[EM] Fixing IRV

[Roy One]

Much has been made of the flaws of IRV. Notably, that it fails to
find
the Condorcet winner when there is one, which casts serious doubt on
its claim of supporting majority rule.

I think we all know the source of the flaw: it doesn't use majority
rule in elimination rounds. It uses (anti-)plurality. WHY???
Proponents seem to have a great attachment to the notion of using
only
the first place votes. Of course, by eliminating the anti-plurality
choice, they've eliminated a majority of people's lower choices
before
they ever had a chance to be considered.

There is a better way to eliminate candidates, based on majority
rule:
eliminate the candiate with the lowest median rank. The median rank
is
the level at which half consider the candidate that high or higher,
and half consider him that low or lower. (If you like, you can take
the vote after the median vote, for a true, minimal majority.)

A similar method would be to eliminate all candidates whose median
rank is not in the top half -- i.e., a majority of people believe
those candidates should be ranked in the bottom half. It works a
little faster, and in my (admittedly rather limited) testing, has
always resulted in the same winner as Ranked Pairs.

Notes: if the median point is, say 1.5 (because there are 3
candidates), count half of the 2nd place votes as well as all of the
1st place votes for each candidate. If candidates can be ranked equal
to each other, they all get ranked as the average of the positions
they span, e.g., if 2 candidates tie for 2nd, they each rank 2.5; if
3
share 2nd, they each get ranked 3rd. Similarly as before, half of the
between-value votes count toward the rank a half-step up (half of
2.5's count toward a candidate's being in the top two). In case all
candidates are equally divided in the top N spots, consider the
median value of only those votes and discard the lowest.

Wouldn't it be nice if a system with the support of IRV could be
patched to make it Condorcet-compliant?

Roy Johnson


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