# [EM] For Better or for Worse ... an MJ variant

Forest Simmons forest.simmons21 at gmail.com
Sat Oct 16 20:11:46 PDT 2021

```Steve Bosworth's steadfast advocacy for MJ has made me wonder if there
might be a version of MJ that satisfies the Reverse Symmetry Criterion, and
perhaps Participation, as well.

Here's my idea ...

Each voter judges each candidate with an appropriate specialized vocabulary
word by writing the word next to the candidate's name on the ballot.

The words must be spelled using only letters from the set {B, W}.

They can be short or long, but they have to fit (left justified) into the
spaces provided next to the candidate names. Fortunately, B and W are easy
for optical scanner/digitzers to distinguish.

For example, if a voter writes the word

BBWBWWB

next to the name José Jiménez,  she is describing José as being among the
better possible candidates... in fact among the better of the better, yet
among the worse of the better of the better, etc. Each letter refines the
partial judgment represented by the preceding letters ... so it's more like
Romance languages where the modifiers conform to post-fix rather than
pre-fix conventions ... Casa Blanca vs White House.

If you are thinking that we are going to convert each word into a binary
point number ... well, no ...we're going to do something much more subtle
and interesting for which the arithmetic operations on binary numbers are
not well adapted (though alpha numeric string operations could work, but
let's stick with literature!):

For convenience list all of the ballot words judging José in alphabetical
(lexicographical) order...

BBBBB
BBBBB
BBBBW
...
WWBBW
WWWBB
...
WWWWW

Suppose that most of these judgment words start with B..Then the first
letter of the majority judgment (of José) will be a B.

Before continuing we have to modify the losing words ... the ones that
started with W ... cross out the initial W, but replace the remaining
letters (if there are any) with W's to reflect these voters' opinion that
the majority judgment (B) was too nice, so on the question of remaining
letters, all of these voters' words will come down on the side of W.

After these modifications, determine by majority rule the next letter in
Jose's judgment, and make the usual adjustments to the losing words.

What if there is a tie, meaning both letters get equal support. Then put a
neutral letter n for "neither better nor worse" in that position of Jose's
majority judgment word, and base its next letter on whether there are more
W's or B's in the next position of the remaining words in the list (of
voter words judging Jose). Continue as necessary until the tie is fully
resolved.

So we see that the majority judgment words for the various candidates will
be formed with letters from the set

{B, n, W}

The order of finish is the dictionary order of the respective majority
judgment words ... assuming a really up to date comprehensive English
dictionary .

Have I overlooked anything? Is Mono-Add satisfied? Reverse Symmetry?

Do the rules make sense heuristically?

FWS
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