[EM] Worst Elimination Comments

[Forest Simmons]

To make Worst Elimination versions that are ISDA compliant the ideal ballot
type is something like Ted Stern's three level approval preference ballots
that he uses for his most advanced version of Peak Approval Sorted Margins.

As I recall he has three levels of approval ... I don't remember their
exact designations ... for now let's just call them Top, SoSo, and Bottom.

Within those approval categories there are additional distinctions that are
used for the pairwise comparisons but not for the construction of the
approval agenda to be sorted.

In our "worst elimination" context this separation of church and state or
division of labor is important if we want to have Independence from Smith
Dominated Alternatives (ISDA).

As Kristofer pointed out to me ... if we are not careful, when the Smith
Dominated Alternatives are withdrawn from the ballots a Smith Candidate may
drift up (or down) from SoSo into the Top (or Bottom) category on some
ballots in an unintended renormalization.

For example on an olympic score ballot where no Smith candidate has a score
of ten ... when the non-Smith candidates are withdrawn, a Smith candidate
with a score of only nine may drift up to fill the vacuum at Top by a
default renormalization.

That change could then change the relative order of the Smith candidates in
the elimination agenda ... which in turn could change which Smith candidate
gets elected ... thus violating ISDA.

I'm afraid that my previous definition of Top fell into that "unintended
automatic renormalization" trap ... because it extended Top status to any
candidate that was not outranked or out-rated on the ballot ...
unintentionally including those newly reaching that status when the non
Smith candidates entirely vacate the highest rating.

So from now on, let's limit Top ballot status to alternatives explicitly
voted into an official top approval category ... and limit Bottom ballot
status to those so designated, as well as those completely ignored by the
ballot.

Finally, for those just joining us "Worst Elimination" is a method template
for which the user provides a procedure for determining the nominally
"worst" in a subset of alternatives.

In this context, when a majority of the participating voters prefer the
nominally "worst" alternative over some other alternative ... that
alternative is deemed to be "no better than the worst."

For example, a Condorcet Loser is never deemed to be better than the worst.

Worst Loser Elimination:

Until all alternatives have been eliminated ... eliminate the nominally
"worst" remaining alternative ... after first eliminating the alternatives
deemed to be no better than it.

Elect the last eliminated alternative. [That last elimination was just for
fun.]

Does that make sense?

-Forest
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