# [EM] MJ Symmetrized

Forest Simmons forest.simmons21 at gmail.com
Sat Oct 23 18:35:53 PDT 2021

```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.