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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-weight: bold;"><font face="Calibri">To
Kristofer and everyone,</font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><font face="Calibri"><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-weight: bold;">Thank
you for your quick response.<span style="mso-spacerun: yes;"> </span>I would like better to understand why you say that ‘</span><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;">MJ
… doesn't make any assumptions about how far away Excellent is from Very Good or Very Good from Poor’.<span style="mso-spacerun: yes;">
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri"> </font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri">I
read Balinski and Laraki as saying that these grades are elements of a ‘common language’ through which each voter can meaningfully express his or her evaluation of each candidate.<span style="mso-spacerun: yes;">
</span>People who understand that language, in the light of their own concept of Excellence, can meaningfully also judge the differences between the remaining 5 grades of candidate.<span style="mso-spacerun: yes;">
</span>They at least see that a candidate they judge to be Very Good as less worthy than their Excellent candidate, and Good less worthy than Very Good, etc.<span style="mso-spacerun: yes;">
</span>Consequently, B&L and I would say, for example, when one candidate has received a majority judgment composed of some Excellents and/or Very Goods, as well as ‘median-grades’, and a 2<sup>nd</sup> candidate has received a majority judgment composed entirely
of grades equal to the ‘median-grade’ of the 1<sup>st</sup> candidate, society has judged that the 1<sup>st</sup> candidate should win.<span style="mso-spacerun: yes;">
</span>Society would be more ‘satisfied’ when the 1<sup>st</sup> candidate wins.</font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri"> </font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri">In
this context, it seems to me that HMJ’s averaging of ordinal scores is meaningful.<span style="mso-spacerun: yes;">
</span>It is meaningful without anyone claiming that the value ‘distance’ between each grade and the next one above it or below it is exactly equal.</font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><font face="Calibri"><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;">At
the same time, B&L would make the point that while your following 2 examples are in one sense mathematically similar, only the 1<sup>st</sup> one takes advantage of the findings of experience and empirical research that most people</span><span style="font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;">
can meaningfully use no more than 7 grades:</span></font></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri">‘…
if you ran MJ with the following assignments:<br>
Excellent = 5</font><span style="color: black;"><br>
<font face="Calibri">Very Good = 4<br>
Good = 3<br>
Acceptable = 2<br>
Poor = 1<br>
Reject = 0<br>
<br>
‘you'd get the same result as if you ran it with these:<br>
<br>
Excellent = 1000<br>
Very Good = 800<br>
Good = 500<br>
Acceptable = 100<br>
Poor = 20<br>
Reject = 0’</font></span></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-weight: bold;"><font face="Calibri">What
do you think?</font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-weight: bold;"><font face="Calibri">Steve</font></span></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><b><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri"> </font></span></b></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><b><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri"> </font></span></b></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><b><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri">From:</font></span></b><font face="Calibri"><span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;">
Kristofer Munsterhjelm <km_elmet@t-online.de><br>
<b>Sent:</b> Sunday, October 30, 2016 9:53 PM<br>
<b>To:</b> steve bosworth; Jameson Quinn; election-methods@lists.electorama.com<br>
<b>Subject:</b> Re: [EM] Tolerating: MJ, HMJ, GMJ, SARA, or MAJORITY SCORE</span><span style="color: black; font-size: 14pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;">
</span></font></p>
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<p style="background: white; margin: 0in 0in 0pt; line-height: normal;"><span style="color: black; font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><font face="Calibri">On
10/30/2016 04:00 PM, steve bosworth wrote:<br>
> Tolerating: MJ, HMJ, GMJ, SARA, MAJORITY SCORE<br>
> <br>
> To Jameson and everyone,<br>
> <br>
> Highest Majority Judgment (HMJ)<br>
> <br>
> Jameson seems to suggest that his SARA or Majority Score methods<br>
> guarantees the election of the candidate with the ‘deepest and widest’<br>
> support from the voters. I am not yet clear that this claim could be<br>
> sustained when compared with my refined version of Balinski &Laraki’s MJ<br>
> which I will call Highest Majority Judgment (HMJ).<br>
> <br>
> There is only one difference between HMJ and B&L’s MJ. Both HMJ and MJ<br>
> start by discovering all the candidates who have receive the highest<br>
> median grade, i.e. ‘majority-grade’. If only one candidate has received<br>
> this grade, she wins. If 2 or more candidates have received this grade,<br>
> the winner in a large election will most probably be discovered simply<br>
> by going on to compare their different ‘majority-guages’ (see below). <br>
> However, if the winner is not obvious from these comparisons, HMJ next<br>
> uses a different tie-breaker than used by B&L. HMJ discovers which has<br>
> received the highest average evaluative score. For example, using<br>
> Excellent (5), Very Good (4), Good (3), Acceptable (2), Poor (1), or<br>
> Reject (0), it divides the sum of the score equivalents of all the<br>
> median and higher grades received by each candidate by the total number<br>
> of these supporting median and higher than median grades.<br>
> <br>
> In contrast, MJ’s most precise if laborious way of discovery the winner<br>
> is to go on to calculate which candidate has received the highest<br>
> ‘majority-value’. B&L see the complete ‘majority-value’ of each<br>
> candidate as expressed by ‘the sequence of his (first) majority-grade,<br>
> his second majority-grade, his third majority-grade, down to his /n/th<br>
> majority-grade (if there are/n/ [voters])’ (B&L, Majority Judgment,<br>
> p.6). Thus, the number expressing this value starts with the score<br>
> equivalent to their common ‘majority-grade’, followed after the decimal<br>
> point by the sequence of each of all the scores of all the remaining<br>
> majority-grades that would result, one by one, by removing each new<br>
> majority-grade once it is found.<br>
</font></span><span style="font-size: 10pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri;"><br>
<font face="Calibri">I'd like to mention, from a theory purist's perspective, that one of the<br>
good things about MJ is that it doesn't make any assumptions about how<br>
far away Excellent is from Very Good or Very Good from Poor. That is, if<br>
you ran MJ with the following assignments:<br>
</font><span style="color: black;"><br>
<font face="Calibri">Excellent = 5<br>
Very Good = 4<br>
Good = 3<br>
Acceptable = 2<br>
Poor = 1<br>
Reject = 0<br>
<br>
you'd get the same result as if you ran it with these:<br>
<br>
Excellent = 1000<br>
Very Good = 800<br>
Good = 500<br>
Acceptable = 100<br>
Poor = 20<br>
Reject = 0<br>
<br>
All that's required for MJ to work is that the grading standard is<br>
reasonably close to the same for every voter.<br>
<br>
If you introduce averaging into the mix, this property is (obviously) lost.<br>
<br>
Since you only do that as a last tiebreaker, the compromise would<br>
probably not be that great in practice, but in theory, it changes the<br>
perspective of the method: no longer do only the grades matter, but it<br>
also matters what relative levels of satisfaction each grade corresponds to.</font></span></span></p>
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