[EM] Election-Methods Digest, Vol 88, Issue 39

[Jameson Quinn]

Kathy:

Below is the explanation of Majority Judgment from Wikipedia. I agree that
it is not the simplest tiebreaker; actually, in the thread "majority
judgement question", there's a discussion of some simpler tiebreakers. All
of the proposed tiebreakers would tend to give the same results almost
always; the underlying idea is to take a median, which is usually one of the
options given, and see "how close it is" to being higher or lower.

Anyway, here's Wikipedia:
Example application

[image: Tennessee and its four major cities: Memphis in the south-west;
Nashville in the centre, Chattanooga in the south, and Knoxville in the
east]<http://en.wikipedia.org/wiki/File:Tennessee_map_for_voting_example.svg>

Imagine that Tennessee <http://en.wikipedia.org/wiki/Tennessee> is having an
election on the location of its
capital<http://en.wikipedia.org/wiki/Capital_(political)>.
The population of Tennessee is concentrated around its four major cities,
which are spread throughout the state. For this example, suppose that the
entire electorate <http://en.wikipedia.org/wiki/Constituency> lives in these
four cities, and that everyone wants to live as near to the capital as
possible.

The candidates for the capital are:

   - Memphis <http://en.wikipedia.org/wiki/Memphis,_Tennessee>, the state's
   largest city, with 42% of the voters, but located far from the other cities
   - Nashville <http://en.wikipedia.org/wiki/Nashville,_Tennessee>, with 26%
   of the voters, near the center of Tennessee
   - Knoxville <http://en.wikipedia.org/wiki/Knoxville,_Tennessee>, with 17%
   of the voters
   - Chattanooga <http://en.wikipedia.org/wiki/Chattanooga,_Tennessee>, with
   15% of the voters

The preferences of the voters would be divided like this:
 42% of voters
(close to Memphis) 26% of voters
(close to Nashville) 15% of voters
(close to Chattanooga) 17% of voters
(close to Knoxville)

   1. *Memphis*
   2. Nashville
   3. Chattanooga
   4. Knoxville


   1. *Nashville*
   2. Chattanooga
   3. Knoxville
   4. Memphis


   1. *Chattanooga*
   2. Knoxville
   3. Nashville
   4. Memphis


   1. *Knoxville*
   2. Chattanooga
   3. Nashville
   4. Memphis

If there were four ratings named "Excellent", "Good", "Fair", and "Poor",
and each voter assigned four different ratings to the four cities, then the
sorted scores would be as follows:
City    ↓ Median pointNashville  Chattanooga  Knoxville   Memphis
  Excellent     Good    Fair    Poor

The median rating for Nashville and Chatanooga is "Good"; for Knoxville,
"Fair"; and for Memphis, "Poor". Nashville and Chatanooga are tied, so
"Good" ratings have to be removed from both, until their medians become
different. After removing 16% "Good" ratings from the votes of each, the
sorted ratings are now:
City    ↓ Median pointNashville   Chattanooga
 Removed ratings (sorted to both ends evenly for easy comparison of
medians with above).

Chatanooga now has the same number of "Fair" ratings as "Good" and
"Excellent" combined, so its median is rounded down to "Fair", while
Nashville's median remains at
"Good"[7]<http://en.wikipedia.org/wiki/Majority_Judgment#cite_note-6>
and
so *Nashville*, the capital in real life, wins.

If voters from Knoxville and Chattanooga were to rate Nashville as "Poor"
and/or both sets of voters were to rate Chattanooga as "Excellent", in an
attempt to make their preferred candidate Chatanooga win, the winner would
still be Nashville.

2011/10/19 Kathy Dopp <kathy.dopp at gmail.com>

> >   3. Re: Declaration Status
>
> I still don't fully understand this statement:
>
> Majority Judgment ... If there is a tie for first place, the method
> repeatedly removes one median score from each tied candidate until the
> tie is broken.
>
> My question is: How is the one median score selected to be removed
> from each tied candidate? And why is this a good tie-breaking method?
>
> Thanks.
>
> Kathy Dopp
> http://electionmathematics.org
> Town of Colonie, NY 12304
> "One of the best ways to keep any conversation civil is to support the
> discussion with true facts."
> "Renewable energy is homeland security."
>
> Fundamentals of Verifiable Elections
> http://kathydopp.com/wordpress/?p=174
>
> View some of my research on my SSRN Author page:
> http://ssrn.com/author=1451051
> ----
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>
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