[EM] MJ Symmetrized ... special cases

[Forest Simmons]

The special cases of 3, 7, 15, 31, or 2^k-1 categories can be handled mucch
more succintly:

WHILE more than one category remains ... [i.e. while 3, 7, ... or 2^k-1
categories remain]...
IF more than half of the judgments are better than the middle remaining
category or more than half are worse than the middle remaining category..
THEN ...
     ... move the remaining middle category judgments and those from the
minority side of the remaining middle category to the majority side
category that they are nearest to....
AND  apply this method recursively to the remaining categoties.
ELSE ...move all  judgments to the middle category among those remaining.
EndWhile

After execution of the above procedure the one remaining category is the MJ
category.




El sáb., 23 de oct. de 2021 6:35 p. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:

> It is easier to bring MJ into compliance with Reverse Symmetry if there
> are an odd number of categories 3, 5, 7, ...
>
> Let's call the middle category "neutral" or Greek "nu" for short because
> it is the only category without either a positive or negative connotation.
>
> A "majority judgment" for X will be one of the judgment categories (of
> which there are an odd number) and which also make up the possible voter
> judgments of the candidates.
>
> To find the voters' Majority Judgment for candidate X, list the induvidual
> voter judgments of X  while respecting the natural judgment order from left
> to right, say. [no slight intended, lefties!]
>
> If there is a median member of the list (because of an odd number of
> judgments of X), then that median judgment is X's Majority Judgment (MJ).
>
> Or (in the even case) if the two middle judgments are the same, then that
> common judgment is the MJ.
>
> Or if the two middle judgments are in categories situated symmetrically
> about neutral, then neutral is the majority judgment.
>
> Otherwise, the outside one (the one furthest away from neutral in the
> category order) is the MJ.
>
> It seems to me that these conventions respect Reverse Summetry: if all
> judgments are reversed (i.e. replaced with their symmetrical opposites),
> then the MJ will also move to its symmetrical opposite.
>
> Comments?
>
> FWS
>
>
>
>
>
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