Re: [EM] Public Proposal Verbiage
The neologism that I am promoting is:"Consistent Majority Candidate".Better than "Beats-all winner" or "Pairwise Champion".Powered by Cricket Wireless------ Original message------From: Colin ChampionDate: Tue, May 31, 2022 2:49 AMTo: election-methods@lists.electorama.com;Cc: Subject:Re: [EM] Public Proposal Verbiage
I’m sorry to say that I
don't like Dasgupta and Maskin’s terminology at all - I think it's
a trick to persuade readers that they've already signed up for the
Condorcet Principle when they signed up for the Majority
Criterion. I agree that "Condorcet winner" sounds forbiddingly
esoteric to the layman - I sometimes consider "outright winner" as
a more down-to-earth term.
Forest's definition is concise and avoids reference fo matrices
of defeat margins and similar machinery, but I'm not sure if that
makes it any easier to understand since the conceptual level is
quite high.
Colin
On 31/05/2022 05:23, Forest Simmons
wrote:
Preface:
In a March 2004 Scientific American article
entitled, "The Fairest Vote of All," Partha Dasgupta and Eric
Maskin (now a Nobel Laureate) argued persuasively for their
conception of a "True Majority Winner" of a single winner
election based on ranked choice ballots.
Taking for granted the Majority Criterion that
mandates electing the candidate that outranks all of the other
candidates on more than half of the ballots (when there is
such a candidate), they propose that when there is no such
candidate, when possible they at least keep this less
demanding but crucial property of a Majority top ranked
candidate: such a candidate outranks any competitor on more
ballots than not.
Why not say, "on more than half of the ballots"
instead of "more ballots than not"?
Because voters are not required to rank all of
the candidates. Indeed, some voters may simply "bullet vote"
for their favorite, while leaving the other candidates
unranked or "truncated."
The dictionary definition of "majority" is
flexible enough to include this usage of "more than not," so
Dasgupta and Maskin's "True Majority Winner" terminology is
perfectly acceptable to Webster, Cambridge, OED, etc.
Their Scientific American article briefly
alluded to the rare public election possibility where a ballot
set might yield neither a "more than half" first place
majority winner nor a (less demanding) True Majority Winner.
It was not the purpose of their article to
prescribe a course of action to cover that rare case, since
they were not making a proposal for a specific election method
to be adopted and written into law for some specific
democratic electorate.
Their purpose was to expound and publicize to
the broader scientific community and other interested citizens
a principle that has been respected among social choice
thinkers at least since the time of Ramón Llull of twelfth
century Spain.
We now pick up where they left off with a
proposal for how to decide the winner in the case of no True
Majority Winner (TMW).
For ease of reference we repeat (my wording of)
the Dasgupta/Maskin definition of True Majority Winner, namely
a candidate that outranks every competitor on more ballots
than not.
Also, "bullet ballot" ... a ballot that
truncates after its top choice.
We also need the concept of a "ballot superset:"
In the current context it is a ballot set augmented with a
number of bullet ballots to gauge how far away a ballot set is
from having a True Majority Winner.
Our idea is to complete the quest for a True
Majority Winner by augmenting the given ballot set with the
bare minimum of bullet ballots to ensure the existence of a
True Majority Winner for the augmented ballot set. In other
words, we elect the candidate closest to being a TMW when
there is no TMW.
So here it is:
If the submitted set of marked ballots does not
have a True Majority Winner (i.e. a candidate that outranks
each opponent on more ballots than not), then elect the True
Majority Winner of the smallest ballot superset that does have
a True Majority Winner.
The above description completely and decisively
defines the winner without recommending one procedure over
another for tallying the submitted ballots.
There are many possible counting procedures,
(some more efficient than others) but any that require
multiple passes through the ballot set (as do elimination
methods like Instant Runoff) are inefficient, hence to be
avoided.
One efficient procedure is to immediately (at
the precinct level) summarize each ballot in the form of a
table with K rows and K columns, where K is the number of
candidates. The i_th entry in the j_th row of the table is a
one or zero depending on whether or not candidate j outranks
candidate i on the ballot being tabulated.
Once a ballot is converted to this K by K
tabular format it can be added in to the precinct total. In
turn the precinct totals are added together at some central
location to arrive at a grand total table T.
Apparently the i_th entry in the j_th row of
table T is the number of ballots on which candidate j outranks
candidate i.
Similarly, the
i_th entry in the j_th column of table T is the number of
ballots on which candidate i outranks candidate j.
Therefore, when we subtract the corresponding
elements of the j_th column from the j_th row we get a new
table D in which the i_th entry of the j_th row is the
difference between the number of ballots on which j out ranks
i and the number of ballots on which i outranks j.
If this difference is positive, then candidate
j outranks candidate i on more ballots than not.
Therefore, if the j_th row of D has all positive
differences, then candidate j is the True Majority Candidate.
If there is no such row j with all positive
entries, find the row j that needs the least multiple of the
"bullet row" added to it in order to wipe out all of its (row
j's) negative entries.
A bullet ballot row consists entirely of ones:
[1, 1, ..., 1].
This row j identifies the True Majority Winner
of the ballot set that has been augmented with the minimum
number of bullet ballots to achieve a TMW ... in ther words
the candidate closest to being a TMW of the original ballot
set.
Don't worry about the details of this tally
procedure .. that's for trained election officials to learn.
But do take note that a methodical method involving mostly
copying and adding of table entries (derived from ranked
ballots) with a subtraction of table columns from
corresponding table rows is all there is before determining
how many bullet ballot rows are need to wipe out all of the
negatives from one row ... just methodical use of arithmetic
... for someone equipped with an adding machine to worry
about.
Questions?
Suggestions for improved exposition?
Gripes?
Thanks!
-Forest
----
Election-Methods mailing list - see https://electorama.com/em for list info
I agree with all your sentiments, and will convert to Consistent Majority
Candidate (or Champion).
I'm very satisfied with the method definition, but not so much with the
suggested tally procedure.
I have some ideas ... along the lines of on stage hand counts..n
El mar., 31 de may. de 2022 6:58 a. m., robert bristow-johnson <
rbj@audioimagination.com> escribió:
The neologism that I am promoting is:
"Consistent Majority Candidate".
Better than "Beats-all winner" or "Pairwise Champion".
Powered by Cricket Wireless
------ Original message------
*From: *Colin Champion
*Date: *Tue, May 31, 2022 2:49 AM
*To: *election-methods@lists.electorama.com;
*Cc: *
*Subject:*Re: [EM] Public Proposal Verbiage
I’m sorry to say that I don't like Dasgupta and Maskin’s terminology at
all - I think it's a trick to persuade readers that they've already signed
up for the Condorcet Principle when they signed up for the Majority
Criterion. I agree that "Condorcet winner" sounds forbiddingly esoteric to
the layman - I sometimes consider "outright winner" as a more down-to-earth
term.
Forest's definition is concise and avoids reference fo matrices of
defeat margins and similar machinery, but I'm not sure if that makes it any
easier to understand since the conceptual level is quite high.
Colin
On 31/05/2022 05:23, Forest Simmons wrote:
Preface:
In a March 2004 Scientific American article entitled, "The Fairest Vote
of All," Partha Dasgupta and Eric Maskin (now a Nobel Laureate) argued
persuasively for their conception of a "True Majority Winner" of a single
winner election based on ranked choice ballots.
Taking for granted the Majority Criterion that mandates electing the
candidate that outranks all of the other candidates on more than half of
the ballots (when there is such a candidate), they propose that when there
is no such candidate, when possible they at least keep this less demanding
but crucial property of a Majority top ranked candidate: such a candidate
outranks any competitor on more ballots than not.
Why not say, "on more than half of the ballots" instead of "more ballots
than not"?
Because voters are not required to rank all of the candidates. Indeed,
some voters may simply "bullet vote" for their favorite, while leaving the
other candidates unranked or "truncated."
The dictionary definition of "majority" is flexible enough to include this
usage of "more than not," so Dasgupta and Maskin's "True Majority Winner"
terminology is perfectly acceptable to Webster, Cambridge, OED, etc.
Their Scientific American article briefly alluded to the rare public
election possibility where a ballot set might yield neither a "more than
half" first place majority winner nor a (less demanding) True Majority
Winner.
It was not the purpose of their article to prescribe a course of action to
cover that rare case, since they were not making a proposal for a specific
election method to be adopted and written into law for some specific
democratic electorate.
Their purpose was to expound and publicize to the broader scientific
community and other interested citizens a principle that has been respected
among social choice thinkers at least since the time of Ramón Llull of
twelfth century Spain.
We now pick up where they left off with a proposal for how to decide the
winner in the case of no True Majority Winner (TMW).
For ease of reference we repeat (my wording of) the Dasgupta/Maskin
definition of True Majority Winner, namely a candidate that outranks every
competitor on more ballots than not.
Also, "bullet ballot" ... a ballot that truncates after its top choice.
We also need the concept of a "ballot superset:" In the current context it
is a ballot set augmented with a number of bullet ballots to gauge how far
away a ballot set is from having a True Majority Winner.
Our idea is to complete the quest for a True Majority Winner by augmenting
the given ballot set with the bare minimum of bullet ballots to ensure the
existence of a True Majority Winner for the augmented ballot set. In other
words, we elect the candidate closest to being a TMW when there is no TMW.
So here it is:
If the submitted set of marked ballots does not have a True Majority
Winner (i.e. a candidate that outranks each opponent on more ballots than
not), then elect the True Majority Winner of the smallest ballot superset
that does have a True Majority Winner.
The above description completely and decisively defines the winner without
recommending one procedure over another for tallying the submitted ballots.
There are many possible counting procedures, (some more efficient than
others) but any that require multiple passes through the ballot set (as do
elimination methods like Instant Runoff) are inefficient, hence to be
avoided.
One efficient procedure is to immediately (at the precinct level)
summarize each ballot in the form of a table with K rows and K columns,
where K is the number of candidates. The i_th entry in the j_th row of the
table is a one or zero depending on whether or not candidate j outranks
candidate i on the ballot being tabulated.
Once a ballot is converted to this K by K tabular format it can be added
in to the precinct total. In turn the precinct totals are added together at
some central location to arrive at a grand total table T.
Apparently the i_th entry in the j_th row of table T is the number of
ballots on which candidate j outranks candidate i.
Similarly, the i_th entry in the j_th column of table T is the number of
ballots on which candidate i outranks candidate j.
Therefore, when we subtract the corresponding elements of the j_th column
from the j_th row we get a new table D in which the i_th entry of the j_th
row is the difference between the number of ballots on which j out ranks i
and the number of ballots on which i outranks j.
If this difference is positive, then candidate j outranks candidate i on
more ballots than not.
Therefore, if the j_th row of D has all positive differences, then
candidate j is the True Majority Candidate.
If there is no such row j with all positive entries, find the row j that
needs the least multiple of the "bullet row" added to it in order to wipe
out all of its (row j's) negative entries.
A bullet ballot row consists entirely of ones: [1, 1, ..., 1].
This row j identifies the True Majority Winner of the ballot set that has
been augmented with the minimum number of bullet ballots to achieve a TMW
... in ther words the candidate closest to being a TMW of the original
ballot set.
Don't worry about the details of this tally procedure .. that's for
trained election officials to learn. But do take note that a methodical
method involving mostly copying and adding of table entries (derived from
ranked ballots) with a subtraction of table columns from corresponding
table rows is all there is before determining how many bullet ballot rows
are need to wipe out all of the negatives from one row ... just methodical
use of arithmetic ... for someone equipped with an adding machine to worry
about.
Questions?
Suggestions for improved exposition?
Gripes?
Thanks!
-Forest
Election-Methods mailing list - see https://electorama.com/em for list info
Election-Methods mailing list - see https://electorama.com/em for list
info
On 05/31/2022 1:07 PM Forest Simmons forest.simmons21@gmail.com wrote:
I agree with all your sentiments, and will convert to Consistent Majority Candidate (or Champion).
I'm very satisfied with the method definition, but not so much with the suggested tally procedure.
The method definition should simply be:
...
(3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The candidate, who is the Condorcet winner, is elected if the rankings on all of the ballots indicate that this one candidate defeats, with a simple majority of voter preferences, every other candidate when compared in turn with each other individual candidate. A selected candidate defeats another candidate by a simple majority when the number of ballots marked ranking the selected candidate higher than the other candidate exceeds the number of ballots marked to the contrary.
(4) If no Condorcet winner exists in subdivision (3), then the candidate having the plurality of first preferences is elected.
...
This can be made more explicit:
...
(3) If no candidate receives a majority of first preferences, a Condorcet-consistent retabulation shall be performed by the presiding election officer. The retabulation shall examine every possible pairing of candidates. Given N as the number of candidates, then the number of possible pairings of candidates is N(N-1)/2. If the number of ballots marked ranking a selected candidate over the other candidate exceeds the number of ballots marked to the contrary, then the other candidate is declared defeated. After all candidate pairings are examined, the candidate who remains not declared defeated is the Condorcet winner and is elected.
(4) If no Condorcet winner exists in subdivision (3), then the candidate having the plurality of first preferences is elected.
...
Tomorrow, I get to meet Howard Dean again (since he ran for prez in 2004) and tell him why I quoted him in my paper https://tinyurl.com/2tety9tj and tell him why his claim that I quoted is technically wrong.
The RCV reform effort in Vermont is close to dead, but not quite dead yet.
L8r,
robert
I have some ideas ... along the lines of on stage hand counts..n
El mar., 31 de may. de 2022 6:58 a. m., robert bristow-johnson rbj@audioimagination.com escribió:
The neologism that I am promoting is:
"Consistent Majority Candidate".
Better than "Beats-all winner" or "Pairwise Champion".
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
El mar., 31 de may. de 2022 12:32 p. m., robert bristow-johnson <
rbj@audioimagination.com> escribió:
On 05/31/2022 1:07 PM Forest Simmons forest.simmons21@gmail.com wrote:
I agree with all your sentiments, and will convert to Consistent
Majority Candidate (or Champion).
I'm very satisfied with the method definition, but not so much with the
suggested tally procedure.
The method definition should simply be:
...
(3) If no candidate receives a majority of first preferences, a
Condorcet-consistent retabulation shall be performed by the presiding
election officer. The candidate, who is the Condorcet winner, is elected if
the rankings on all of the ballots indicate that this one candidate
defeats, with a simple majority of voter preferences, every other candidate
when compared in turn with each other individual candidate. A selected
candidate defeats another candidate by a simple majority when the number of
ballots marked ranking the selected candidate higher than the other
candidate exceeds the number of ballots marked to the contrary.
(4) If no Condorcet winner exists in subdivision (3), then the candidate
having the plurality of first preferences is elected.
...
This can be made more explicit:
...
(3) If no candidate receives a majority of first preferences, a
Condorcet-consistent retabulation shall be performed by the presiding
election officer. The retabulation shall examine every possible pairing of
candidates. Given N as the number of candidates, then the number of
possible pairings of candidates is N(N-1)/2. If the number of ballots
marked ranking a selected candidate over the other candidate exceeds the
number of ballots marked to the contrary, then the other candidate is
declared defeated. After all candidate pairings are examined, the candidate
who remains not declared defeated is the Condorcet winner and is elected.
(4) If no Condorcet winner exists in subdivision (3), then the candidate
having the plurality of first preferences is elected.
Another way to say (4) is ...
If no Condorcet winner exists in subdivision (3), then elect the candidate
requiring the fewest additional first place votes to become the first place
Majority winner.
My proposal is to change it to ...
(4) If no Condorcet winner exists in subdivision (3), then elect the
candidate requiring the fewest additional first place votes to become the
Condorcet winner.
...
Tomorrow, I get to meet Howard Dean again (since he ran for prez in 2004)
and tell him why I quoted him in my paper https://tinyurl.com/2tety9tj
and tell him why his claim that I quoted is technically wrong.
The RCV reform effort in Vermont is close to dead, but not quite dead yet.
L8r,
robert
I have some ideas ... along the lines of on stage hand counts..n
El mar., 31 de may. de 2022 6:58 a. m., robert bristow-johnson <
rbj@audioimagination.com> escribió:
The neologism that I am promoting is:
"Consistent Majority Candidate".
Better than "Beats-all winner" or "Pairwise Champion".
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
Election-Methods mailing list - see https://electorama.com/em for list
info