Covering Embarrassment
Have you every had one of those dreams where you are out in public and
suddenly notice that you are unclothed?
Well, nearly all election methods, Condorcet or not, that are either now in
use, or have been seriously proposed, suffer from the opposite problem:
they have no guarantee against electing covered candidates.
How (outside of a nudist colony) could that be a problem?
Well, suppose candidate A wins an RCV election of some kind, and the
ballots clearly show that candidate B outranks candidate A on a majority of
the ballots, but B is not head-head defeated by any candidate that A
defeats.
In other words, A wins, but A is covered (by B for example). Wouldn't that
embarrass A?
The B supporters would be more indignant, vociferous, and sarcastic than
even Trump, (unless B were like a spineless Gore, who capitulated without a
peep).
Why hasn't anybody addressed this elephant-in-the-room potential
embarrassment?
Answer: for the simple reason that up until very recently, the only known
monotonic RCV method immune to this embarrassment was Copeland, a clone
dependent method lacking a lot in decisiveness.
The first RCV method to decisively crack this barrier (earlier this year)
was Decloned KY Chain Climbing ... nice theoretically, but too esoteric for
public proposal.
More recently, and more practically, Kristofer and I have introduced
(without fanfare) a class of short beatpath methods that always elect
uncovered candidates monotonically and clone-free from RCV ballot sets.
Within that class, methods differ by different gauges of defeat strength,
in the same way that different versions of Ranked Pairs differ among
themselves.
My purpose in this post is not to propound any particular uncovered method,
but to give a general recipe for retro-fitting all currently used RCV
methods ... in order to confer upon them Covering Embarrassment Immunity.
Here is the Afterburner procedure for installing that retro-fit:
Initialize X as the (before retro-fit) method winner.
Then ...
While X is covered, replace it with the alternative (from among those that
cover it) with the one defeating it with the greatest defeat strength.
EndWhile
Elect the the final value of X, (i.e.the last candidate pointed at by the
variable X).
[Now you can see our main purpose for initiating our recent Defeat Strength
thread.]
Notice how naturally this "Afterburner" procedure confers Covering
Embarrassment protection onto Ranked Pairs!
It can do the same thing for IRV, Coombs, Borda, Bucklin, Kemeny Young,
DAC, DSC, etc, as well as for non-RCV methods that may admit inference of
ordinal preferences ... such as MJ, STAR, Approval Sorted Margins, DMC,
SPE, etc.
One of my favorites is Afterburner Fitted Usual Judgment (AFUJ), because UJ
by itself has only one serious technical defect ... potential covering
embarrassment.
In particular, the recent IRV embarrassments in Burlington and Alaska would
have harmlessly, and unceremoniously bounced off this shield.
Also, note that an afterburner shield protects against Burlington
embarrassments, but an upfront CW check does not guarantee protection
against covering embarrassment. Afterburner protection is stronger than a
mere CW or Smith check up front ... even IRV restricted to Smith is not
immune to Covering Embarrassment.
So why would anybody resist zero-cost covering embarrassment protection?
Remember back in the 1970's ... the resistance against retro-fitting older
cars with seat belts?
"People will be trapped inside crashed cars!"
Doubtless we wil see the same reactionary attitudes about retro-fitting
current methods with "Covering Immunity Seatbelts."
Will a democracy ever arise on this planet progressive enough to make use
of it?
I'm optimistic about that possibility, but not optimistic enough to think
it will happen absent some kind of major revolution that saves our planet
from utter destruction.
-Forest
On 09/11/2022 6:12 PM EDT Forest Simmons forest.simmons21@gmail.com wrote:
Have you every had one of those dreams where you are out in public and suddenly notice that you are unclothed?
of course.
Well, nearly all election methods, Condorcet or not, that are either now in use, or have been seriously proposed, suffer from the opposite problem: they have no guarantee against electing covered candidates.
Well, now I need a definition of a what or who is "covered".
How (outside of a nudist colony) could that be a problem?
Well, suppose candidate A wins an RCV election of some kind, and the ballots clearly show that candidate B outranks candidate A on a majority of the ballots, but B is not head-head defeated by any candidate that A defeats.
okay, so A pairwise defeats a bunch of candidates that B also does, but B defeats A. Could there be Candidate C that defeats them both, head to head?
In other words, A wins, but A is covered (by B for example). Wouldn't that embarrass A?
well, obviously minority-elected candidates win and are not embarrassed for winning an election. Like both W and the evil T****. They can deny the problem (like this is too complicated) or they can make up and excuse (Montroll or Begich didn't get enough base support)
The B supporters would be more indignant, vociferous, and sarcastic than even Trump, (unless B were like a spineless Gore, who capitulated without a peep).
Why hasn't anybody addressed this elephant-in-the-room potential embarrassment?
????
Answer: for the simple reason that up until very recently, the only known monotonic RCV method immune to this embarrassment was Copeland, a clone dependent method lacking a lot in decisiveness.
The first RCV method to decisively crack this barrier (earlier this year) was Decloned KY Chain Climbing ... nice theoretically, but too esoteric for public proposal.
More recently, and more practically, Kristofer and I have introduced (without fanfare) a class of short beatpath methods that always elect uncovered candidates monotonically and clone-free from RCV ballot sets.
Within that class, methods differ by different gauges of defeat strength, in the same way that different versions of Ranked Pairs differ among themselves.
My purpose in this post is not to propound any particular uncovered method, but to give a general recipe for retro-fitting all currently used RCV methods ... in order to confer upon them Covering Embarrassment Immunity.
Here is the Afterburner procedure for installing that retro-fit:
Initialize X as the (before retro-fit) method winner.
Then ...
While X is covered, replace it with the alternative (from among those that cover it) with the one defeating it with the greatest defeat strength. EndWhile
Elect the the final value of X, (i.e.the last candidate pointed at by the variable X).
[Now you can see our main purpose for initiating our recent Defeat Strength thread.]
Notice how naturally this "Afterburner" procedure confers Covering Embarrassment protection onto Ranked Pairs!
It can do the same thing for IRV, Coombs, Borda, Bucklin, Kemeny Young, DAC, DSC, etc, as well as for non-RCV methods that may admit inference of ordinal preferences ... such as MJ, STAR, Approval Sorted Margins, DMC, SPE, etc.
One of my favorites is Afterburner Fitted Usual Judgment (AFUJ), because UJ by itself has only one serious technical defect ... potential covering embarrassment.
In particular, the recent IRV embarrassments in Burlington and Alaska would have harmlessly, and unceremoniously bounced off this shield.
Also, note that an afterburner shield protects against Burlington embarrassments, but an upfront CW check does not guarantee protection against covering embarrassment. Afterburner protection is stronger than a mere CW or Smith check up front ... even IRV restricted to Smith is not immune to Covering Embarrassment.
So why would anybody resist zero-cost covering embarrassment protection?
Remember back in the 1970's ... the resistance against retro-fitting older cars with seat belts?
"People will be trapped inside crashed cars!"
Doubtless we wil see the same reactionary attitudes about retro-fitting current methods with "Covering Immunity Seatbelts."
Will a democracy ever arise on this planet progressive enough to make use of it?
I'm optimistic about that possibility, but not optimistic enough to think it will happen absent some kind of major revolution that saves our planet from utter destruction.
This being "covered" thing isn't a problem if the Condorcet winner is elected, if a CW exists, is it? Does it manifest when there is a CW?
How many elections do we expect to lack a Condorcet winner? So far, FairVote has looked at, they used to say, 440 U.S. RCV elections, all had a CW, and only one failed to elect the CW. Now there are two anomalous elections, Alaska 2022 and Bulington 2009. So far 100% having CW and 99.6% electing the CW using Hare RCV.
Must we use Copeland if there are easier ways to get the CW elected?
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
On Sun, Sep 11, 2022, 4:05 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 09/11/2022 6:12 PM EDT Forest Simmons forest.simmons21@gmail.com
wrote:
Have you every had one of those dreams where you are out in public and
suddenly notice that you are unclothed?
of course.
Well, nearly all election methods, Condorcet or not, that are either now
in use, or have been seriously proposed, suffer from the opposite problem:
they have no guarantee against electing covered candidates.
Well, now I need a definition of a what or who is "covered".
How (outside of a nudist colony) could that be a problem?
Well, suppose candidate A wins an RCV election of some kind, and the
ballots clearly show that candidate B outranks candidate A on a majority of
the ballots, but B is not head-head defeated by any candidate that A
defeats.
okay, so A pairwise defeats a bunch of candidates that B also does, but B
defeats A.
Not so fast. B covers A only if B not only defeats A, but also B defeats
or ties abdolutely every (not just a "bunch of") candidate defeated by A.
Could there be Candidate C that defeats them both, head to head?
Yes, and if C were the CW then every candidate except C would be covered.
A Condorcet winner is always uncovered, and when there is no Condorcet
winner, at least one member of the Smith set will be uncovered. In general
every non-Smith candidate is covered by every Smith candidate ... the
uncovered set (the "Landau set") is always contained in (sometimes
properly) the Smith set.
In other words, A wins, but A is covered (by B for example). Wouldn't
that embarrass A?
well, obviously minority-elected candidates win and are not embarrassed
for winning an election. Like both W and the evil T****. They can deny
the problem (like this is too complicated) or they can make up and excuse
(Montroll or Begich didn't get enough base support)
The B supporters would be more indignant, vociferous, and sarcastic than
even Trump, (unless B were like a spineless Gore, who capitulated without a
peep).
Why hasn't anybody addressed this elephant-in-the-room potential
embarrassment?
????
Answer: for the simple reason that up until very recently, the only
known monotonic RCV method immune to this embarrassment was Copeland, a
clone dependent method lacking a lot in decisiveness.
The first RCV method to decisively crack this barrier (earlier this
year) was Decloned KY Chain Climbing ... nice theoretically, but too
esoteric for public proposal.
More recently, and more practically, Kristofer and I have introduced
(without fanfare) a class of short beatpath methods that always elect
uncovered candidates monotonically and clone-free from RCV ballot sets.
Within that class, methods differ by different gauges of defeat
strength, in the same way that different versions of Ranked Pairs differ
among themselves.
My purpose in this post is not to propound any particular uncovered
method, but to give a general recipe for retro-fitting all currently used
RCV methods ... in order to confer upon them Covering Embarrassment
Immunity.
Here is the Afterburner procedure for installing that retro-fit:
Initialize X as the (before retro-fit) method winner.
Then ...
While X is covered, replace it with the alternative (from among those
that cover it) with the one defeating it with the greatest defeat strength.
EndWhile
Elect the the final value of X, (i.e.the last candidate pointed at by
the variable X).
[Now you can see our main purpose for initiating our recent Defeat
Strength thread.]
Notice how naturally this "Afterburner" procedure confers Covering
Embarrassment protection onto Ranked Pairs!
It can do the same thing for IRV, Coombs, Borda, Bucklin, Kemeny Young,
DAC, DSC, etc, as well as for non-RCV methods that may admit inference of
ordinal preferences ... such as MJ, STAR, Approval Sorted Margins, DMC,
SPE, etc.
One of my favorites is Afterburner Fitted Usual Judgment (AFUJ), because
UJ by itself has only one serious technical defect ... potential covering
embarrassment.
In particular, the recent IRV embarrassments in Burlington and Alaska
would have harmlessly, and unceremoniously bounced off this shield.
Also, note that an afterburner shield protects against Burlington
embarrassments, but an upfront CW check does not guarantee protection
against covering embarrassment. Afterburner protection is stronger than a
mere CW or Smith check up front ... even IRV restricted to Smith is not
immune to Covering Embarrassment.
So why would anybody resist zero-cost covering embarrassment protection?
Remember back in the 1970's ... the resistance against retro-fitting
older cars with seat belts?
"People will be trapped inside crashed cars!"
Doubtless we wil see the same reactionary attitudes about retro-fitting
current methods with "Covering Immunity Seatbelts."
Will a democracy ever arise on this planet progressive enough to make
use of it?
I'm optimistic about that possibility, but not optimistic enough to
think it will happen absent some kind of major revolution that saves our
planet from utter destruction.
This being "covered" thing isn't a problem if the Condorcet winner is
elected, if a CW exists, is it? Does it manifest when there is a CW?
No, only when there is no CW.
So a simple way to ensure that the CW will always win when there is one, to
apply the "afterburner" to every election as a matter of policy. This
policy ensures more ... it ensures that a Smith candidate will win if there
is one, and that that Smith member will also be a Landau member.
How many elections do we expect to lack a Condorcet winner? So far,
FairVote has looked at, they used to say, 440 U.S. RCV elections, all had a
CW, and only one failed to elect the CW. Now there are two anomalous
elections, Alaska 2022 and Bulington 2009. So far 100% having CW and 99.6%
electing the CW using Hare RCV.
Not every ballot CW is a sincere CW.
In fact, because IRV is so defacto vulnerable to compromise, as well as to
Duverger's Law, voters tend to make up for IRV''s lack of sincere
Condorcet efficiency by both nominating and voting for compromise
candidates ... ballot CW's that are not necessarily sincere CW's.
Must we use Copeland if there are easier ways to get the CW elected?
As I mentioned, Copeland is not a good option, because it is neither
decisive, nor clone free.
That's why a much more practical option is to add a simple, zero cost
"afterburner" that protects any method against Covering Embarrassment.
That said, we now have clean, short beatpath versions of RP that can serve
as stand-alone Landau efficient methods ... the ones mentioned above that
we introduced a few weeks ago ... "without fanfare" ... maybe we should
have hired a brass band:-)
-Forest
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.
For the benefit of people new to the concept of covering, I should point
out that not being covered by A is equivalent to having a beatpath to A of
two or fewer steps. So an "unqualifiedly" uncovered candidate has, for each
candidate X, a short beatpath (fewer than three steps) to X.
The beauty of a short beatpath is its immediacy compared to a longer one
... as the path gets longer it kind of leaks information like the telephone
game.
Note, for example, that a beatpath whose weakest step is a 100%n/(n+1)
defeat cannot cycle in fewer than (n +1) steps ... the stronger the
beatpath, the more steps necessary to lose transitivity. Conversely. the
shorter the beatpath, the more likely the defeats will survive the entire
length of the bestpath.
Notice, in particular, that if B defeats both A and every candidate that A
defeats, then there is no beatpath of length one or two from A to B.
Note also that the covering relation (unlike the ordinary defeat relation)
is transitive: if C covers B, and B covers A, then C also covers A.
-Forest
On Sun, Sep 11, 2022, 5:18 PM Forest Simmons forest.simmons21@gmail.com
wrote:
On Sun, Sep 11, 2022, 4:05 PM robert bristow-johnson <
rbj@audioimagination.com> wrote:
On 09/11/2022 6:12 PM EDT Forest Simmons forest.simmons21@gmail.com
wrote:
Have you every had one of those dreams where you are out in public and
suddenly notice that you are unclothed?
of course.
Well, nearly all election methods, Condorcet or not, that are either
now in use, or have been seriously proposed, suffer from the opposite
problem: they have no guarantee against electing covered candidates.
Well, now I need a definition of a what or who is "covered".
How (outside of a nudist colony) could that be a problem?
Well, suppose candidate A wins an RCV election of some kind, and the
ballots clearly show that candidate B outranks candidate A on a majority of
the ballots, but B is not head-head defeated by any candidate that A
defeats.
okay, so A pairwise defeats a bunch of candidates that B also does, but B
defeats A.
Not so fast. B covers A only if B not only defeats A, but also B defeats
or ties abdolutely every (not just a "bunch of") candidate defeated by A.
Could there be Candidate C that defeats them both, head to head?
Yes, and if C were the CW then every candidate except C would be covered.
A Condorcet winner is always uncovered, and when there is no Condorcet
winner, at least one member of the Smith set will be uncovered. In general
every non-Smith candidate is covered by every Smith candidate ... the
uncovered set (the "Landau set") is always contained in (sometimes
properly) the Smith set.
In other words, A wins, but A is covered (by B for example). Wouldn't
that embarrass A?
well, obviously minority-elected candidates win and are not embarrassed
for winning an election. Like both W and the evil T****. They can deny
the problem (like this is too complicated) or they can make up and excuse
(Montroll or Begich didn't get enough base support)
The B supporters would be more indignant, vociferous, and sarcastic
than even Trump, (unless B were like a spineless Gore, who capitulated
without a peep).
Why hasn't anybody addressed this elephant-in-the-room potential
embarrassment?
????
Answer: for the simple reason that up until very recently, the only
known monotonic RCV method immune to this embarrassment was Copeland, a
clone dependent method lacking a lot in decisiveness.
The first RCV method to decisively crack this barrier (earlier this
year) was Decloned KY Chain Climbing ... nice theoretically, but too
esoteric for public proposal.
More recently, and more practically, Kristofer and I have introduced
(without fanfare) a class of short beatpath methods that always elect
uncovered candidates monotonically and clone-free from RCV ballot sets.
Within that class, methods differ by different gauges of defeat
strength, in the same way that different versions of Ranked Pairs differ
among themselves.
My purpose in this post is not to propound any particular uncovered
method, but to give a general recipe for retro-fitting all currently used
RCV methods ... in order to confer upon them Covering Embarrassment
Immunity.
Here is the Afterburner procedure for installing that retro-fit:
Initialize X as the (before retro-fit) method winner.
Then ...
While X is covered, replace it with the alternative (from among those
that cover it) with the one defeating it with the greatest defeat strength.
EndWhile
Elect the the final value of X, (i.e.the last candidate pointed at by
the variable X).
[Now you can see our main purpose for initiating our recent Defeat
Strength thread.]
Notice how naturally this "Afterburner" procedure confers Covering
Embarrassment protection onto Ranked Pairs!
It can do the same thing for IRV, Coombs, Borda, Bucklin, Kemeny Young,
DAC, DSC, etc, as well as for non-RCV methods that may admit inference of
ordinal preferences ... such as MJ, STAR, Approval Sorted Margins, DMC,
SPE, etc.
One of my favorites is Afterburner Fitted Usual Judgment (AFUJ),
because UJ by itself has only one serious technical defect ... potential
covering embarrassment.
In particular, the recent IRV embarrassments in Burlington and Alaska
would have harmlessly, and unceremoniously bounced off this shield.
Also, note that an afterburner shield protects against Burlington
embarrassments, but an upfront CW check does not guarantee protection
against covering embarrassment. Afterburner protection is stronger than a
mere CW or Smith check up front ... even IRV restricted to Smith is not
immune to Covering Embarrassment.
So why would anybody resist zero-cost covering embarrassment protection?
Remember back in the 1970's ... the resistance against retro-fitting
older cars with seat belts?
"People will be trapped inside crashed cars!"
Doubtless we wil see the same reactionary attitudes about retro-fitting
current methods with "Covering Immunity Seatbelts."
Will a democracy ever arise on this planet progressive enough to make
use of it?
I'm optimistic about that possibility, but not optimistic enough to
think it will happen absent some kind of major revolution that saves our
planet from utter destruction.
This being "covered" thing isn't a problem if the Condorcet winner is
elected, if a CW exists, is it? Does it manifest when there is a CW?
No, only when there is no CW.
So a simple way to ensure that the CW will always win when there is one,
to apply the "afterburner" to every election as a matter of policy. This
policy ensures more ... it ensures that a Smith candidate will win if there
is one, and that that Smith member will also be a Landau member.
How many elections do we expect to lack a Condorcet winner? So far,
FairVote has looked at, they used to say, 440 U.S. RCV elections, all had a
CW, and only one failed to elect the CW. Now there are two anomalous
elections, Alaska 2022 and Bulington 2009. So far 100% having CW and 99.6%
electing the CW using Hare RCV.
Not every ballot CW is a sincere CW.
In fact, because IRV is so defacto vulnerable to compromise, as well as to
Duverger's Law, voters tend to make up for IRV''s lack of sincere
Condorcet efficiency by both nominating and voting for compromise
candidates ... ballot CW's that are not necessarily sincere CW's.
Must we use Copeland if there are easier ways to get the CW elected?
As I mentioned, Copeland is not a good option, because it is neither
decisive, nor clone free.
That's why a much more practical option is to add a simple, zero cost
"afterburner" that protects any method against Covering Embarrassment.
That said, we now have clean, short beatpath versions of RP that can serve
as stand-alone Landau efficient methods ... the ones mentioned above that
we introduced a few weeks ago ... "without fanfare" ... maybe we should
have hired a brass band:-)
-Forest
--
r b-j . _ . _ . _ . _ rbj@audioimagination.com
"Imagination is more important than knowledge."
.
.
.