[EM] Best Single-Winner Method (Steve Bosworth)
Ted Stern
dodecatheon at gmail.com
Tue May 28 10:06:46 PDT 2019
Hi Steve,
Relevant Ratings is designed to be as similar as possible to Majority
Judgment while being "immune" from irrelevant ballots. It's just that the
comparison for "at-and-above" total ratings is the highest approved
candidate on complementary ballots, instead of the abstract quantity of 50%
of the electorate. So in the following example with no irrelevant
candiidates, both RR and MJ get the same result while ER-Bucklin and IBIFA
get a different result:
17: A>C
18: A>B
16: B>C
17: B>A
15: C>A
17: C>B
For your purposes, you can count the top rating as Excellent, and the
second highest as very good, but this also works with a 3 slot ballot of
Good, OK, Disapprove.
Round1, A most top ranked with 35, but B has higher approval of 49 on
A-not-top ballots.
Round 2: B has approval 68 (vs A 32 or C32 on B-non-approving ballots), A
has approval 67 (vs B33 or C33 on A-non-approving ballots), C has approval
65 (vs A35 or B35 on C-non-approving ballots), so B wins IBIFA.
But, looking at the top rank, A has 35 vs B or C 33 on A-non-approving
ballots, while B has 33 vs A or C 32 on B-non-approving ballots, so A wins
relevant rating.
Using median rating instead of comparison with the complementary approval
winner, Majority Judgment also chooses A with a median rating of very good,
with the tie between A and B broken because removing median votes for A
switches to a higher rating of excellent before B does. That's because the
highest approved candidate on complementary ballots is on every one of
those ballots.
However, if you add 5 ballots that vote top rating for D, and 5 ballots
with top rating for E, then the tie-breaker breaks for B instead of A in MJ.
(Note, A and B are pairwise tied in this example, while both beat C)
So I think we have reached a fundamental disagreement here. In MJ, the
preference of the majority is paramount, even if not all of the opposing
support is consolidated behind a single candidate. For
Irrelevent-Ballot-Immune methods, we desire the method to be stable even
when new ballots do not contribute to a contending candidate. There's no
way to get around it. You have to decide if you value majority more than
stability. And asking RR to satisfy your preferred criterion is assuming
the consequent.
On Sun, May 26, 2019 at 1:04 PM steve bosworth <stevebosworth at hotmail.com>
wrote:
> Hi Ted,
>
> Thank you both for your response to Cris’s IBIFA and for your discussion
> of your proposed Relevant Rating (RR) method.
>
> Of course, both IBIRA and RR are great improvements on the methods that
> are actually being used to elect single-winners. However, it still seems
> to me that both fall short of the advantages offered by MJ. With regard
> to your description of RR, please correct any of the self
> [clarifications which I’ve added within the square brackets]. At the
> same time, I still seem to be misunderstanding RR because, as yet, I do not
> see how you have arrived at your conclusions with regard your example
> election.
>
> In the hope of assisting our dialogue, below I have added a table which
> records the way MJ would count that election. That table uses Balinski’s
> recommended grading language. He argues that the following 6 grades provide
> a most discerning, meaningful, and informative way for voters to express
> their judgments about the suitability of candidates for office: Excellent,
> Very Good, Good, Acceptable, Poor, or Reject. These six follow the
> empirical evidence and arguments offered by G.A. Miller (1956,”The
> magical number seven, plus or minus two: Some limits on our capacity for
> processing information”. *Psychological Review *63: 89-97) and use by
> Balinski and Laraki Majority Judgment, 2010 MIT.
>
> Correct me if I’m mistaken, but in contrast to MJ, it currently seem to me
> that your RR suffers from two major flaws:
>
> 1. RR does not guarantee that the winner is the one candidate who has
> received the highest available grade on at least 50% plus one of all the
> ballots containing at least one rating other than 0 (i.e. other than Poor
> or Reject in the language suggested by Balinski). Provided an MJ
> citizen marks their ballot at least with one of the following grades for
> one of the candidates (Excellent, Very Good, Good, or Acceptable), this
> grade together with all their default “Rejects” for all the other
> candidates are counted. Thus each and every voter equally and
> necessarily helps to determine each candidates median-grade. The MJ
> candidate who has received the highest median-grade is the winner. My
> previous post (copied below) explains the strong and relatively simple
> process by which any tie is broken.
> 2. RR does not treat each citizen’s vote equally. All the relatively
> small number of Rejects given to the most popular candidates who gave at
> least Acceptable to a much less popular candidate are ignored when
> determining the median-grade of all the candidates (or such median-grades
> have no relevance for RR). This is why RR seems both not to guarantee
> that the winner will be supported by an absolute majority of all those
> voting, and effectively wastes (ignores) all the votes of at least
> Acceptable given to unpopular candidates. This inequality encourages
> voters to vote dishonestly (tactically).
>
> SEE BELOW PLEASE
>
> I look forward to your clarifications and/or refutations.
>
> Steve
>
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>
> *From:* Ted Stern <dodecatheon at gmail.com>
> *Sent:* Friday, May 24, 2019 7:10 PM
> *To:* cbenham at adam.com.au
> *Cc:* election-methods at lists.electorama.com; steve bosworth
> *Subject:* Re: [EM] Best Single-Winner Method
>
>
>
> T: Here's an attempt at a statement of Relevant Rating. I would welcome
> any improvements in the explanation.
>
> 1. Voters rate each candidates a rating of max rating down to 0.
> Blank ballots [regarding any particular candidate] will be counted as 0 /
> Disapproved [i.e. Reject]. Any non-zero rating is counted as
> approved [i.e. Acceptable, Good, Very Good, or Excellent]. A ballot can
> contain any number of candidates at any rating level, but all equal-bottom
> rated candidates [Poor or Reject] will be counted as 0. In other words, a
> ballot must disapprove at least one candidate [no, must grade at least one
> candidate as Acceptable, and by doing so will be counted as also graded
> every other candidate as Reject].
> 2. A candidate's total approval rating on a set of ballots is the
> total number of those ballots rating the candidate above zero.
> 3. For each candidate X, imagine dividing the ballots into MAXRATE+1
> piles [i.e. ballots that give each candidate either Excellent or one of the
> other 5 Balinski grades ]. [I.e.] In each pile are [all] the ballots rating
> X at rating R [with any of Balinski’s grades] from MAXRATE down to
> zero [i.e. Reject]. For a particular rating R [i.e. median-rating], we can
> see the total vote for X at and above that rating by adding up the sizes of
> the piles from MAXRATE down to R. Then, looking at the [number of] ballots
> in the remaining piles (R-1 down to 0) [i.e. the number lower than the
> median-rating grade], look for the candidate with highest total approval
> [i.e. the number higher than the median-grade plus the median-grade].
> 4. If [the number of] X's votes at and above a rating R [i.e. X’s
> median-grade] exceed the highest total [number of ballots which approve approval
> for any candidate on ballots that rate X below R [i.e. X’s
> median-grade], then X's relevant rating is R [?].
> 5. Starting at the top rating, see if any candidates have that
> relevant rating (i.e., they satisfy criterion 4).
> 6. If there is at least one such candidate, then see if there is among
> them a candidate Y for whom the total number of ballots rating Y
> *above* R is also greater [in number] than the highest total approval
> for any candidate on the ballots that rate Y below R. If so, the candidate
> Y with highest total number of ballots rating Y above R is the winner.
> Otherwise, the candidate X satisfying criterion 5 with highest total number
> of ballots rating X at R and above is the winner [I am still not clear
> whether this description might only be a more cumbersome way of expressing
> the count used by MJ and which I presented in the last paragraph of my
> earlier post as copied at the end of this post – please clarify?].
> 7. If there is no non-zero rating at which a candidate can be found
> who satisfies criterion 4, then the candidate with highest total approval
> is the winner.
>
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> S: Stern’s example election :
>
> Converted to Balinisk’s MJ vocabulary (Excellent (e), Very Good (vg),
> Good (g), Acceptable (a), Poor (p), or Reject (r).
>
> Possible translation by Balinski’’s MJ:
>
> 49: A > B
> 03: B > A > C
> 10: D > B > C
> 38: E > F > C
> 05: G > D > H
>
> Candidates: A B C D E F
> G H
>
> 49:e 49:vg 03:a 10:e 38:e
> 38:vg 05:e 05:a
>
> 03:vg 03:e 10:a 05:vg 03:E
>
> 0 10:vg 38:a 0 0
>
> 0 0 0 0 0
>
> Total High: 52 62 51 15 41 38
> 05 05
>
> *Median: r vg r r
> r r r r *
>
> Total Low: 53 43 54 90 67 67
> 100 100
>
> 0 0 0 0 0
> 05:r 0 0
>
> 0 0 0 0:
> 05:r 0 38:r 38:r
>
> 05:r 05:r 05:r 38:r 10:r
> 10:r 10:r 10:r
>
> 38:r 38:r 0 03:r 03:r
> 03:r 03:r 03:r
>
> 10:r 0 49:r 49:r 49:r
> 49:r 49:r 49:r
>
> B is the winner with a median-grade of Very Good. However, if the 5
> citizens who voted for GDH were absent or entirely ignored as seems to be
> the case with RR, A would be the winner with a new median-grade of
> Excellent (e). At the same time, since these 5 citizens did vote, but
> RR elects A, A is being elected by a large minority of all the votes cast.
> How can this be justified if every citizens’ vote must be treated with
> equal respect in a democracy?
> T: Here's a somewhat contrived example of an election in which
> Relevant Rating and IBIFA get a different result.
>
> 49: A > B
>
> 03: B > A > C
>
> 10: D > B > C
>
> 38: E > F > C
>
> 05: G > D > H
>
>
>
> Ratings of 3, 2, 1, 0.
>
>
>
> At rating 3, we see that A has 49 vs total approval C:51 on the
> complementary ballots, so A's relevant rating must be below 3.
>
>
>
> At rating 2, A has 51 [?52] ballots at and above rating 2, as opposed
> to C's approval of 48 [?51] on complementary ballots, so A's relevant
> rating is 2. But we see that B has 61 [62] ballots at and above rating 2,
> meeting the same criterion. If we are using IBIFA, B wins with 61 [?62] vs
> A's 48. But using Relevant Rating, we see that A's 3-level total of 49 is
> greater than the total for C on ballots voting for A below 2, and B's total
> at rating 3 does not exceed the highest approved candidate on ballots that
> exclude B at 3, so A wins the RR tie-breaker.
>
>
>
> S: Please clarify all the above reasoning.
>
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>
> Stern’s RESULTs (printed in red:???????????????????????):
>
>
>
>
>
> Candidates: A B C D E F
> G H
>
> 49:3 49:2 03:1 10:e 38:e
> 38:vg 05:e 05:a
>
> 03:2 03:3 10:1 05:vg 03:e
>
> 0 10:2 38:1 0 0
>
> 0 0 0 0 0
>
> Total High: 52 62 51 15 41 38
> 05 05
>
> *Median: r vg approval *
>
> Total Low: 48 38 49 90 67 67
> 100 100
>
>
> 0 0 0 0 0
> 05:r 0 0
>
> 0 0 0 0:
> 05:r 0 38:r 38:r
>
> 05:r 05:r 05:r 38:r 10:r
> 10:r 10:r 10:r
>
> 38:r 38:r 0 03:r 03:r
> 03:r 03:r 03:r
>
> 10:r 0 49:r 49:r 49:r
> 49:r 49:r 49:r
>
> [….]
>
> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>
> On 21/05/2019 5:16 am, steve bosworth wrote:
>
> Re: Best Single- Winner Method
>
> [….]
>
> Firstly, please correct me if I am mistaken but currently I am
> assuming that we all would ideally want the Best Single-Winner Method:
>
>
> 1. To be simple enough so voters can both use it and understand how
> it is counted;
> 2. To minimize the wasting of citizens’ votes (see below), and
> 3. To guarantee that the winner among 3 or more candidates is the
> candidate most supported by at least 50% plus one (an absolute majority) of
> all the citizens voting, and
> 4. To offer as few incentives and opportunities as possible to vote
> tactical.
>
> Given these desires, currently I see Majority Judgment (MJ) as
> superior to all of the above methods on each of these counts. However,
> since the above discussions have not mentioned MJ, I assume that many
> contributors would reject this claim for MJ. This is why I would very much
> appreciate receiving any of your clarifications or explanations of how my
> claim for MJ cannot be sustained. What important flaws to you see in MJ?
>
> To help you to marshal your criticisms of MJ, please let me explain
> more full my own understandings and reasons for favoring MJ. Firstly, I
> see a citizen’s vote as being wasted * quantitatively* to the degree
> that it fails equally to help one of their most trusted candidates to win.
> A citizen’s vote is wasted *qualitatively* to the degree that it
> instead helps to elect a candidate whom they judge less *fit* for
> office, rather than an available candidate judged to be more fit.
>
> Other than in MJ, such waste is present in all the existing methods,
> whether they ask voters to rank, score, or approve as many of the
> candidates as they might wish. Of course, most dramatic is the waste
> provided by plurality or First-Past-The-Post voting.
>
> To counter qualitative waste, Balinski and Laraki (*Majority Judgment,
> *2010 MIT) argue that our capacity for judging qualities of human
> behavior can be most meaningfully expressed in an election by each voter
> grading each candidate’s suitability for office as either Excellent (
> *ideal*), Very Good, Good, Acceptable, Poor, or “Reject” (*entirely
> unsuitable*). These grades are more discerning, meaningful, and
> informative than merely expressing preferences or using numeric scores ,
> X’s or ticks. Such grading makes it more likely that the highest quality
> candidate will be elected in the eyes of the electorate.
>
> Each candidate who is not explicitly graded is counted as ”Reject” by
> that voter. As a result, all the candidates will receive the same number
> of evaluations, but a different set of grades from the voters. The
> Majority Judgment (MJ) winner is the one who has received grades from an
> absolute majority of all the voters that are equal to, or higher than, the
> highest *median-grade* given to any candidate. This median-grade is
> found as follows:
>
>
> - Place all the grades, high to low, top to bottom, in side-by-side
> columns, the name of each candidate at the top of each of these columns.
> - The median-grade for each candidate is the grade located half way
> down each column, i.e. in the middle if there is an odd number of voters,
> the lower middle if the number is even.
>
> If more than one candidate has the same highest median-grade, the MJ
> winner is discovered by removing (one-by-one) any grades equal in value to
> the current highest median grade from each tied candidate’s total until
> only one of the previously tied candidates currently has the highest
> remaining median-grade.
>
> Also, in contrast to the alternatives, Balinski explains how MJ
> reduces by almost half, both the incentives and opportunities for effective
> tactical voting. Thus, each voter has every appropriate incentive, not
> only to vote but to reveal their honest evaluations of each candidate.
>
> Thus, to me, using MJ should be simpler and more satisfying because
> grading many candidates is both easier and more meaningful than ranking or
> scoring them. Also, finding and comparing the median-grades of all the
> candidate is quite simple. Unlike MJ, IRV, Condorcet methods, and Scoring
> do not guarantee the election of the candidate most preferred by at least
> 50% plus one of all the citizens voting. Unlike IRV but like Condorcet
> methods and Score, MJ does not eliminate any candidate until the winner is
> discovered.
>
> Finally, I would favor the following Asset option to be added at the
> bottom of each MJ ballot: Any citizen who currently feels that they do not
> yet know enough about any of the candidates to grade them, can instead give
> their proxy vote to the Register Elector who will do this for them. They
> could do this by WRITING-IN the published code of that Registered Elector.
>
> I look forward to your comments.
> Steve
>
>
>
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