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

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

steve bosworth

Hi Ten,

I’ll respond inline below.

From: Ted Stern <[hidden email]>
To: steve bosworth <[hidden email]>
Cc: "[hidden email]"
        <[hidden email]>
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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Re: [EM] Best Single-Winner Method: RR vs. MJ

Ted Stern
Steve:

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 (https://en.wikipedia.org/wiki/Majority_judgment#Outcome_in_political_environments):

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
101,6,5,4,3,2,1,0
101,5,6,5,4,3,2,1
101,4,5,6,5,4,3,2
050,3,4,5,6,5,4,3
099,2,3,4,5,6,5,4
099,1,2,3,4,5,6,5
099,0,1,2,3,4,5,6

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 correctly?

On Sat, Jun 22, 2019 at 1:55 PM steve bosworth <[hidden email]> wrote:

Hi Ten,

I’ll respond inline below.

From: Ted Stern <[hidden email]>
To: steve bosworth <[hidden email]>
Cc: "[hidden email]"
        <[hidden email]>
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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