[EM] One more Condorcet algorithm (and one more Approval-Condorcet hybrid)

[Etjon Basha]

Dear gentlemen,


I’ve been playing with idea of the Serious Candidate Set (set of candidates
who would, in the context of a ranked ballot, win an approval count if they
were to serve as universal approval cutoffs, SCS below) a bit more and,
having done some improvements on my earlier thinking (h/t Chris Benham and
Kristofer Munsterhjelm), I think I have chanced upon a half-decent method,
a Condorcet-Approval hybrid. Alas, a complex count which is, at the very
least, non-monotonic, non-additive and fails Later-no-Harm.

The count applies to ranked ballots where equal ranking and truncation are
allowed.



STEP 1, if any remaining candidate has a majority of first preferences,
elect them. Otherwise,

STEP 2, remove the last preference from any ballot that ranks all remaining
candidates. Then,

STEP 3, compute the SCS. If the SCS includes only one candidate, elect
them. Otherwise,

STEP 4, remove all candidates not in the SCS from all ballots. If at least
one candidate is thus removed, return to STEP 1. Otherwise (and this would
occur in a minority of cases),

STEP 5, [put a backup resolution method here, I go with Iterated Bucklin
because of course I do].



I believe the first 4 steps (which should produce a resolution and won’t
require step 5 most of the time, even when there isn’t a CW) are an
alternative algorithm suited to electing the Condorcet Winner if there is
one. Not a particularly efficient algorithm of course, but one that will
elect a winner even if there is no CW. Unlike algos like Nanson/Baldwin
though, these first steps may, at times, enter a cycle with no resolution
requiring a backstop method.


This may seem like an “elect the CW if there is one, otherwise elect the IB
winner” method, but it isn’t, since there’s quite a few scenarios where
this method elects a Smith Set winner different to the one the IB algorithm
does.


Regards,



Etjon
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