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TS

Ted Stern

Mon, Jun 3, 2019 9:42 PM

Hi Chris,

You are so close to Relevant Ratings in your proposal. I just want to
point out how close and why the one missing factor is important.

You write:

My idea (originally my misunderstanding of Ted's Relevant Ratings method)
is that if at some (quasi-Bucklin) IBIFA round after the first (but before
we have reached just counting total approval scores) we find more than one
candidate Q qualified to win then instead of (Bucklin-like) giving the win
to the Q with the highest score in that round we elect the Q with the
highest score in the round before.

Where this differs from RR is as follows:

For each candidate Q qualified to win IBIFA, their total ballots from
highest rating down to the current round rating exceed some highest total
approval on complementary ballots excluding Q down to that rating. Say
that the highest total approval on such complementary ballots is TC.
Your modified IBIFA just looks at the Q totals from the previous round.
My Relevant Ratings method looks only at the previous round Q totals
that are larger than their respective TC opposition in the current
round!

In most situations, the Q you find with your modified IBIFA would be the
same. But it is possible that they might not be. Let's carefully
construct a 4 slot example, working backwards:

Say we want at least 3 candidates, ratings 3 = Excellent ("A"), 2 = Very
Good ("B"), 1 = OK ("C"), 0 = disapproved ("D").

round 1 totals (scores at 3) of A48, B49, with other candidates below
that (and not qualifying in any method)
round 2 totals (scores at 2 and above) of A52, B51, with other
candidates below that (and not qualifying in any method)
round 3 totals (scores above 0) of A52, B52, and C > 54, with other
candidates below that (only C qualifying under MCA or MJ)
In round 1, we want A48's most approved complementary candidate to be
B or C with at least 49
In round 1, we want B49's most approved complementary candidate to be
A or C with at least 50
In round 2, we want A52's most approved complementary candidate to be
C with at most 47
In round 2, we want B51's most approved complementary candidate to be
C with exactly 50.
We want A and B's total approval to be less than 50%, so there must be
at least 105 ballots. So we expect at least 5 irrelevant ballots.

Under this scenario, C will win both MCA and MJ in round 3. B will win in
modified IBIFA, as round 2 qualifier with the highest round 1 score.

But A will win both original IBIFA and relevant rating because while both A
and B qualify in round 2, only A's round 1 score exceeds A's round 2
complementary approval winner C's approval of 47, while B's round 2 score
of 49 is below B's complementary approval winner C's score of 50.

Here is a set of ballots that I think satisfies those constraints.

02: A > B > C
24: A > D > C
22: A > E > C
04: B > F > C
25: B > F > C
21: B > G > C
02: E > D=A > C
02: F > E=A > H
06: G > F > H

Round 1: A48 vs complementary approval winner C with 51, B49 vs
complementary approval winner C with 50. Neither qualifies
Round 2: A52 vs complementary approval winner C with 47, B51 vs
complementary approval winner C with 48. Both qualify in IBIFA-derived
methods, but not in MCA or MJ with less than 50% of ballots
Round 3: C99 passes 50% threshold, while A and B still less than 50%
threshold for tiebreaker.

A52 pairwise beats B51 and is the Condorcet winner (Please check my
arithmetic!)

The main point here is that while both IBIFA, modified IBIFA and Relevant
Ratings can avoid electing a non-CW candidate C, the lowest level
compromise approval winner elected by standard median ratings, your
modified IBIFA will fail to choose the CW while relevant ratings and
original IBIFA will find that candidate.

You suggestion of using undefeated tied-at-top winner first, then falling
back to some IBI method, is an interesting one, however.

On Sun, Jun 2, 2019 at 8:16 PM Chris Benham cbenhamau@yahoo.com.au
[RangeVoting] RangeVoting@yahoogroups.com wrote:

IBIFA was conceived as an Irrelevant Ballot independent version of
Bucklin, with the added benefits of having a less
severe truncation and/or compress at the top incentive and also being
much more (and absolutely more) Condorcet-consistent.

Inspired by an example from Ted Stern of?? his "Relevant Ratings" method
(which I gather is IBIFA
modified to more closely resemble Majority Judgement), I've come to
believe that if ratings ballots
with four or more slots (or grades) are used then a simple rule change
can make the method still
more Condorcet-consistent?? at no cost.

My idea (originally my misunderstanding of Ted's Relevant Ratings
method) is that if at some
(quasi-Bucklin) IBIFA round after the first (but before we have reached
just counting total approval scores)
we find more than one candidate Q qualified to win then instead of??
(Bucklin-like) giving the win to the Q
with the highest score in that round we elect the Q with the highest
score in the round before.

A link to the electowiki entry on my original version of IBIFA:

https://wiki.electorama.com/wiki/IBIFA

And the EM post in which I first suggested it:

http://lists.electorama.com/pipermail/election-methods-electorama.com//2010-May/091807.html

Here is the description of the revised 4-slot version, referring to
A-B-C-D grading ballots:

*Voters fill out 4-slot ratings ballots, say with A B C D grades.
??Default rating/grade is D, signifying least preferred and unapproved.

Any grade above D is interpreted as Approval.

If any candidate/s X has an A score that is higher than any other
candidate's approval
score on ballots that?? don't give X an A grade, elect the X with the
highest A score.

Otherwise, if any candidate/s X has a A+B score that is higher than any
other candidate's
approval score on ballots that don't give X an A or B grade, elect the X
with the highest
??A score.

Otherwise, elect the candidate with the highest Approval score.*

??35: A
??10: A=B
??30: B>C
??25: C

With my Condorcet hat on, in this example I've said that B is the
weakest candidate.?? A bit unfortunately
IBIFA here elects B, but FBC is a bit more "expensive" than Condorcet,
and so does Winning Votes and Margins.
Bucklin elects the most approved candidate C, but at least B both
pairwise beats and is more top-rated than C.

Ted Stern's eye-opening example:

49: A > B
03: B > A > C
10: D > B > C
38: E > F > C
05: G > D > H

The Condorcet winner is A.?? Ted's Relevant Ratings and my revised 4+
slot IBIFA elect A.
My original version of IBIFA?? and?? Median Ratings methods such as
Bucklin and MJ elect B.

Top Ratings (A) scores:?? A49,?? E38,?? D10,?? G5,?? B3,?? C0
A + B scores:???????????????????????????????????? A51,?? E38,?? D15,??
G5,?? B62,?? C0

In the second round A and B both "qualify".???? On ballots that don't??
give A one of the two
top grades the most approved candidate is E with a score of 38, lower
than 51 so A qualifies.

On ballots that don't give B one of the top two grades the most approved
candidate is again
E with again a score of 38, lower than 62 so B qualifies. In the "round
before" A?? has the
higher score (49 versus 3) so revised IBIFA gives the win to A.

A>B 49-13,???? A>E 51-38,?? A>D 51-15,?? A>G 51>5, A>C?? 51-48.

At the cost of being a quite a bit more complicated,?? IBIFA can be
combined?? with Kevin Venzke's
special "tied-at-the-top" rule used in his "Improved Condorcet Approval"
method to make
the method even more Condorcet-consistent?? (possibly as much as it
possible for a FBC method
to be).
https://wiki.electorama.com/wiki/Improved_Condorcet_Approval

If one candidate T pairwise beats all others by the tied-at-the-top
rule then T wins. If there is no
such T then we elect the (revised) IBIFA winner.
If there is more than one T then we elect the one that "qualifies"
(according to IBIFA) in the earliest
IBIFA round. If there is more than one of these, then elect the one with
the highest score in the previous
round if there was one, otherwise simply with the highest top-ratings
score.

4: A>B
6: A>C
6: B>A
2: B>C
3: C>B

B is the narrow Condorcet winner:?? B>A 11-10,?? B>C?? 12-9. No ballots
have any candidates tied at the top,
so B wins.?? Plain IBIFA elects A, which is positionally dominant: Top
scores: A10, B8, C2. Approval scores: A16,?? B13,?? C10.

For the time being the name I suggest?? for?? this is Quasi-Condorcet
IBIFA.

Chris Benham

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Hi Chris, You are *so* close to Relevant Ratings in your proposal. I just want to point out how close and why the one missing factor is important. You write: > My idea (originally my misunderstanding of Ted's Relevant Ratings method) > is that if at some (quasi-Bucklin) IBIFA round after the first (but before > we have reached just counting total approval scores) we find more than one > candidate Q qualified to win then instead of (Bucklin-like) giving the win > to the Q with the highest score in that round we elect the Q with the > highest score in the round before. Where this differs from RR is as follows: - For each candidate Q qualified to win IBIFA, their total ballots from highest rating down to the current round rating exceed some highest total approval on complementary ballots excluding Q down to that rating. Say that the highest total approval on such complementary ballots is TC. - Your modified IBIFA just looks at the Q totals from the previous round. - My Relevant Ratings method looks only at the previous round Q totals that are larger than their respective TC opposition *in the current round!* In most situations, the Q you find with your modified IBIFA would be the same. But it is possible that they might not be. Let's carefully construct a 4 slot example, working backwards: Say we want at least 3 candidates, ratings 3 = Excellent ("A"), 2 = Very Good ("B"), 1 = OK ("C"), 0 = disapproved ("D"). - round 1 totals (scores at 3) of A48, B49, with other candidates below that (and not qualifying in any method) - round 2 totals (scores at 2 and above) of A52, B51, with other candidates below that (and not qualifying in any method) - round 3 totals (scores above 0) of A52, B52, and C > 54, with other candidates below that (only C qualifying under MCA or MJ) - In round 1, we want A48's most approved complementary candidate to be B or C with at least 49 - In round 1, we want B49's most approved complementary candidate to be A or C with at least 50 - In round 2, we want A52's most approved complementary candidate to be C with at most 47 - In round 2, we want B51's most approved complementary candidate to be C with exactly 50. - We want A and B's total approval to be less than 50%, so there must be at least 105 ballots. So we expect at least 5 irrelevant ballots. Under this scenario, C will win both MCA and MJ in round 3. B will win in modified IBIFA, as round 2 qualifier with the highest round 1 score. But A will win both original IBIFA and relevant rating because while both A and B qualify in round 2, only A's round 1 score exceeds A's round 2 complementary approval winner C's approval of 47, while B's round 2 score of 49 is below B's complementary approval winner C's score of 50. Here is a set of ballots that I think satisfies those constraints. 02: A > B > C 24: A > D > C 22: A > E > C 04: B > F > C 25: B > F > C 21: B > G > C 02: E > D=A > C 02: F > E=A > H 06: G > F > H Round 1: A48 vs complementary approval winner C with 51, B49 vs complementary approval winner C with 50. Neither qualifies Round 2: A52 vs complementary approval winner C with 47, B51 vs complementary approval winner C with 48. Both qualify in IBIFA-derived methods, but not in MCA or MJ with less than 50% of ballots Round 3: C99 passes 50% threshold, while A and B still less than 50% threshold for tiebreaker. A52 pairwise beats B51 and is the Condorcet winner (Please check my arithmetic!) The main point here is that while both IBIFA, modified IBIFA and Relevant Ratings can avoid electing a non-CW candidate C, the lowest level compromise approval winner elected by standard median ratings, your modified IBIFA will fail to choose the CW while relevant ratings and original IBIFA will find that candidate. You suggestion of using undefeated tied-at-top winner first, then falling back to some IBI method, is an interesting one, however. On Sun, Jun 2, 2019 at 8:16 PM Chris Benham cbenhamau@yahoo.com.au [RangeVoting] <RangeVoting@yahoogroups.com> wrote: > > IBIFA was conceived as an Irrelevant Ballot independent version of > Bucklin, with the added benefits of having a less > severe truncation and/or compress at the top incentive and also being > much more (and absolutely more) Condorcet-consistent. > > Inspired by an example from Ted Stern of?? his "Relevant Ratings" method > (which I gather is IBIFA > modified to more closely resemble Majority Judgement), I've come to > believe that if ratings ballots > with four or more slots (or grades) are used then a simple rule change > can make the method still > more Condorcet-consistent?? at no cost. > > My idea (originally my misunderstanding of Ted's Relevant Ratings > method) is that if at some > (quasi-Bucklin) IBIFA round after the first (but before we have reached > just counting total approval scores) > we find more than one candidate Q qualified to win then instead of?? > (Bucklin-like) giving the win to the Q > with the highest score in that round we elect the Q with the highest > score in the round before. > > A link to the electowiki entry on my original version of IBIFA: > > https://wiki.electorama.com/wiki/IBIFA > > And the EM post in which I first suggested it: > > http://lists.electorama.com/pipermail/election-methods-electorama.com//2010-May/091807.html > > Here is the description of the revised 4-slot version, referring to > A-B-C-D grading ballots: > > *Voters fill out 4-slot ratings ballots, say with A B C D grades. > ??Default rating/grade is D, signifying least preferred and unapproved. > > Any grade above D is interpreted as Approval. > > If any candidate/s X has an A score that is higher than any other > candidate's approval > score on ballots that?? don't give X an A grade, elect the X with the > highest A score. > > Otherwise, if any candidate/s X has a A+B score that is higher than any > other candidate's > approval score on ballots that don't give X an A or B grade, elect the X > with the highest > ??A score. > > Otherwise, elect the candidate with the highest Approval score.* > > ??35: A > ??10: A=B > ??30: B>C > ??25: C > > With my Condorcet hat on, in this example I've said that B is the > weakest candidate.?? A bit unfortunately > IBIFA here elects B, but FBC is a bit more "expensive" than Condorcet, > and so does Winning Votes and Margins. > Bucklin elects the most approved candidate C, but at least B both > pairwise beats and is more top-rated than C. > > Ted Stern's eye-opening example: > > 49: A > B > 03: B > A > C > 10: D > B > C > 38: E > F > C > 05: G > D > H > > The Condorcet winner is A.?? Ted's Relevant Ratings and my revised 4+ > slot IBIFA elect A. > My original version of IBIFA?? and?? Median Ratings methods such as > Bucklin and MJ elect B. > > Top Ratings (A) scores:?? A49,?? E38,?? D10,?? G5,?? B3,?? C0 > A + B scores:???????????????????????????????????? A51,?? E38,?? D15,?? > G5,?? B62,?? C0 > > In the second round A and B both "qualify".???? On ballots that don't?? > give A one of the two > top grades the most approved candidate is E with a score of 38, lower > than 51 so A qualifies. > > On ballots that don't give B one of the top two grades the most approved > candidate is again > E with again a score of 38, lower than 62 so B qualifies. In the "round > before" A?? has the > higher score (49 versus 3) so revised IBIFA gives the win to A. > > A>B 49-13,???? A>E 51-38,?? A>D 51-15,?? A>G 51>5, A>C?? 51-48. > > At the cost of being a quite a bit more complicated,?? IBIFA can be > combined?? with Kevin Venzke's > special "tied-at-the-top" rule used in his "Improved Condorcet Approval" > method to make > the method even more Condorcet-consistent?? (possibly as much as it > possible for a FBC method > to be). > https://wiki.electorama.com/wiki/Improved_Condorcet_Approval > > *If one candidate T pairwise beats all others by the tied-at-the-top > rule then T wins. If there is no > such T then we elect the (revised) IBIFA winner. > If there is more than one T then we elect the one that "qualifies" > (according to IBIFA) in the earliest > IBIFA round. If there is more than one of these, then elect the one with > the highest score in the previous > round if there was one, otherwise simply with the highest top-ratings > score.* > > 4: A>B > 6: A>C > 6: B>A > 2: B>C > 3: C>B > > B is the narrow Condorcet winner:?? B>A 11-10,?? B>C?? 12-9. No ballots > have any candidates tied at the top, > so B wins.?? Plain IBIFA elects A, which is positionally dominant: Top > scores: A10, B8, C2. Approval scores: A16,?? B13,?? C10. > > For the time being the name I suggest?? for?? this is Quasi-Condorcet > IBIFA. > > Chris Benham > > > > > > > --- > This email has been checked for viruses by AVG. > https://www.avg.com > > > > ------------------------------------ > Posted by: Chris Benham <cbenhamau@yahoo.com.au> > ------------------------------------ > > > ------------------------------------ > > Yahoo Groups Links > > <*> To visit your group on the web, go to: > http://groups.yahoo.com/group/RangeVoting/ > > <*> Your email settings: > Individual Email | Traditional > > <*> To change settings online go to: > http://groups.yahoo.com/group/RangeVoting/join > (Yahoo! ID required) > > <*> To change settings via email: > RangeVoting-digest@yahoogroups.com > RangeVoting-fullfeatured@yahoogroups.com > > <*> To unsubscribe from this group, send an email to: > RangeVoting-unsubscribe@yahoogroups.com > > <*> Your use of Yahoo Groups is subject to: > https://info.yahoo.com/legal/us/yahoo/utos/terms/ > >

C

C.Benham

Wed, Jun 5, 2019 10:33 PM

Ted,

Why does your example have the "B>F>C" voters divided into two groups?

04: B > F > C
25: B > F > C

Is there a typo?

Chris Benham

On 4/06/2019 7:12 am, Ted Stern wrote:

Hi Chris,

You are /so/ close to Relevant Ratings in your proposal. I just want
to point out how close and why the one missing factor is important.

You write:

 My idea (originally my misunderstanding of Ted's Relevant
 Ratings method) is that if at some (quasi-Bucklin) IBIFA round
 after the first (but before we have reached just counting total
 approval scores) we find more than one candidate Q qualified to
 win then instead of (Bucklin-like) giving the win to the Q with
 the highest score in that round we elect the Q with the highest
 score in the round before.

Where this differs from RR is as follows:

For each candidate Q qualified to win IBIFA, their total ballots
from highest rating down to the current round rating exceed some
highest total approval on complementary ballots excluding Q down
to that rating. Say that the highest total approval on such
complementary ballots is TC.
Your modified IBIFA just looks at the Q totals from the previous
round.
My Relevant Ratings method looks only at the previous round Q
totals that are larger than their respective TC opposition /in the
current round!/

In most situations, the Q you find with your modified IBIFA would be
the same. But it is possible that they might not be. Let's carefully
construct a 4 slot example, working backwards:

Say we want at least 3 candidates, ratings 3 = Excellent ("A"), 2 =
Very Good ("B"), 1 = OK ("C"), 0 = disapproved ("D").

round 1 totals (scores at 3) of A48, B49, with other candidates
below that (and not qualifying in any method)
round 2 totals (scores at 2 and above) of A52, B51, with other
candidates below that (and not qualifying in any method)
round 3 totals (scores above 0) of A52, B52, and C > 54, with
other candidates below that (only C qualifying under MCA or MJ)
In round 1, we want A48's most approved complementary candidate to
be B or C with at least 49
In round 1, we want B49's most approved complementary candidate to
be A or C with at least 50
In round 2, we want A52's most approved complementary candidate to
be C with at most 47
In round 2, we want B51's most approved complementary candidate to
be C with exactly 50.
We want A and B's total approval to be less than 50%, so there
must be at least 105 ballots. So we expect at least 5 irrelevant
ballots.

Under this scenario, C will win both MCA and MJ in round 3. B will
win in modified IBIFA, as round 2 qualifier with the highest round 1
score.

But A will win both original IBIFA and relevant rating because while
both A and B qualify in round 2, only A's round 1 score exceeds A's
round 2 complementary approval winner C's approval of 47, while B's
round 2 score of 49 is below B's complementary approval winner C's
score of 50.

Here is a set of ballots that I think satisfies those constraints.

02: A > B > C
24: A > D > C
22: A > E > C
04: B > F > C
25: B > F > C
21: B > G > C
02: E > D=A > C
02: F > E=A > H
06: G > F > H

Round 1: A48 vs complementary approval winner C with 51, B49 vs
complementary approval winner C with 50. Neither qualifies
Round 2: A52 vs complementary approval winner C with 47, B51 vs
complementary approval winner C with 48. Both qualify in
IBIFA-derived methods, but not in MCA or MJ with less than 50% of ballots
Round 3: C99 passes 50% threshold, while A and B still less than 50%
threshold for tiebreaker.

A52 pairwise beats B51 and is the Condorcet winner (Please check my
arithmetic!)

The main point here is that while both IBIFA, modified IBIFA and
Relevant Ratings can avoid electing a non-CW candidate C, the lowest
level compromise approval winner elected by standard median ratings,
your modified IBIFA will fail to choose the CW while relevant ratings
and original IBIFA will find that candidate.

You suggestion of using undefeated tied-at-top winner first, then
falling back to some IBI method, is an interesting one, however.

On Sun, Jun 2, 2019 at 8:16 PM Chris Benham cbenhamau@yahoo.com.au
mailto:cbenhamau@yahoo.com.au [RangeVoting]
<RangeVoting@yahoogroups.com mailto:RangeVoting@yahoogroups.com> wrote:

 IBIFA was conceived as an Irrelevant Ballot independent version of
 Bucklin, with the added benefits of having a less
 severe truncation and/or compress at the top incentive and also being
 much more (and absolutely more) Condorcet-consistent.

 Inspired by an example from Ted Stern of?? his "Relevant Ratings"
 method
 (which I gather is IBIFA
 modified to more closely resemble Majority Judgement), I've come to
 believe that if ratings ballots
 with four or more slots (or grades) are used then a simple rule
 change
 can make the method still
 more Condorcet-consistent?? at no cost.

 My idea (originally my misunderstanding of Ted's Relevant Ratings
 method) is that if at some
 (quasi-Bucklin) IBIFA round after the first (but before we have
 reached
 just counting total approval scores)
 we find more than one candidate Q qualified to win then instead of??
 (Bucklin-like) giving the win to the Q
 with the highest score in that round we elect the Q with the highest
 score in the round before.

 A link to the electowiki entry on my original version of IBIFA:

 https://wiki.electorama.com/wiki/IBIFA

 And the EM post in which I first suggested it:
 http://lists.electorama.com/pipermail/election-methods-electorama.com//2010-May/091807.html

 Here is the description of the revised 4-slot version, referring to
 A-B-C-D grading ballots:

 *Voters fill out 4-slot ratings ballots, say with A B C D grades.
  ??Default rating/grade is D, signifying least preferred and
 unapproved.

 Any grade above D is interpreted as Approval.

 If any candidate/s X has an A score that is higher than any other
 candidate's approval
 score on ballots that?? don't give X an A grade, elect the X with the
 highest A score.

 Otherwise, if any candidate/s X has a A+B score that is higher
 than any
 other candidate's
 approval score on ballots that don't give X an A or B grade, elect
 the X
 with the highest
  ??A score.

 Otherwise, elect the candidate with the highest Approval score.*

  ??35: A
  ??10: A=B
  ??30: B>C
  ??25: C

 With my Condorcet hat on, in this example I've said that B is the
 weakest candidate.?? A bit unfortunately
 IBIFA here elects B, but FBC is a bit more "expensive" than
 Condorcet,
 and so does Winning Votes and Margins.
 Bucklin elects the most approved candidate C, but at least B both
 pairwise beats and is more top-rated than C.

 Ted Stern's eye-opening example:

 49: A > B
 03: B > A > C
 10: D > B > C
 38: E > F > C
 05: G > D > H

 The Condorcet winner is A.?? Ted's Relevant Ratings and my revised 4+
 slot IBIFA elect A.
 My original version of IBIFA?? and?? Median Ratings methods such as
 Bucklin and MJ elect B.

 Top Ratings (A) scores:?? A49,?? E38,?? D10,?? G5,?? B3,?? C0
 A + B scores:???????????????????????????????????? A51,?? E38,??
 D15,?? G5,?? B62,?? C0

 In the second round A and B both "qualify".???? On ballots that
 don't??
 give A one of the two
 top grades the most approved candidate is E with a score of 38, lower
 than 51 so A qualifies.

 On ballots that don't give B one of the top two grades the most
 approved
 candidate is again
 E with again a score of 38, lower than 62 so B qualifies. In the
 "round
 before" A?? has the
 higher score (49 versus 3) so revised IBIFA gives the win to A.

 A>B 49-13,???? A>E 51-38,?? A>D 51-15,?? A>G 51>5, A>C?? 51-48.

 At the cost of being a quite a bit more complicated,?? IBIFA can be
 combined?? with Kevin Venzke's
 special "tied-at-the-top" rule used in his "Improved Condorcet
 Approval"
 method to make
 the method even more Condorcet-consistent?? (possibly as much as it
 possible for a FBC method
 to be).
 https://wiki.electorama.com/wiki/Improved_Condorcet_Approval

 *If one candidate T pairwise beats all others by the tied-at-the-top
 rule then T wins. If there is no
 such T then we elect the (revised) IBIFA winner.
 If there is more than one T then we elect the one that "qualifies"
 (according to IBIFA) in the earliest
 IBIFA round. If there is more than one of these, then elect the
 one with
 the highest score in the previous
 round if there was one, otherwise simply with the highest top-ratings
 score.*

 4: A>B
 6: A>C
 6: B>A
 2: B>C
 3: C>B

 B is the narrow Condorcet winner:?? B>A 11-10,?? B>C?? 12-9. No
 ballots
 have any candidates tied at the top,
 so B wins.?? Plain IBIFA elects A, which is positionally dominant:
 Top
 scores: A10, B8, C2. Approval scores: A16,?? B13,?? C10.

 For the time being the name I suggest?? for?? this is
 Quasi-Condorcet IBIFA.

 Chris Benham






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 This email has been checked for viruses by AVG.
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 ------------------------------------
 Posted by: Chris Benham <cbenhamau@yahoo.com.au
 <mailto:cbenhamau@yahoo.com.au>>
 ------------------------------------


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Ted, Why does your example have the "B>F>C" voters divided into two groups? > 04: B > F > C > 25: B > F > C Is there a typo? Chris Benham On 4/06/2019 7:12 am, Ted Stern wrote: > Hi Chris, > > You are /so/ close to Relevant Ratings in your proposal. I just want > to point out how close and why the one missing factor is important. > > You write: > > My idea (originally my misunderstanding of Ted's Relevant > Ratings method) is that if at some (quasi-Bucklin) IBIFA round > after the first (but before we have reached just counting total > approval scores) we find more than one candidate Q qualified to > win then instead of (Bucklin-like) giving the win to the Q with > the highest score in that round we elect the Q with the highest > score in the round before. > > > Where this differs from RR is as follows: > > * For each candidate Q qualified to win IBIFA, their total ballots > from highest rating down to the current round rating exceed some > highest total approval on complementary ballots excluding Q down > to that rating. Say that the highest total approval on such > complementary ballots is TC. > * Your modified IBIFA just looks at the Q totals from the previous > round. > * My Relevant Ratings method looks only at the previous round Q > totals that are larger than their respective TC opposition /in the > current round!/ > > In most situations, the Q you find with your modified IBIFA would be > the same. But it is possible that they might not be. Let's carefully > construct a 4 slot example, working backwards: > > Say we want at least 3 candidates, ratings 3 = Excellent ("A"), 2 = > Very Good ("B"), 1 = OK ("C"), 0 = disapproved ("D"). > > * round 1 totals (scores at 3) of A48, B49, with other candidates > below that (and not qualifying in any method) > * round 2 totals (scores at 2 and above) of A52, B51, with other > candidates below that (and not qualifying in any method) > * round 3 totals (scores above 0) of A52, B52, and C > 54, with > other candidates below that (only C qualifying under MCA or MJ) > * In round 1, we want A48's most approved complementary candidate to > be B or C with at least 49 > * In round 1, we want B49's most approved complementary candidate to > be A or C with at least 50 > * In round 2, we want A52's most approved complementary candidate to > be C with at most 47 > * In round 2, we want B51's most approved complementary candidate to > be C with exactly 50. > * We want A and B's total approval to be less than 50%, so there > must be at least 105 ballots. So we expect at least 5 irrelevant > ballots. > > Under this scenario, C will win both MCA and MJ in round 3. B will > win in modified IBIFA, as round 2 qualifier with the highest round 1 > score. > > But A will win both original IBIFA and relevant rating because while > both A and B qualify in round 2, only A's round 1 score exceeds A's > round 2 complementary approval winner C's approval of 47, while B's > round 2 score of 49 is below B's complementary approval winner C's > score of 50. > > Here is a set of ballots that I think satisfies those constraints. > > 02: A > B > C > 24: A > D > C > 22: A > E > C > *04: B > F > C* > *25: B > F > C* > 21: B > G > C > 02: E > D=A > C > 02: F > E=A > H > 06: G > F > H > > Round 1: A48 vs complementary approval winner C with 51, B49 vs > complementary approval winner C with 50. Neither qualifies > Round 2: A52 vs complementary approval winner C with 47, B51 vs > complementary approval winner C with 48. Both qualify in > IBIFA-derived methods, but not in MCA or MJ with less than 50% of ballots > Round 3: C99 passes 50% threshold, while A and B still less than 50% > threshold for tiebreaker. > > A52 pairwise beats B51 and is the Condorcet winner (Please check my > arithmetic!) > > The main point here is that while both IBIFA, modified IBIFA and > Relevant Ratings can avoid electing a non-CW candidate C, the lowest > level compromise approval winner elected by standard median ratings, > your modified IBIFA will fail to choose the CW while relevant ratings > and original IBIFA will find that candidate. > > You suggestion of using undefeated tied-at-top winner first, then > falling back to some IBI method, is an interesting one, however. > > On Sun, Jun 2, 2019 at 8:16 PM Chris Benham cbenhamau@yahoo.com.au > <mailto:cbenhamau@yahoo.com.au> [RangeVoting] > <RangeVoting@yahoogroups.com <mailto:RangeVoting@yahoogroups.com>> wrote: > > > IBIFA was conceived as an Irrelevant Ballot independent version of > Bucklin, with the added benefits of having a less > severe truncation and/or compress at the top incentive and also being > much more (and absolutely more) Condorcet-consistent. > > Inspired by an example from Ted Stern of?? his "Relevant Ratings" > method > (which I gather is IBIFA > modified to more closely resemble Majority Judgement), I've come to > believe that if ratings ballots > with four or more slots (or grades) are used then a simple rule > change > can make the method still > more Condorcet-consistent?? at no cost. > > My idea (originally my misunderstanding of Ted's Relevant Ratings > method) is that if at some > (quasi-Bucklin) IBIFA round after the first (but before we have > reached > just counting total approval scores) > we find more than one candidate Q qualified to win then instead of?? > (Bucklin-like) giving the win to the Q > with the highest score in that round we elect the Q with the highest > score in the round before. > > A link to the electowiki entry on my original version of IBIFA: > > https://wiki.electorama.com/wiki/IBIFA > > And the EM post in which I first suggested it: > http://lists.electorama.com/pipermail/election-methods-electorama.com//2010-May/091807.html > > Here is the description of the revised 4-slot version, referring to > A-B-C-D grading ballots: > > *Voters fill out 4-slot ratings ballots, say with A B C D grades. > ??Default rating/grade is D, signifying least preferred and > unapproved. > > Any grade above D is interpreted as Approval. > > If any candidate/s X has an A score that is higher than any other > candidate's approval > score on ballots that?? don't give X an A grade, elect the X with the > highest A score. > > Otherwise, if any candidate/s X has a A+B score that is higher > than any > other candidate's > approval score on ballots that don't give X an A or B grade, elect > the X > with the highest > ??A score. > > Otherwise, elect the candidate with the highest Approval score.* > > ??35: A > ??10: A=B > ??30: B>C > ??25: C > > With my Condorcet hat on, in this example I've said that B is the > weakest candidate.?? A bit unfortunately > IBIFA here elects B, but FBC is a bit more "expensive" than > Condorcet, > and so does Winning Votes and Margins. > Bucklin elects the most approved candidate C, but at least B both > pairwise beats and is more top-rated than C. > > Ted Stern's eye-opening example: > > 49: A > B > 03: B > A > C > 10: D > B > C > 38: E > F > C > 05: G > D > H > > The Condorcet winner is A.?? Ted's Relevant Ratings and my revised 4+ > slot IBIFA elect A. > My original version of IBIFA?? and?? Median Ratings methods such as > Bucklin and MJ elect B. > > Top Ratings (A) scores:?? A49,?? E38,?? D10,?? G5,?? B3,?? C0 > A + B scores:???????????????????????????????????? A51,?? E38,?? > D15,?? G5,?? B62,?? C0 > > In the second round A and B both "qualify".???? On ballots that > don't?? > give A one of the two > top grades the most approved candidate is E with a score of 38, lower > than 51 so A qualifies. > > On ballots that don't give B one of the top two grades the most > approved > candidate is again > E with again a score of 38, lower than 62 so B qualifies. In the > "round > before" A?? has the > higher score (49 versus 3) so revised IBIFA gives the win to A. > > A>B 49-13,???? A>E 51-38,?? A>D 51-15,?? A>G 51>5, A>C?? 51-48. > > At the cost of being a quite a bit more complicated,?? IBIFA can be > combined?? with Kevin Venzke's > special "tied-at-the-top" rule used in his "Improved Condorcet > Approval" > method to make > the method even more Condorcet-consistent?? (possibly as much as it > possible for a FBC method > to be). > https://wiki.electorama.com/wiki/Improved_Condorcet_Approval > > *If one candidate T pairwise beats all others by the tied-at-the-top > rule then T wins. If there is no > such T then we elect the (revised) IBIFA winner. > If there is more than one T then we elect the one that "qualifies" > (according to IBIFA) in the earliest > IBIFA round. If there is more than one of these, then elect the > one with > the highest score in the previous > round if there was one, otherwise simply with the highest top-ratings > score.* > > 4: A>B > 6: A>C > 6: B>A > 2: B>C > 3: C>B > > B is the narrow Condorcet winner:?? B>A 11-10,?? B>C?? 12-9. No > ballots > have any candidates tied at the top, > so B wins.?? Plain IBIFA elects A, which is positionally dominant: > Top > scores: A10, B8, C2. Approval scores: A16,?? B13,?? C10. > > For the time being the name I suggest?? for?? this is > Quasi-Condorcet IBIFA. > > Chris Benham > > > > > > > --- > This email has been checked for viruses by AVG. > https://www.avg.com > > > > ------------------------------------ > Posted by: Chris Benham <cbenhamau@yahoo.com.au > <mailto:cbenhamau@yahoo.com.au>> > ------------------------------------ > > > ------------------------------------ > > Yahoo Groups Links > > <*> To visit your group on the web, go to: > http://groups.yahoo.com/group/RangeVoting/ > > <*> Your email settings: > Individual Email | Traditional > > <*> To change settings online go to: > http://groups.yahoo.com/group/RangeVoting/join > (Yahoo! ID required) > > <*> To change settings via email: > RangeVoting-digest@yahoogroups.com > <mailto:RangeVoting-digest@yahoogroups.com> > RangeVoting-fullfeatured@yahoogroups.com > <mailto:RangeVoting-fullfeatured@yahoogroups.com> > > <*> To unsubscribe from this group, send an email to: > RangeVoting-unsubscribe@yahoogroups.com > <mailto:RangeVoting-unsubscribe@yahoogroups.com> > > <*> Your use of Yahoo Groups is subject to: > https://info.yahoo.com/legal/us/yahoo/utos/terms/ >

TS

Ted Stern

Thu, Jun 13, 2019 12:39 AM

See inserted correction below:

On Mon, Jun 3, 2019 at 2:42 PM Ted Stern dodecatheon@gmail.com wrote:

Hi Chris,

You are so close to Relevant Ratings in your proposal. I just want to
point out how close and why the one missing factor is important.

You write:

My idea (originally my misunderstanding of Ted's Relevant Ratings method)
is that if at some (quasi-Bucklin) IBIFA round after the first (but before
we have reached just counting total approval scores) we find more than one
candidate Q qualified to win then instead of (Bucklin-like) giving the win
to the Q with the highest score in that round we elect the Q with the
highest score in the round before.

Where this differs from RR is as follows:

- For each candidate Q qualified to win IBIFA, their total ballots
from highest rating down to the current round rating exceed some highest
total approval on complementary ballots excluding Q down to that rating.
Say that the highest total approval on such complementary ballots is TC.
- Your modified IBIFA just looks at the Q totals from the previous
round.
- My Relevant Ratings method looks only at the previous round Q totals
that are larger than their respective TC opposition *in the current
round!*

In most situations, the Q you find with your modified IBIFA would be the
same. But it is possible that they might not be. Let's carefully
construct a 4 slot example, working backwards:

Say we want at least 3 candidates, ratings 3 = Excellent ("A"), 2 = Very
Good ("B"), 1 = OK ("C"), 0 = disapproved ("D").

- round 1 totals (scores at 3) of A48, B49, with other candidates
below that (and not qualifying in any method)
- round 2 totals (scores at 2 and above) of A52, B51, with other
candidates below that (and not qualifying in any method)
- round 3 totals (scores above 0) of A52, B52, and C > 54, with other
candidates below that (only C qualifying under MCA or MJ)
- In round 1, we want A48's most approved complementary candidate to
be B or C with at least 49
- In round 1, we want B49's most approved complementary candidate to
be A or C with at least 50
- In round 2, we want A52's most approved complementary candidate to
be C with at most 47
- In round 2, we want B51's most approved complementary candidate to
be C with exactly 50.
- We want A and B's total approval to be less than 50%, so there must
be at least 105 ballots.  So we expect at least 5 irrelevant ballots.

Under this scenario, C will win both MCA and MJ in round 3. B will win in
modified IBIFA, as round 2 qualifier with the highest round 1 score.

But A will win both original IBIFA and relevant rating because while both
A and B qualify in round 2, only A's round 1 score exceeds A's round 2
complementary approval winner C's approval of 47, while B's round 2 score
of 49 is below B's complementary approval winner C's score of 50.

Here is a set of ballots that I think satisfies those constraints.

02: A > B > C
24: A > D > C
22: A > E > C
04: B > F > C

The 04: B > F > C ballots are a typo. They should be

04: B > A > C

25: B > F > C
21: B > G > C
02: E > D=A > C
02: F > E=A > H
06: G > F > H

Round 1: A48 vs complementary approval winner C with 51, B49 vs
complementary approval winner C with 50. Neither qualifies
Round 2: A52 vs complementary approval winner C with 47, B51 vs
complementary approval winner C with 48. Both qualify in IBIFA-derived
methods, but not in MCA or MJ with less than 50% of ballots
Round 3: C99 passes 50% threshold, while A and B still less than 50%
threshold for tiebreaker.

A52 pairwise beats B51 and is the Condorcet winner (Please check my
arithmetic!)

Pairwise array (equal rated whole):

['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H']
A [56. 52. 56. 56. 54. 54. 56. 56.]
B [50. 52. 52. 52. 52. 52. 52. 52.]
C [46. 48. 100. 74. 76. 75. 79. 100.]
D [ 2. 26. 26. 26. 24. 26. 26. 26.]
E [ 4. 26. 26. 26. 26. 24. 26. 26.]
F [33. 8. 33. 33. 33. 33. 27. 33.]
G [27. 6. 27. 27. 27. 27. 27. 27.]
H [ 6. 8. 8. 8. 6. 0. 2. 8.]

A is definitely the Condorcet Winner.