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

Wed Jun 5 15:33:51 PDT 2019

```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 at yahoo.com.au
> <mailto:cbenhamau at yahoo.com.au> [RangeVoting]
> <RangeVoting at yahoogroups.com <mailto: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
>     <mailto:cbenhamau at yahoo.com.au>>
>     ------------------------------------
>
>
>     ------------------------------------
>
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