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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Tolerating: MJ, HMJ, GMJ, SARA, MAJORITY SCORE</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">To Jameson and everyone,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Highest Majority Judgment (HMJ)</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Jameson seems to suggest that his SARA or Majority Score methods guarantees the election of the candidate with the ‘deepest and widest’ support from the voters.<span style="mso-spacerun: yes;">
</span>I am not yet clear that this claim could be sustained when compared with my refined version of Balinski &Laraki’s MJ which I will call Highest Majority Judgment (HMJ).</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">There is only one difference between HMJ and B&L’s MJ.<span style="mso-spacerun: yes;">
</span>Both HMJ and MJ start by discovering all the candidates who have receive the highest median grade, i.e. ‘majority-grade’.<span style="mso-spacerun: yes;">
</span>If only one candidate has received this grade, she wins.<span style="mso-spacerun: yes;">
</span>If 2 or more candidates have received this grade, the winner in a large election will most probably be discovered simply by going on to compare their different ‘majority-guages’ (see below).<span style="mso-spacerun: yes;">
</span>However, if the winner is not obvious from these comparisons, HMJ next uses a different tie-breaker than used by B&L.<span style="mso-spacerun: yes;">
</span>HMJ discovers which has received the highest average evaluative score.<span style="mso-spacerun: yes;">
</span>For example, using Excellent (5), Very Good (4), Good (3), Acceptable (2), Poor (1), or Reject (0), it divides the sum of the score equivalents of all the median and higher grades received by each candidate by the total number of these supporting median
and higher than median grades. </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">In contrast, MJ’s most precise if laborious way of discovery the winner is to go on to calculate which candidate has received the highest ‘majority-value’.<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span>B&L see the complete ‘majority-value’ of each candidate as expressed by ‘the sequence of his (first) majority-grade, his second majority-grade, his third majority-grade, down to his
<i style="mso-bidi-font-style: normal;">n</i>th majority-grade (if there are<i style="mso-bidi-font-style: normal;"> n</i> [voters])’ (B&L, Majority Judgment, p.6).<span style="mso-spacerun: yes;">
</span>Thus, the number expressing this value starts with the score equivalent to their common ‘majority-grade’, followed after the decimal point by the sequence of each of all the scores of all the remaining majority-grades that would result, one by one, by
removing each new majority-grade once it is found.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">I see this procedure as needlessly laborious.<span style="mso-spacerun: yes;">
</span>Also, it makes the mistake of allowing, in some cases, the votes of those who gave less than the common majority-grade to each of these candidates to determine the winner.</font></p>
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<font face="Calibri">Next, please correct me if I am mistaken but I see Jameson’s following definition of GMJ as different from HMJ: ‘<span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman";">GMJ: Graduated
Majority Judgment. 4 or more grade levels, highest median, tiebreaker is [the] average between number of votes at or above median and number of votes above median.’<span style="mso-spacerun: yes;">
</span>He offered this brief definition in his glossary when he</span> recently joined the ‘toleration of MJ’ thread (<span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman";">Monday, September 5, 2016
8:30 PM).<span style="mso-spacerun: yes;"> </span>As it stands, I do not really understand this definition of GMJ.<span style="mso-spacerun: yes;">
</span>Is anyone willing to explain it and defend it?</span></font></p>
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<span style="color: black; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman";"><font face="Calibri">In contrast, Electowiki defines GMJ differently below.<span style="mso-spacerun: yes;">
</span>I have also tried to add some clarifying addition to it within {these brackets}.<span style="mso-spacerun: yes;">
</span>I do not yet fully understand the parts I have placed with [square brackets].<span style="mso-spacerun: yes;">
</span>I would very much appreciate it if anyone could clarify these elements.<span style="mso-spacerun: yes;">
</span>Also, can anyone explain how MJ or any of these versions of GMJ are superior to HMJ?
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Finally, I would also appreciate any explanations of how MAC, SARA, or Majority Score are superior in your view to HMJ</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Steve</font></p>
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