# [EM] [RangeVoting] 4+slot IBIFA revision

Ted Stern dodecatheon at gmail.com
Mon Jun 3 14:42:52 PDT 2019

```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 at yahoo.com.au
[RangeVoting] <RangeVoting at 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
>
> *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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>
>
> ------------------------------------
> Posted by: Chris Benham <cbenhamau at yahoo.com.au>
> ------------------------------------
>
>
> ------------------------------------
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