# [EM] Plurality Loser Elimination And Trunk Yanking Proposals

Forest Simmons forest.simmons21 at gmail.com
Tue Aug 24 12:08:34 PDT 2021

```While there is no pairwise winner among the remaining alternatives ...
eliminate from among said remaining alternatives the alternative X with the
fewest (transferred) votes along with all of the alternatives beaten
pairwise by X
EndWhile.

Then elect the pairwise winner among the remaining alternatives (possibly
the only remaining alternative).
EndProcedure

The idea is that if the Plurality Loser is a weak alternative deserving
removal, then so are the alternatives beaten by it pairwise (if any).

In this context "eliminate" means remove from the ballots and transfer the
Plurality votes to the top remaining alternative on each ballot.

It turns out that this method always elects from a subset of Smith called
Banks.

Note that the procedure becomes IRV by removal of the phrase, "along with
all of the alternatives beaten pairwise by X".

If that phrase is too big of a price to pay for Condorcet compliance, then
there is no hope for tweaking IRV into a decent proposal.

In that case, better to replace Plurality Loser with Implicit Approval
Loser, and get a monotonic Banks method:

While there is no pairwise winner among the remaining alternatives ...
eliminate from among the remaining alternatives the alternative X ranked on
the fewest ballots along with all of the alternatives beaten pairwise by X
EndWhile.

Then elect the pairwise winner among the remaining alternatives (possibly
the only remaining alternative).
EndProcedure

You may recognize this method as a reformulation of TACC (Total Approval
Chain Climbing) with "total approval" replaced by "implicit approval".

Note that "ranked on the fewest" is the same as "truncated on the most" so
the method could be called "Truncation Yanking," since the most truncated
alternative yanks the alternatives it beats pairwise.

As I mentioned, Truncation Yanking (TY) is monotone (unlike any IRV tweak)
and it is much simpler to tally than any IRV tweak.

Also, since true clones do not straddle truncation boundaries, the method
is clone independent.

Anybody know of another simple Banks compliant method with these nice
properties?

Forest
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