[EM] Public Proposal Verbiage
robert bristow-johnson
rbj at audioimagination.com
Tue May 31 06:58:08 PDT 2022
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 at 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
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