[EM] Tolerating: MJ, HMJ, GMJ, SARA, or MAJORITY SCORE

[steve bosworth]

Tolerating: MJ, HMJ, GMJ, SARA, MAJORITY SCORE

To Jameson and everyone,

Highest Majority Judgment (HMJ)

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.  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).

There is only one difference between HMJ and B&L's MJ.  Both HMJ and MJ start by discovering all the candidates who have receive the highest median grade, i.e. 'majority-grade'.  If only one candidate has received this grade, she wins.  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).  However, if the winner is not obvious from these comparisons, HMJ next uses a different tie-breaker than used by B&L.  HMJ discovers which has received the highest average evaluative score.  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.

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'.   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 nth majority-grade (if there are n [voters])' (B&L, Majority Judgment, p.6).  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.

I see this procedure as needlessly laborious.  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.

Next, please correct me if I am mistaken but I see Jameson's following definition of GMJ as different from HMJ: '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.'  He offered this brief definition in his glossary when he recently joined the 'toleration of MJ' thread (Monday, September 5, 2016 8:30 PM).  As it stands, I do not really understand this definition of GMJ.  Is anyone willing to explain it and defend it?



In contrast, Electowiki defines GMJ differently below.  I have also tried to add some clarifying addition to it within {these brackets}.  I do not yet fully understand the parts I have placed with [square brackets].  I would very much appreciate it if anyone could clarify these elements.  Also, can anyone explain how MJ or any of these versions of GMJ are superior to HMJ?



Finally, I would also appreciate any explanations of how MAC, SARA, or Majority Score are superior in your view to HMJ

Steve

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