[EM] [RangeVoting] 4+slot IBIFA revision
Ted Stern
dodecatheon at gmail.com
Thu Jun 13 13:56:04 PDT 2019
I've begun documenting Relevant Rating on electowiki:
https://electowiki.org/wiki/Relevant_rating
I will add examples eventually as I get time, otherwise, if you wish to
edit the page, please feel free to do so!
On Wed, Jun 12, 2019 at 5:39 PM Ted Stern <dodecatheon at gmail.com> wrote:
> 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
>>>
>>>
>>>
>>>
>>>
>>>
>>> ---
>>> This email has been checked for viruses by AVG.
>>> https://www.avg.com
>>>
>>>
>>>
>>> ------------------------------------
>>> Posted by: Chris Benham <cbenhamau at yahoo.com.au>
>>> ------------------------------------
>>>
>>>
>>> ------------------------------------
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