[EM] Best Single-Winner Method--MJ

steve bosworth stevebosworth at hotmail.com
Mon May 27 15:36:54 PDT 2019

Hi Cris,

Thank you for commenting on my post asking for any criticisms of MJ.  I will respond inline to your two relevant posts and I look forward to the next stage of our dialogue.

Steve Bosworth

Message: 3
Date: Wed, 22 May 2019 01:24:41 +0930
From: Chris Benham <cbenhamau at yahoo.com.au>
To: election-methods at lists.electorama.com
Subject: Re: [EM] Burlington and Condorce methods
Message-ID: <5e95b93f-398e-c151-a448-6f2632c7ca76 at yahoo.com.au>
Content-Type: text/plain; charset="windows-1252"; Format="flowed"

On 21/05/2019 8:07 am, steve bosworth wrote:
> 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 tactically.


C:  Re. your point 1, yes.   Although I consider the first part to be a bit
more important than the second. If all the acknowledged "unbiased"
experts all agree that the way the votes are counted is fair it's not a huge problem if
some of the voters don't understand it.

Re. your point 2, yes.

Re. your point 3, that isn't possible.

S:  Please reconsider this mistaken assertion in the light of the exact way that Balinski and Laraki MJ counts every citizens’ vote equally (2010, Majority Judgment, MIT, p. 5).

C:  And I'm wary of standards/criteria that refer to some fraction of "all the citizens
voting", because they are vulnerable to Irrelevant Ballots.??? But yes, we can approach this by
requiring that the method meet say "Mutual Relevant Majority".

S:  No, with MJ every ballot is “relevant”.  That is how MJ ensures that each citizen’s vote will count equally until the winner is discovered.

C:  Re. your point 4, yes.

That does not encompass my full list of highly desirable or essential
properties.??? The method shouldn't needlessly have the feature that adding or
removing a few ballots that express complete indifference among the
remotely viable candidates should change the winner, as does MJ and Bucklin.

S:  No, each and every MJ voter is interpreted to have expressed a judgment on each and every candidate.--- no “indifference” regarding any candidate.  Each citizen’s ballot will help to determine which of the ”viable candidates” will win.

> Given these desires, currently I see Majority Judgment (MJ) as
> superior to all of the above methods on each of these counts.

C:  Re. your point 1, second part, I don't think MJ does very well. I don't
completely understand it.??? Bucklin is similar and much simpler, and IBIFA is
much better and not less simple.

S:  MJ’s count is relatively easy to understand:  every citizen’s vote helps to determine every candidate’s median-grade even if they explicitly only grade one candidate as acceptable or above.  The candidate with the highest median-grade is the winner. T

Chris Benham



From: C.Benham <cbenham at adam.com.au>
Sent: Wednesday, May 22, 2019 12:12 PM
To: election-methods at lists.electorama.com
Cc: steve bosworth
Subject: Re: [EM] Best Single-Winner Method

C:  To expand a bit, MJ is a Median Ratings method with a relatively complicated tie-breaker, justified by I've no idea what.

Bucklin is likewise a Median Ratings method and will usually give the same winner, but the "tie breaker" is simple.

S:  I don’t see it as complicated at all.  Please look again at the description at the end of my original post (all copied below) of MJ’s count and tie breaking method, also describe on page 5 as mentioned above.

C: An example I recently came up with to critique another Bucklin-like proposal:

46: A
03: A>B
25: C>B
23: D>B

97 ballots  (majority threshold = 48)

(If  you want MJ-style  multi-slot ratings ballots, assume that all the voters have given their favourite the highest possible rating and those that rated B above bottom all gave B the same middle rating and that truncating here signifies giving the
lowest possible rating).

MJ and Bucklin  both rightly elect A.   IBIFA  and IRV also elect A.  A is the Condorcet winner: A>B 49-48, A>C 49-25, A>D 49-23,
A>E 49>0.

A is the most Top-rated candidate:  A49,  C25,  D23,  B0, E0.

S:  No, Balinski’s MJ not simply counts all the number of “Top-rated” grades give to all the candidates, but all the grade above each of their median-grade, plus the median-grade.

C:  So suppose the votes are counted and it is announced that A has won, but just before this is officially and irrevocably confirmed
someone pipes up, "Hang on a minute, we found a few more ballots!"  (Maybe they are late-arriving postal votes that had been
thought lost.)

These 3 new ballots are inspected and found that all they do is give the highest possible rating to E, a candidate with no support on any of the other 97 ballots. What do we do now?  Laugh and carry on with confirming A as still the winner?  No.

S: No, Balinski’s MJ proceeds to discover any new median-grades of any of all the candidates running, including all of the candidates not mentioned by these additional ballots, i.e. all the candidates at the bottom (i.e. all the candidates counted as “Reject” by these additional ballots).  Please consider my translation below of your above example election using the terminology and symbols used by Balinski.

46: A
03: A>B
25: C>B
23: D>B
03: E

100 ballots  (majority threshold = 51)

Now MJ and Bucklin and any other Median Ratings method elects B.  All methods that I find acceptable elect A both with and without those 3E ballots.

S:  And by doing so you count the value of each of these 3 votes as 0 contained in these 3 additional ballots, needless waste each, needlessly elect a candidate rejected by an absolute majority of all the voters rather than the candidate who is at least Accepted by an absolute majority.  You do not fulfill MJ’s promise to allow each citizen to help to determine the median-grade of all the candidates by explicitly expressing their judgment of the suitability for office of each of all the candidates, by grading at least one candidate as at least Acceptable.  You deny the equality of each voting citizen.  Would your currently preferred method (IBIBA) also waste votes?  If so, how could this be justified?


Cris Benham

S:  Balinski’s recommended “grades” for voters to award to as many of the candidates as they wish with regard to their suitability for office:  Excellent (e) [ideal], Very Good (vg), Good (g), Acceptable (a), Poor, or Reject (r) [entirely unsuitable].

Benham’s 1st example :

46: A

03: A>B

25: C>B

23: D>B

Possibly translated using Balinski’’s MJ as follows:  A is the winner with a median-grade of Excellent (e):

Candidates:     A                     B                      C                     D

                        46:e                 03:vg               25:e                 23:e

                        03:e                 25:vg               0                      0

                        0                      23:vg               0                      0

Total High       49                    51                    25                    23

Median            e                      vg                    r                       r  ­­­

Total Low        48                    46                    72                    74

                        0                      0                      23:r                  25:r

                        23:r                  0                      03:r                  03:r

                        25:r                  46:r                  46:r                  46:r


Benham’s 2nd example :

46: A

03: A>B

25: C>B

23: D>B

03: E

Possible translation by Balinski’s MJ:  B is the winner with a median-grade of Very Good (vg) :

Candidates:     A                     B                      C                     D                     H

                        46:e                 03:vg               25:e                 23:e                 03:e

                        03:e                 25:vg               0                      0                      0

                        0                      23:vg               0                      0                      0

Total High       49                    51                    25                    23                    03

Median            r                       vg                    r                       r                       r

Total Low        51                    49                    75                    77                    97

                        03:r                  03:r                  03:r                  03:r                  23:r

0                      0                      23:r                  25:r                  25:r

                        23:r                  0                      03:r                  03:r                  03:r

                        25:r                  46:r                  46:r                  46:r                  46:r


What do you think?

Steve Bosworth

On 21/05/2019 5:16 am, steve bosworth wrote:

Re: Best Single- Winner Method

Sennet Williams,  Forest Simmons, Robert Bristow-Johnson, Abd dul Raman Lomax, and Chris Benham have recently addressed each others’ claims about IRV, 3-slot Methods, IBIFA, and Asset.  This discussion prompts me to request some help later after I have clarified several issues.

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 possibilities for voting 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[MOU1]<https://outlook.live.com/mail/inbox/id/AQMkADAwATExADY1Ny00YzM0LTAyOWItMDACLTAwCgBGAAADSTHcdM%2FHlEis5wp3r9KYSwcA0CuwkNT%2FUU2SYZznlLihTwAAAgEMAAAA0CuwkNT%2FUU2SYZznlLihTwACzUpKADcAAAA%3D#x__msocom_1> , 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 receiv 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.


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