[EM] MJ rules expressed in Bucklin terminology

Jameson Quinn jameson.quinn at gmail.com
Sat Jul 21 10:56:38 PDT 2012

I like median-based methods; I think they have the best balance between
strategy-resistance and sensitivity of any non-delegated methods. Among the
median-based methods, Majority Judgment is the most well-known of the
well-defined methods[1]. Yet when you express it as "median grade with a
tiebreaker", people's eyes glaze over. So here's an attempt to express MJ
as a Bucklin-like process:

Voters grade candidates on a familiar nominal scale (such as A,B,C,D,F for
US voters). Start with only A votes; add in B, then C, etc, until one or
more candidates have over 50%. If just one candidate passed the 50%
threshold, they win. Otherwise, for all candidates with over 50% at or
above the threshold, make two tallies for all the votes strictly above, and
for those strictly below, the threshold. Of all those tallies, choose the
highest. If it is a count of votes strictly above the threshold, then that
candidate wins. If it is a count of votes below, then that candidate is
eliminated from the tie, and the procedure is repeated if necessary until
one candidate is left.

I'm sure this wording could be improved somewhat, but I think it's
reasonably understandable as it is. Comments or suggestions?


[1] In fact, there aren't too many well-defined methods among the
median-based ones. "Bucklin" is really just an ill-defined soup. So I can
really only think of two other specific median methods worth mentioning:

   - MCA: Ballots rate each candidate Preferred, Approved, or Rejected.
   Higest majority preferred wins; if no majority preferred, highest
   (preferred + approved) wins.
   - What I call "Real-valued Majority Judgment" (RVMJ): Assign each
   candidate the score of

(median rating) + ((votes above median) - (votes below median)) / (2 *
(votes at median))

Highest score wins. This score is within 0.5 of the median; and the result
is strictly equivalent as if you used the score:

(median rating) + ((votes above median) - (votes below median)) / ((votes
at median) + abs((votes above median) - (votes below median)))

which in turn is usually equivalent to the narrowest symmetrically-trimmed
mean which includes all the votes at the median. (They are the same as long
as the trimmed mean only includes votes at the median and one neighboring
rating, which will usually be true, unless the "slope" of the cumulative
grade distribution is somehow unusually uneven inside the narrow central
"trimmed" region)

I personally like RVMJ better than MJ, but MJ is more famous and the
difference is tiny, so I'm happy to chalk myself up as an MJ supporter.
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