs (as opposed to implicit approval) with default approval as top rank only. The other
>method I have in mind is not quite as
>simple, but it has the added advantage of satisfying the FBC, while almost always electing from Smith.








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Re: [EM] What are some simple methods that accomplish the following conditions?

Kevin Venzke
In reply to this post by C.Benham
Hi Chris,

Le dimanche 9 juin 2019 à 21:20:34 UTC−5, C.Benham <[hidden email]> a écrit :
>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".

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.

>
>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.

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.

>
>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?

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,

>>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?  

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.

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

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.

>
>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.  

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.

>
>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.

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 [hidden email] 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 [hidden email] 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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Re: [EM] What are some simple methods that accomplish the following conditions?

C.Benham

Kevin,

When I wrote my last message I was probably under-estimating the chance of the burial strategy
succeeding even when all those who prefer the target candidate to the buriers' candidate place
their approval cutoffs between them.  So I only had in mind the scenario where two big factions
both use (rank but not approve) the same presumed sure loser to bury against each other.

You didn't address my question as how big you think that fraction should be. Forest suggested it
should only be 1/2.

I still think that the chance that burial strategy will either succeed or disastrously backfire is very
small.  My idea is to have the runoff triggered only in very bad situations which might otherwise
have people calling for the method to be scrapped, so that buriers don't often have an easy option
to repair the damage caused by their strategy backfiring.

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.

Only if the voted CW is less than half as approved as the AW and only if the AW is your candidate, plus you have the "penalty" of having to vote again.

Chris Benham

On 12/06/2019 10:00 am, Kevin Venzke wrote:
Hi Chris,

Le dimanche 9 juin 2019 à 21:20:34 UTC−5, C.Benham [hidden email] a écrit :
>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".
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.

>
>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.

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.

>
>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?

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,

>>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?  

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.

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

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.

>
>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.  

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.

>
>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.

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 [hidden email] 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 [hidden email] 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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