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

[Ted Stern]

X-ASM! I like it.

I'll see if I can modify my ASM code to do X-ASM as well. Should be a small
change.

On Tue, Oct 5, 2021 at 4:32 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> 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
>>
>>
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