[EM] Median systems, branding, and activism strategy

Jameson Quinn jameson.quinn at gmail.com
Wed Jun 12 15:40:32 PDT 2013

2013/6/12 Richard Fobes <ElectionMethods at votefair.org>

> On 6/12/2013 7:55 AM, Jameson Quinn wrote:
>>       ... (As far as I know, MJ can only be expressed in one
>>       way).  ...
> I wrote the following brief description of Majority Judgment.  Is this
> correct?  If so, perhaps it's useful?
> "Starting with any candidate, count the number of voters who give this
> candidate the lowest score.   If the count is more than half the voters,
> then the candidate is given this score.   If the count is less than half
> the voters, the number of voters who assign the next-higher score is added,
> and the process is repeated until the count exceeds half the voters.
> Repeat this process to identify each candidate's 'median' score.
> Whichever candidate has the highest median score is the winner.
> Frequently two or more candidates have the same median score, so the tie is
> broken by removing ballots one at a time as needed, where the removed
> ballots are the ones that assign the same median score to the tied
> candidates."

Right, that's a good description of MJ. And my point was, any description
of MJ will use essentially those same words, or equivalent ones, for the
tiebreaker. On the other hand, GMJ can be described without a separate
tiebreaker step, in three separate ways:
1. Count the votes at the highest grade for each candidate. If any one
candidate has a majority, they win. If not, add in lower grades, one at a
time, until some candidate or candidates get a majority. If two candidates
would reach a majority at the same grade level, add the votes at that level
in a graduated manner; that is, first add 10% of all votes at that grade to
each candidate, then 20%, stopping when exactly one candidate has reached a
majority; that candidate wins.
For the purposes of reporting results, a candidate's score is the grade
level they reached a majority at, plus one half, minus the fraction of the
votes at that level which it took to reach a majority. (This is the same
number as the formula below gives.)
2. Calculate (median + (V> - V<) / (V= * 2)) for each candidate. The
highest score wins. V>, V<, and V= represent the number of votes above,
below, and at the median, respectively.
(If V= is zero, then (V> - V<) will also be zero by the definition of
"median", so in that case you can assume that V= is 1, or any other
non-zero number, to avoid division-by-zero problems.)
3. For each candidate, graph the cumulative grade distribution using
rectangles for each grade that meet at the corners. Draw a single line that
goes diagonally across each of the rectangles. The candidate who's line is
highest at the 50% mark is the winner. (This explanation makes more sense
if you see an example).

Note that all of these descriptions do essentially the same thing whether
or not there's a tie. In description one there's an aspect of "go back and
do it slowly", but not "try something completely different" as with MJ.


> (I'm aware that the description does not specify which score is used if
> the median lands on a transition point.  The purpose of this description is
> just to introduce the general concept.)
> Richard Fobes
> ----
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