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

[Forest Simmons]

I have a simpler approach to MJ that makes resolution of ties easier to
describe ... coming soon.

Preview ... a Judgment of a candidate is an ordered set [s(1), s(2), ...
s(k)] for some ordinal k, where each s(i) is in the set S = {Worse,
neutral, Better}, which we use interchangeably with the set of signs, {-,
0, +}, when convenient.

So our MJ method converts finite sets of Judgments of each candidate into
Majority Judgments of each candidate, which can then be used to obtain a
complete social order (once ties are broken appropriately) satisfying
Reverse Symmetry.

Importantly, the input judgments and the output majority judgments are of
the same type ... members of {S^m | m is an ordinal number}, in conformity
with the basic social choice amalgamation goal.

To be continued .
.

FWS

El sáb., 16 de oct. de 2021 8:11 p. m., Forest Simmons <
forest.simmons21 at gmail.com> escribió:

> 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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