Re: [EM] Election-Methods Digest, Vol 207, Issue 3
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:
-
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.
-
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.
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@hotmail.com
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@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@hotmail.com
Election-Methods mailing list - see https://electorama.com/em for list
info
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@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@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@hotmail.com
Election-Methods mailing list - see https://electorama.com/em for list
info
Election-Methods mailing list - see https://electorama.com/em for list
info
Hi Steve,
From: Steve Bosworth
TO: Kevin Venzke
Kevin Venzke wants to replace Top Two Primaries.
I would say Rob wants to replace the current top-two primary, and I want to argue for
non-eliminative two-round (NETR) methods.
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)?
I think it's better to have a primary as part of the method, than to leave it out and have
parties determine privately which candidates they want to nominate. (They will probably do it to
some extent in any case, but perhaps they will do less of it if the method handles it well.)
There are certainly single-round methods that I think are good, which in theory they can handle
any number of candidates.
But I feel very suspicious that a lot of voters fixate on their favorite candidates only, and
will vote as though they are confident that these candidates will win. Or, that they are just
indifferent to the result if they don't win.
(This will cause at least the appearance of a chicken dilemma within a party. But CD discussions
tend to assume that the voters understand that they are participants in such a dilemma. I'm not
at all sure that voters will actually see their situation in such a way.)
If this is the case, how do we account for this in a design? Basic approaches:
- Parties privately determine ahead of the election who should be nominated, so that voters
have fewer choices in the single-round election. - The method has two rounds, and in the final round voters have perhaps only two options left.
- The method has two rounds, but the second round doesn't remove any options. Instead, try to
get voters to focus on defeating a specific candidate, that they may not like, who is "likely
to win."
This third one is untested, of course.
Kevin
On 10.10.2021 22:11, Kevin Venzke wrote:
Hi Steve,
From: Steve Bosworth
TO: Kevin Venzke
Kevin Venzke wants to replace Top Two Primaries.
I would say Rob wants to replace the current top-two primary, and I want to argue for
non-eliminative two-round (NETR) methods.
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)?
I think it's better to have a primary as part of the method, than to leave it out and have
parties determine privately which candidates they want to nominate. (They will probably do it to
some extent in any case, but perhaps they will do less of it if the method handles it well.)
I mentioned this privately to Forest, but I suppose I could do so here
too. James Green-Armytage has suggested a "semi-eliminative" method
where candidates may withdraw between rounds. His paper is here:
http://jamesgreenarmytage.com/dodgson.pdf
Apparently, when combined with a last resort IRV-style elimination (if
nothing changes between rounds), and assuming that a certain type of
strategy is not often executed, it has better strategy resistance than
plain eliminative Condorcet methods.
Perhaps this kind of mechanism could also be applied to Approval-style
runoffs? Candidate withdrawal might not appear to make much of a
difference to Approval ballots since they technically pass IIA, but
since the voters may alter their ballots between rounds, that's not a
problem.
It may not help in a Burr dilemma if the voters err too much towards the
center candidate, because the center candidate would claim support and
ask the wing candidate to withdraw (and definitely wouldn't withdraw,
himself), but if the voters err the other way, then the wing candidate
might drop out in the second round to stop the greater evil from winning.
-km