[EM] Best Single-Winner Method: RR vs. MJ

Ted Stern dodecatheon at gmail.com
Mon Jun 24 13:25:41 PDT 2019


Relevant Ratings is a ratings method, not a rankings method, as documented
on electowiki (https://electowiki.org/wiki/Relevant_rating).  My example
was given with rankings for illustrative purposes only.  In the actual
example, any candidate ranked highest should be assumed to be given the
highest possible grade of Excellent, next highest as Very Good, etc.,
though without loss of generality, the ratings scale could be truncated
down to 3 slots.

So your modified example is not the same as what I presented, and one might
view your presentation of my position as a straw man, which is not
conducive to productive discourse.  Please try again, using the following
CSV ratings, with 5 = excellent, 4 = very good, etc.  The first line of the
file is a header, indicating that the first column is the number of ballots
with the subsequent ratings, while the second through 6th columns are
ratings on that ballot type for the correspondingly named candidate:

#ballots, A, B, C, D, E
46, 5, 0, 0, 0, 0
03, 5, 4, 0, 0, 0
25, 0, 4, 5, 0, 0
23, 0, 4, 0, 5, 0

with the addition of 3 ballots voting for an "irrelevant" candidate:

03, 0, 0, 0, 0, 0

The point Chris and I have been trying to make is not whether the voters
are using the expressivity of ratings correctly, but rather, what could
happen if a small proportion of "irrelevant" or protest voters joined the
election?  Does your method handle that in a robust way?

I think what you actually demonstrated that MJ can only deliver reasonable
results for this example when interpreting A's victory before adding E
votes in the worst possible light.

And again, I think it is worth considering whether Majority Judgment or
even Relevant Rating is able to determine the candidate closest to the
centroid of voting sentiment (my own preferred goal for a single-winner
method).  I am leaning toward Chris's suggestion of pre-filtering the
candidates to the Smith Set before looking for the highest rated candidate,
based on the following example from the Wikipedia page on Majority Judgment

101: A > B > C > D > E > F > G
101: B > A = C > D > E > F > G
101: C > B = D > A = E > F > G
050: D > C = E > B = F > A = G
099: E > D = F > C = G > B > A
099: F > E = G > D > C > B > A
099: G > F > E > D > C > B > A

which can also be written as

101: A:6, B:5, C:4, D:3, E:2, F:1, G:0
101: A:5, B:6, C:5, D:4, E:3, F:2, G:1
101: A:4, B:5, C:6, D:5, E:4, F:3, G:2
050: A:3, B:4, C:5, D:6, E:5, F:4, G:3
099: A:2, B:3, C:4, D:5, E:6, F:5, G:4
099: A:1, B:2, C:3, D:4, E:5, F:6, G:5
099: A:0, B:1, C:2, D:3, E:4, F:5, G:6

or, in CSV format,

###, A, B, C, D, E, F, G

If your goal is a simple majority, both Majority Judgment and Relevant
Rating will chose the Left candidate, "B", over the Center Left candidate,
"C", even though C is preferred by more voters to any other candidate and
has a higher total score.  So B may be able to govern using only simple
majority votes of a legislature, but any decisions requiring more general
consensus will be more difficult.

To summarize, I think that we are arguing two different points completely.
I have expressed a preference for single winner methods that determine the
candidate closest to the centroid of the population (that is, minimizing
the sum of the distance squared from all voters to the winning candidate),
and I am willing to consider any method that is able to achieve that in a
robust and strategy resistant manner, while you appear to be arguing the
position that finding a rating that is supported by a bare majority of
voters is the only possible metric for judging a candidate, even when that
leads to a winning candidate who is the strongest member of a majority
cooalition rather than the centroid candidate.  Have i assessed that

On Sat, Jun 22, 2019 at 1:55 PM steve bosworth <stevebosworth at hotmail.com>

> Hi Ten,
> I’ll respond inline below.
> From: Ted Stern <dodecatheon at gmail.com>
> To: steve bosworth <stevebosworth at hotmail.com>
> Cc: "election-methods at lists.electorama.com"
>         <election-methods at lists.electorama.com>
> Subject: Re: [EM] (3) Best Single-Winner Method
> Hi Steve,
> T:  You seem to have not processed the response from Chris Benham which
> was
> posted earlier, with the example I proposed 18 months ago:
> [….]
> 46: A
> 03: A>B
> 25: C>B
> 23: D>B
> 03: E
> S: i.e.
> A>B (46+03>25+23)=(49>48)
> A>C (46+03>25)
> A>D (46+03>23)
> A>E  (46+03>03)
> B>C (03+23>25)
> B>D (03+25>23)
> B>E (03+25+23>03)
> C>D (25>23)
> C>E (25>03)
> D>E (23>03)
> ________________________________________________________________
> S: I hope you will see below that I have “processed” this example in a way
> that shows that these voters could be treated more fairly by MJ, i.e. if
> each voter had defined their preferences by using something like the
> clearest, richest and most meaningful language for expressing the observed
> different levels of desired human behavior, e.g. by using the following six
> grades suggested by Balinski & Laraki regarding the suitability of each
> candidate for office:  Excellent (ideal), Very Good, Good, Acceptable,
> Poor, and Reject (entirely unsuitable).  At least this is the plausible
> claim made by B & L in *Majority Judgment* (pp.171, 169, 283, 306, 310, &
> 389).  They were assisted in this regard 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).
> On this basis, I propose to compare and contrast the use of Stern’s RR
> with MJ when applied to the above example election.  The above summary
> records how RR finds A to be the winner: A>B (49>48).
> One of the proofs that grades provide a richer and more meaningful
> language than preferences used alone is to note that preferences can be
> inferred from a list of grades but grades cannot be inferred from a list of
> rankings.  Consequently, the preferences listed in the above example
> might have resulted from any combination of the following possible grades
> that the same voters might have given to the above candidates if they had
> been asked.  The range of possibilities are listed below.  For example,
> each of the 46 voters who expressed their preference for A over all the
> other candidates might grade A as either e (Excellent), vg (Very Good), g
> (Good), or  a (Acceptable):
> 46: A……….i.e. A is graded as either e, vg, g or a; and B, C, D and E are
> graded as r.
> 03: A>B……i.e. A is graded as either e, vg, or g; and B is graded as vg, g,
> or a; and C,  D and E are graded as r.
> 25: C>B……i.e. C is graded as either e, vg, or g; and B is graded as vg, g,
> or a; and A,  D and E are graded as r.
> 23: D>B……i.e. D is graded as either e, vg, or g; and B is graded as vg, g,
> or a; and A,  C and E are graded as r.
> 03: E…………i.e. E is graded as either e, vg, g or a; and A, B, C, and D are
> graded as r.
> Within these options, the following lowest possible grades for A, and
> highest possible grades for B would produce the following conversion of the
> above Condorcet example into one possible MJ election:
> Candidates:   A        B        C        D        E
>                      3e       3vg     25e     23e     3e
>                      46a     25vg   0        0        0
>                      0        23vg   0        0        0
> TOTAL+ ….  49       51       25       23       3
> Median-
> Grade:  …….  r …   vg  …  r  …..   r  …   r
> TOTAL-  …   51       49       75       77       97
>                      0        03r     03r     03r     23r
>                      03r     0        23r     25r     25r
>                      23r     0        03r     03r     03r
>                      25r     46r     46r     46r     46r
> In spite of the fact that A is the Condorcet minority winner (also for
> IBIFA & RR),  B is the MJ majority winner with 51 grades of Very Good.  MJ
> finds A to be the second best and minority candidate with 3 Excellents and
> 46 Acceptables (i.e. a minority of all the votes cast).  Am I mistaken in
> assuming that even Condorcet minded citizens would feel that B should be
> the winner in such a case?
> Does not this example illustrate why, as a method, MJ is superior to any
> Condorcet method?
> Unlike Condorcet,
>    1. MJ allows every discerning person (and every other citizen) most
>    meaningfully and simply to express their judgment about the suitability for
>    office of as many candidates as they might want;
>    2. Using MJ’s six grades removes the ambiguity that needlessly remains
>    when using preferences alone;
>    3. MJ guarantees that an absolute majority of all the votes will elect
>    the winner whom they see as having the highest available quality, i.e. at
>    least the quality expressed by having received the highest median-grade.
>    4. MJ’s grading of a large number of candidates is much easier than
>    ranking them.
>    5. MJ’s method for finding the winner by determining median-grades is
>    much easier for each ordinary citizen to understand than is any of the
>    Condorcet methods.
> What do you think?  In your view, what mistakes am I making?
> I look forward to the next stage of our dialogue.
> Steve
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