[EM] [RangeVoting] 4+slot IBIFA revision
Ted Stern
dodecatheon at gmail.com
Wed Jun 12 17:39:00 PDT 2019
See inserted correction below:
On Mon, Jun 3, 2019 at 2:42 PM Ted Stern <dodecatheon at 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.
>
> 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
>> 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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>>
>>
>>
>> ------------------------------------
>> Posted by: Chris Benham <cbenhamau at yahoo.com.au>
>> ------------------------------------
>>
>>
>> ------------------------------------
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