# [EM] (2) Best Single-Winner Method-IBIFA vs. MJ

steve bosworth stevebosworth at hotmail.com
Thu Jun 13 13:48:50 PDT 2019

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Hi Chris,

I'll respond inline below. I look forward to our next exchange.

Steve

Sent: Wednesday, June 12, 2019 2:40 AM
To: steve bosworth; cbenham at adam.com.au; EM list
Cc: John M
Subject: Re: Best Single-Winner Method-IBIFA vs. MJ

Chris Benham wrote:

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.

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.

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.

On 12/06/2019 6:34 am, steve bosworth wrote:

S: Your concept of “irrelevant ballots” seems to be central to your IBIFA method of counting.  Do you also see this concept as conflicting with my own assumption that in a workable and ideal democracy, each citizen’s vote would count equally – one-person-one-vote?

C:  Of course not.  ….

S: Please remember that my claim is that "in a workable and ideal democracy, [MJ makes it possible for] each citizen’s vote [to] count equally – one-person-one-vote.   No citizen’s vote would be needlessly wasted either quantitatively or qualitatively.  This also means that the…  single-winner in an election will have received at least 50% plus one of all the citizens’ votes cast.".

S: By saying, "of course not", I understanding that you instead mean that your concept of an ideal democracy only guarantees that the winner will be support by a plurality of voting citizens who Top-rated them, I.e. like FPTP in this respect.  Correct me if I'm mistaken.

S:  In any case, the plain fact is the MJ guarantees all the above benefits while IBIFA does not.

C:  …. But "count" only has some positive sensible meaning if we are talking about counting towards a result that the voter prefers (as expressed on the voter's ballot) over what would have resulted if the voter had stayed home.

S:  It seems to me that we can only reliably talk about the recorded votes that citizens have actually made. The citizens who could or would have stayed at home are unknowable.  We only know who in fact voted and those citizens who did not vote. Of course, the results of any particular election would be different in almost any way we might choose by hypothetically removing any key votes relevant to our purpose.

S:  In your above example, the 3 citizens who voted for E also Bottomed (Rejected) all the other candidates.  Why do you think that the 51 citizens who gave B their 2nd preference (and who thereby would elect B by an absolute majority (if MJ were used) are a less important than the group of 49 citizens who gave their 1st preference to A?

S: No citizen’s vote would be needlessly wasted either quantitatively or qualitatively.

C: Refreshing our memories on what you mean by that:

S:  I see a citizen’s vote as being wasted quantitatively to the degree when 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.

C: If we cross out "most trusted" and replace it with 'preferred (for whatever reason)', that is fine.

S:  What other appropriate reason can a citizen have for supporting a candidate to win other than they "trust" them to represent their own scale of political values and concerns?

S: This also means that whenever possible, the single-winner in an election will have received at least 50% plus one of all the citizens’ votes cast.

C:  No it doesn't.  Why doesn't it mean that the winner should preferably come from the Smith set (be the Condorcet winner or come from the smallest set S of candidates that pairwise beat all the outside-S candidates)?

S:  The discovery of MJ means that it is always possible for the winner to have this majority, and that is currently a necessary element in my concept of "workable and ideal democracy".  It is because the candidate from the "Smith set", etc. may still not be supported by such a majority that they are less attractive winner than one who this majority support.

S:  In contrast to MJ, the trouble in my view with IBIFA is that it gives more weight to higher preferences than lower preferences, e.g. a citizen’s Top-rated vote for a candidate is given more weight than a citizen’s Middle-rated vote for a different candidate.

C:  Yes, I can imagine the voters would hate that.

S:  This leads to the demeaning identification of some citizens votes as being “irrelevant”.

C:  MJ brilliantly avoids that by "counting" those ballots so that they cause the winner to change from A (perhaps a Condorcet winner) to B, when those ballots express indifference between A and B.

S: Contrary to what you may be implying, MJ does not count "those ballots [intending] to change" the winner.  MJ counts all the grades given to all the candidates by all the voters equally in order to fine the absolute majority winner, the one with the highest median-grade.  The grade of Reject given both to A and B by the 3 citizens who only preferred E simply  caused a new highest median-grade to exist.  The new median-grade for A became Bottom (Reject) while B's became 2nd preference.

S:  IBIFA also prompts dishonest voting (tactical voting) because it gives more weight to a Top-rating than a Middle-rating.

C:  I've already explained, and gave an example, that MJ has a much stronger truncation incentive than does IBIFA.

S:: As far as I can see, truncation is not a problem for MJ.  It automatically counts a grade of Reject for each candidate not explicitly give one of its other grades by a citizen:  Excellent, Very Good, Good, Acceptable, or Poor.  This both gives the count as much relevant information as possible and makes it as easy as possible for each citizen to vote.  In your view, please explain the nature of the problem that  truncation can sometimes pose.

C:  Imagine how happy the A>B voters are that MJ doesn't "give more weight to higher preferences than lower preferences" and ensures that "whenever possible, the single-winner in an election will have received at least 50% plus one of all the citizens’ votes cast."

S: Please again note that 49 of the IBIFA voter are "happy" with their winner, while 51 of the MJ voters would be happy with their winner.  Again, how do you justify IBIFA’s needlessly giving fewer citizen satisfaction with the result of the election?

C:  MJ elects B.  Obviously MJ punished the A>B voters ….

S: I think you already know that to "punish" means to treat someone differently while MJ treats every grade given by every citizen in exactly the same way.

[….]

C: I think you'll find that Balinski’s claim that MJ is so wonderful at resisting tactical voting is mainly based on the comparison with Average Rating (now aka Score Voting) which gives voters a very strong incentive to just submit approval ballots (i.e. only use the top and bottom grades).

C:  MJ just gives voters a weaker (but still quite strong) incentive to do that.

S:  Please study Balinski's reasons for concluding that MJ reduces both the incentives and opportunities for successful dishonest voting by almost "half" (Majority Judgment,  pp. 14, 15, 19, 187-198, 374).  Also, I think you can already see that IBIFA's promise to give Top-rating more weight than Middle-ratings creates an incentive to give their first preference candidate a Top-rating, even if they would have honestly graded that candidate as only Acceptable if using MJ rather than IBIAF for that elections.    Also, IBIFA gives more of an incentive dishonestly to Bottom all of their less preferred candidates.    With MJ you cannot give any extra help to the candidate you most favor, no matter which grade you give them provide it is one of the grades above that candidate's median-grade.  Nor can you give extra damage to the candidate who do not want to win provided you award them a grade lower than his median-grade.

[….]

Chris Benham

Steve

________________________________
Sent: Wednesday, June 12, 2019 2:40 AM
To: steve bosworth; cbenham at adam.com.au; EM list
Cc: John M
Subject: Re: Best Single-Winner Method-IBIFA vs. MJ

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.

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.

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.

Steve,

On 12/06/2019 6:34 am, steve bosworth wrote:
Your concept of “irrelevant ballots” seems to be central to your IBIFA method of counting.  Do you also see this concept as conflicting with my own assumption that in a workable and ideal democracy, each citizen’s vote would count equally – one-person-one-vote?

Of course not.  But "count" only has some positive sensible meaning if we are talking about counting towards a result that the voter prefers
(as expressed on the voter's ballot) over what would have resulted if the voter had stayed home.

No citizen’s vote would be needlessly wasted either quantitatively or qualitatively.
Refreshing our memories on what you mean by that:
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.

If we cross out "most trusted" and replace it with 'preferred (for whatever reason)', that is fine.

This also means that whenever possible, the single-winner in an election will have received at least 50% plus one of all the citizens’ votes cast.

No it doesn't.  Why doesn't it mean that the winner should preferably come from the Smith set (be the Condorcet winner or come from the smallest
set S of candidates that pairwise beat all the outside-S candidates)?

In contrast to MJ, the trouble in my view with IBIFA is that it gives more weight to higher preferences than lower preferences, e.g. a citizen’s Top-rated vote for a candidate is given more weight than a citizen’s Middle-rated vote for a different candidate.

Yes, I can imagine the voters would hate that.

This leads to the demeaning identification of some citizens votes as being “irrelevant”.

MJ brilliantly avoids that by "counting" those ballots so that they cause the winner to change from A (perhaps a Condorcet winner) to B,
when those ballots express indifference between A and B.

It also prompts dishonest voting (tactical voting) because a Top-rating counts more than a Middle-rating when using IBIFA.

I've already explained, and gave an example, that MJ has a much stronger truncation incentive than does IBIFA.

45: A>B
30: B
25: C

IBIFA elects  A  (the CW:  A>B 45-30,  A>C 45-25).

Imagine how happy the A>B voters are that MJ doesn't "give more weight to higher preferences than lower preferences" and
ensures that "whenever possible, the single-winner in an election will have received at least 50% plus one of all the citizens’ votes cast."

MJ elects B.  Obviously MJ punished the A>B voters for not "dishonestly" simply voting A, and IBIFA didn't.

IBIFA is much more Condorcet-ish than MJ.  In the example no Condorcet method would punish those A>B voters like MJ does.

That is one of the reasons that "some people" continue to propose the "less than satisfactory Condorcet methods."

I think you'll find that the Balinski claim that MJ is so wonderful at resisting tactical voting is mainly based on the comparison with
Average Rating (now aka Score Voting) which gives voters a very strong incentive to just submit approval ballots (i.e. only use the

MJ just gives voters a weaker (but still quite strong) incentive to do that.  I would say that in general the best Condorcet
methods plus IRV plus IBIFA  are all somewhat better than MJ at not penalising voters for voting sincerely.

Chris Benham

On 12/06/2019 6:34 am, steve bosworth wrote:

Hi Chris,

Your concept of “irrelevant ballots” seems to be central to your IBIFA method of counting.  Do you also see this concept as conflicting with my own assumption that in a workable and ideal democracy, each citizen’s vote would count equally – one-person-one-vote?  No citizen’s vote would be needlessly wasted either quantitatively or qualitatively.  This also means that whenever possible, the single-winner in an election will have received at least 50% plus one of all the citizens’ votes cast.

If we do disagree, how to you justify IBIFA’s violations of the above democratic principles, especially when MJ provides a simpler and more meaningful method which guarantees that its elections conform to the above democratic principles?

In contrast to MJ, the trouble in my view with IBIFA is that it gives more weight to higher preferences than lower preferences, e.g. a citizen’s Top-rated vote for a candidate is given more weight than a citizen’s Middle-rated vote for a different candidate.  This leads to the demeaning identification of some citizens votes as being “irrelevant”. It also prompts dishonest voting (tactical voting) because a Top-rating counts more than a Middle-rating when using IBIFA.

In contrast to IBIFA, please note that MJ gives the same weight to each of the different grades that might be given to the its winner. Only one of the grades given by a voter can be added to the total which defines the winner’s majority.  An Excellent only has the priority of being looked for first.

What do you think of the following possible explanation of how you have been needlessly lead to adopt your idea of “irrelevant ballots”.  As I see it, perhaps this flaw in IBIFA stems from a Condorcet habit of minds which mistakenly assumes that the primary electoral concern is to find the candidate who is preferred, head to head, over each of the other candidates.  The voter is only to focus on comparing and ranking the particular candidates in the race.  These comparisons and rankings presumably proceed upon the qualities intuitively identified by the voter as needed for an ideal candidate for the office being sought.  Alternatively, it would proceed most rationally after the voter analyzes and clarifies the hierarchy of such ideal qualities.

In contrast, Balinski suggests that each candidate should, in the light of these qualities, be given one of the 6 grades regarding their suitability for office (Excellent, Very Good, Good, Acceptable, Poor, or Reject).  However, a follower of Condorcet does not grade the candidates but simply proceeds to ranking them.  Next he uses a Condorcet method to see if a Condorcet winner exists.  However, this is less than satisfactory because we all know that each Condorcet method sometimes fails to find such a winner, let alone a winner who has received an absolute majority of the preferences.

Given that MJ guarantees the election of the candidate who is judged to be most fit for the office by an absolute majority of the grades given to this winner, (i.e. grades equal to or higher than the highest median-grade given to any of the candidate), why does anyone continues to propose the less than satisfactory Condorcet methods?

Finally, you have also said that you do not understand MJ's procedure for breaking ties.   Please let me try to clarify this again:

In a single-office election, 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 temporarily 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.

What do you think?  What telling criticism of MJ can be made?

I look forward to the next step in our dialogue.

Steve