# [EM] Election-Methods Digest, Vol 207, Issue 3

Forest Simmons forest.simmons21 at gmail.com
Tue Oct 5 16:31:57 PDT 2021

```Steve,

Great questions and suggestion!

However, in some venues not every voter has the patience to grade
potentially dozens if not hundreds of candidates as in past California
governor recall elections which were plenty cumbersome with FPTP style
ballots (which should have been voted and tallied under Approval rules). In
that context many more voters will have enough patience to vote in the
final round.

In my opinion MJ is a great improvement on most Cardinal Ratings/Score
based methods, but the certainty of tied median grades is a drawback
despite its signature clever method for resolving such ties.

A closely related but more robust method invented by Andy Jennings makes
ties vanishingly rare while preserving all of the advantages of MJ
including use of familiar, easy to understand grade style ballots with
minimal strategic incentive for grade inflation/exaggeration.

The voter instructions and other features of the voter interface
environment for Jennings' method are identical to those of MJ.

The method is called Chiastic Approval  (XA) because of an X shaped (i.e.
Chi shaped) graphical interpretation showing how MJ, Approval, and XA are
related to the candidates' grade distributions.

[Those distributions are discontinuous graphs that stair step down through
the six grade levels. A vertical line through the middle of such a graph
crosses at the midrange approval cutoff point between acceptable and poor.
An horizontal line through the middle of the graph crosses it at the median
... which illustrates the ambiguity of the median, since an horizontal line
will either miss the stair stepping graph entirely, or will intersect it
along an entire line segment. On the other hand, a diagonal line of unit
slope will cross the graph at precisely one point .. at the instant it
crosses from below to above the graph. The descending distribution graph
and the ascending diagonal line (segment) form the shape of the Greek
letter chi.]

It is pleasant for election geeks to contemplate such schematic diagrams,
but the beauty will be lost on anybody else ... best to save it for those
who might appreciate it :-)

The algebraic representation will be even more of an imposition ... best to
shred any  reference to it except as documentation of the software:

The distribution function F whose graph forms the descending staircase
alluded to above is defined as follows:

F(x) is the percentage of ballots that rate  candidate C greater than or
equal to x ... as x increases F(x) decreases.

So the chiastic approval of candidate C is the greatest value of x such
F(x) is no greater than x.

Putting it all together we have ...

The chiastic approval for candidate C is the greatest value of x such that
x is less than or equal to the percentage of ballots that rate (i.e. grade)
candidate C at or above x.

I warned you!

How many of you understand the Huntingto-Hill method of apportionment? Yet
that is the official method for determining how many representatives each
state gets in Congress and the Electoral College. And people trust in it
unquestioningly just as they implicitly trust the medical pharmaceutical
complex.

Chiastic Approval is arguably easier to explain than MJ except perhaps at a
superficial level that avoids the tie breaking details of MJ.

Once you understand the beauty and efficiency of both Chiastic Approval and
Approval Sorted Margins it becomes apparent that no Condorcet compliant
deterministic social order (single winner order of finish) can surpass
XASM,  Chiastic Approval Sorted Margins, IMHO:-)

Forest

El mar., 5 de oct. de 2021 11:33 a. m., steve bosworth <
stevebosworth at hotmail.com> escribió:

>
> Today's Topics: Replacing Top Two primaries
>
> From: Steve Bosworth
> TO: Kevin Venzke
>
> Kevin Venzke wants to replace Top Two Primaries.
>
> Could not the objections to top two primaries be optimally satisfied by
> removing such primaries altogether, and instead electing the winner in the
> general election by using Majority Judgment (MJ)?  Regardless of the
> number of candidates, MJ guarantees that the winner has received the
> highest median grade from at least 50% plus 1 of all the ballots cast. As
> you know, MJ invites each voter to judge the suitability for office of at
> least one of the candidates as either Excellent (*ideal*), Very Good,
> Good, Acceptable, Poor, or Reject (*entirely unsuitable*). Voters may
> give the same grade to any number of candidates. Each candidate who is not
> explicitly graded is counted as a ‘Reject’ by that voter. As a result, all
> candidates have the same number of evaluations but a different set of
> grades awarded from all voters. The MJ winner is the one who receives an
> absolute majority of all the grades equal to, or higher than, the highest *median
> grade* given to any candidate. This median grade can be found as follows:
>
>    1.
>
>    Place all the grades given to each candidate, high to low, left to
>    right in a row, with the name of each candidate on the left of each row.
>    2.
>
>    The median grade for each candidate is in the middle of each row.
>    Specifically, the middle grade for an odd number of voters, or the grade on
>    the right in the middle for an even number of voters.
>    3.
>
>    The winner is the candidate with the highest median grade. If more
>    than one candidate has the same highest median grade, remove the current
>    median grade from each tied candidate and start again at step 1 with those
>    tied candidates.
>
>    4. What do you think?
>    5. Steve Bosworth (stevebosworth at hotmail.com
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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