Approval-enhanced IRV
This idea is inspired by our recent and ongoing "war on Burial".
Approval-enhanced IRV
*Voters strictly rank from the top however many candidates they choose
and have the option of
marking their highest-ranked approved candidate. Default approval is to
only the candidate ranked
above all others.
Find the winner of the pairwise comparison between the IRV winner and
the candidate X with the most
approval opposition to the IRV winner.
The IRV winner is elected if it wins (or say if ties) that pairwise
comparison.
If X wins it, then do the whole thing again as if all ballots truncate
just below X.
If that doesn't produce a new winner, then elect X.
If it does, then elect the original IRV winner.*
This should hang on to LNHelp while meeting modified versions of LNHarm
and Minimal Defense.
Here is a maybe-good-enough-most-of-the-time shorter prettier variation:
*Voters strictly rank from the top however many candidates they choose
and have the option of
marking their highest-ranked approved candidate. Default approval is to
only the candidate ranked
above all others.
If the IRV winner is also the most approved candidate then it is elected.
Otherwise elect the winner of the pairwise comparison between the IRV
winner and the candidate
with the most approval opposition to the IRV winner.*
Not a Condorcet method and probably nothing like a practical proposal.
Chris Benham
For us old lazy guys who sometimes need help seeing the obvious ... how
about a couple of pertinent examples with their most pertinent features
high lighted?
On Sat, Aug 5, 2023, 8:29 PM C.Benham cbenham@adam.com.au wrote:
This idea is inspired by our recent and ongoing "war on Burial".
Approval-enhanced IRV
*Voters strictly rank from the top however many candidates they choose
and have the option of
marking their highest-ranked approved candidate. Default approval is to
only the candidate ranked
above all others.
Find the winner of the pairwise comparison between the IRV winner and
the candidate X with the most
approval opposition to the IRV winner.
The IRV winner is elected if it wins (or say if ties) that pairwise
comparison.
If X wins it, then do the whole thing again as if all ballots truncate
just below X.
If that doesn't produce a new winner, then elect X.
If it does, then elect the original IRV winner.*
This should hang on to LNHelp while meeting modified versions of LNHarm
and Minimal Defense.
Here is a maybe-good-enough-most-of-the-time shorter prettier variation:
*Voters strictly rank from the top however many candidates they choose
and have the option of
marking their highest-ranked approved candidate. Default approval is to
only the candidate ranked
above all others.
If the IRV winner is also the most approved candidate then it is elected.
Otherwise elect the winner of the pairwise comparison between the IRV
winner and the candidate
with the most approval opposition to the IRV winner.*
Not a Condorcet method and probably nothing like a practical proposal.
Chris Benham
49 A (sincere might be A>B)
24 B
27 C>B
This is the classic example used by fans of the Minimal Defense
criterion to attack any method that elects A here, like IRV and Margins.
More than half the voters rank B above A and A no higher than
equal-bottom, and yet (failing MD) A wins.
A big point for it is that the 27 C>B voters have reason to regret not
compromising and voting B>C.
With this method, if their main concern is to defeat A they can mark B
as approved and achieve that goal without having to insincerely
order-reverse.
A is the IRV winner. B will be the candidate with the most approval
opposition to A. B pairwise beats A. All the ballots that rank B already
truncate just below B, so B wins.
The MD criterion has gone a bit out of fashion because it directly
contradicts the Chicken Dilemma criterion.
49 A
24 B (sincere is B>C)
27 C>B
That says that the B faction should not be able to steal the election
from B by this defection (insincere truncation against a faction that is
giving
yours its second-preference votes). Normal IRV meets CD.
Here if the C>B voters have maybe not such a strong B>A preference and
want to guard against being stung by Defection, then they can not
mark B as approved. Then C will be the candidate with the most approval
opposition to the IRV winner A. A wins that pairwise comparison and
so is elected.
The reason for the last part of the method in the full version is that
without it I fear that some voters might be able to rank one or more extra
candidates that changes the IRV winner from one that wins the pairwise
comparison against a candidate they prefer to one that loses it,
thereby breaking LNHelp.
Chris B.
On 6/08/2023 1:37 pm, Forest Simmons wrote:
For us old lazy guys who sometimes need help seeing the obvious ...
how about a couple of pertinent examples with their most pertinent
features high lighted?
On Sat, Aug 5, 2023, 8:29 PM C.Benham cbenham@adam.com.au wrote:
This idea is inspired by our recent and ongoing "war on Burial".
Approval-enhanced IRV
*Voters strictly rank from the top however many candidates they
choose
and have the option of
marking their highest-ranked approved candidate. Default approval
is to
only the candidate ranked
above all others.
Find the winner of the pairwise comparison between the IRV winner and
the candidate X with the most
approval opposition to the IRV winner.
The IRV winner is elected if it wins (or say if ties) that pairwise
comparison.
If X wins it, then do the whole thing again as if all ballots
truncate
just below X.
If that doesn't produce a new winner, then elect X.
If it does, then elect the original IRV winner.*
This should hang on to LNHelp while meeting modified versions of
LNHarm
and Minimal Defense.
Here is a maybe-good-enough-most-of-the-time shorter prettier
variation:
*Voters strictly rank from the top however many candidates they
choose
and have the option of
marking their highest-ranked approved candidate. Default approval
is to
only the candidate ranked
above all others.
If the IRV winner is also the most approved candidate then it is
elected.
Otherwise elect the winner of the pairwise comparison between the IRV
winner and the candidate
with the most approval opposition to the IRV winner.*
Not a Condorcet method and probably nothing like a practical proposal.
Chris Benham
Hi Chris,
Le dimanche 6 août 2023 à 01:37:25 UTC−5, C.Benham cbenham@adam.com.au a écrit :
The MD criterion has gone a bit out of fashion because it directly contradicts the
Chicken Dilemma criterion.
I'm not sure if MD (even as SDSC) was ever in fashion exactly, but what it is, as you
know, is a special case of trying to minimize compromise incentive. If you say that has
gone out of fashion too, well, maybe you'd be right. I don't think CD is the reason for
that though. In any case I think it would be a mistake for a Condorcet advocate to omit
compromise incentive from their vocabulary.
CD doesn't seem like much of an alternative to me. It has a high cost, and the proposed
benefit is speculative, dependent on one set of its resulting incentives prevailing over
another.
Otherwise elect the winner of the pairwise comparison between the IRV
winner and the candidate
with the most approval opposition to the IRV winner.*
Just a comment on this aspect. I'm concerned that on its face it may seem a little unfair
to choose two finalists, such that one finalist has some specific merit, and the other
finalist is someone specifically expected to have high odds of beating the first
finalist. It makes one wonder if the merit of the first finalist is being penalized
sometimes.
This isn't to say I haven't proposed such designs myself.
Kevin
votingmethods.net
On 8/6/23 22:28, Kevin Venzke wrote:
Hi Chris,
Le dimanche 6 août 2023 à 01:37:25 UTC−5, C.Benham cbenham@adam.com.au a écrit :
The MD criterion has gone a bit out of fashion because it directly contradicts the
Chicken Dilemma criterion.
I'm not sure if MD (even as SDSC) was ever in fashion exactly, but what it is, as you
know, is a special case of trying to minimize compromise incentive. If you say that has
gone out of fashion too, well, maybe you'd be right. I don't think CD is the reason for
that though. In any case I think it would be a mistake for a Condorcet advocate to omit
compromise incentive from their vocabulary.
The Condorcification logic gives a link between Condorcet itself and
compromise resistance, namely that if a majority can always compromise
for X no matter what other candidate was elected, then perhaps one
should elect X to begin with.
So I wouldn't say that compromise incentive has gone entirely out of
fashion :-)
From its perspective, if there is a majority-strength Condorcet cycle,
then no matter who you elect, there exists a majority who could've
compromised to get someone else elected, which also would seem to bound
what can be done.
-km
Kristofer,
So I wouldn't say that compromise incentive has gone entirely out of
fashion :-)
And neither would or did I. In English, there is a big difference in
meaning between "a bit" and "entirely".
But if you as Condorcet advocate over-emphasise "compromise resistance",
what is your argument when it is
pointed out that Condorcet is incompatible with Favorite Betrayal and
suggested that if it is all about compromise
resistance why not get the maximum possible with a method that meets
Favorite Betrayal?
Chris B.
On 7/08/2023 6:21 am, Kristofer Munsterhjelm wrote:
On 8/6/23 22:28, Kevin Venzke wrote:
Hi Chris,
Le dimanche 6 août 2023 à 01:37:25 UTC−5, C.Benham
cbenham@adam.com.au a écrit :
The MD criterion has gone a bit out of fashion because it directly
contradicts the
Chicken Dilemma criterion.
I'm not sure if MD (even as SDSC) was ever in fashion exactly, but
what it is, as you
know, is a special case of trying to minimize compromise incentive.
If you say that has
gone out of fashion too, well, maybe you'd be right. I don't think CD
is the reason for
that though. In any case I think it would be a mistake for a
Condorcet advocate to omit
compromise incentive from their vocabulary.
The Condorcification logic gives a link between Condorcet itself and
compromise resistance, namely that if a majority can always compromise
for X no matter what other candidate was elected, then perhaps one
should elect X to begin with.
So I wouldn't say that compromise incentive has gone entirely out of
fashion :-)
From its perspective, if there is a majority-strength Condorcet cycle,
then no matter who you elect, there exists a majority who could've
compromised to get someone else elected, which also would seem to
bound what can be done.
-km
On 8/7/23 11:03, C.Benham wrote:
Kristofer,
So I wouldn't say that compromise incentive has gone entirely out of
fashion :-)
And neither would or did I. In English, there is a big difference in
meaning between "a bit" and "entirely".
I'll rephrase. What I'm saying is that there is, from a Condorcet
perspective at least, a natural bound to how much the method can
backslide on compromise incentive. Hence, even if it looks like it's
going "a bit" out of fashion, it does not imply that the tendency can
continue to the degree where everybody gets so focused on say, burial
resistance, that they forget compromise entirely.
And that this bound is fairly high; and the wiggle room is fairly narrow
for strict ballots due to the observation about compromise incentive
always existing with a majority-strength cycle.
But if you as Condorcet advocate over-emphasise "compromise
resistance", what is your argument when it is pointed out that
Condorcet is incompatible with Favorite Betrayal and suggested that
if it is all about compromise resistance why not get the maximum
possible with a method that meets Favorite Betrayal?
In short: because FBC is very demanding and thus it may be too much to
ask. But research is still possible, and we might be surprised.
To expand on that:
I would approach that in three ways. First, that strong FBC is too
strong and that this is just the way the math goes (see Alex Small's
paper); and second, that if cycles are rare, there's no problem (when
there's a CW, we pass IIA etc).
Third, that the Condorcification logic says nothing about what happens
when there's no majority strength CW, such as when you equal-rank or
truncate, which is the domain of the ordinary (weak) FBC. So it should
be possible to find a range of methods all the way from something that
doesn't pass Condorcet with equal-rank, say something like MMPO, and to
classical Condorcet methods like Schulze, that don't pass the weak FBC.
More investigation into these wouldd of course be welcome. Most of them
seem to have other problems (e.g. MMPO's egregious Plurality failure, or
the way at least some tied-at-the-top methods degrade to Approval
because min-maxing is so beneficial).
When we talked about Condorcification earlier, Kevin mentioned that
these FBC methods don't necessarily have a lower general compromise
incentive either. So what is and isn't possible in this domain is still
pretty unclear.
If one wants to get the maximum possible with a method that meets the
FBC, then that's not necessarily incompatible with majority-strength
Condorcet. But as it stands, FBC methods seem to go too far. At least
the ones I know; either they have other problems (like MMPO) or they
degrade into Approval, which has that manual DSV/Burr dilemma that I
really don't like.
-km
On Mon, Aug 7, 2023, 2:34 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 8/7/23 11:03, C.Benham wrote:
Kristofer,
So I wouldn't say that compromise incentive has gone entirely out of
fashion :-)
And neither would or did I. In English, there is a big difference in
meaning between "a bit" and "entirely".
I'll rephrase. What I'm saying is that there is, from a Condorcet
perspective at least, a natural bound to how much the method can
backslide on compromise incentive. Hence, even if it looks like it's
going "a bit" out of fashion, it does not imply that the tendency can
continue to the degree where everybody gets so focused on say, burial
resistance, that they forget compromise entirely.
And that this bound is fairly high; and the wiggle room is fairly narrow
for strict ballots due to the observation about compromise incentive
always existing with a majority-strength cycle.
But if you as Condorcet advocate over-emphasise "compromise
resistance", what is your argument when it is pointed out that
Condorcet is incompatible with Favorite Betrayal and suggested that
if it is all about compromise resistance why not get the maximum
possible with a method that meets Favorite Betrayal?
In short: because FBC is very demanding and thus it may be too much to
ask. But research is still possible, and we might be surprised.
To expand on that:
I would approach that in three ways. First, that strong FBC is too
strong and that this is just the way the math goes (see Alex Small's
paper); and second, that if cycles are rare, there's no problem (when
there's a CW, we pass IIA etc).
Third, that the Condorcification logic says nothing about what happens
when there's no majority strength CW, such as when you equal-rank or
truncate, which is the domain of the ordinary (weak) FBC. So it should
be possible to find a range of methods all the way from something that
doesn't pass Condorcet with equal-rank, say something like MMPO, and to
classical Condorcet methods like Schulze, that don't pass the weak FBC.
More investigation into these wouldd of course be welcome. Most of them
seem to have other problems (e.g. MMPO's egregious Plurality failure, or
the way at least some tied-at-the-top methods degrade to Approval
because min-maxing is so beneficial).
When we talked about Condorcification earlier, Kevin mentioned that
these FBC methods don't necessarily have a lower general compromise
incentive either. So what is and isn't possible in this domain is still
pretty unclear.
If one wants to get the maximum possible with a method that meets the
FBC, then that's not necessarily incompatible with majority-strength
Condorcet. But as it stands, FBC methods seem to go too far. At least
the ones I know; either they have other problems (like MMPO) or they
degrade into Approval,
In a way MMPO can be used to make Approval more meaningful ... by using the
MMPO candidate C as the approval cutoff candidate ... the approval of X
could be the number of ballots on which X is ranked above C plus the number
of ballots on which they are ranked equal top, plus half the number on
which they are ranked equal below top (but above bottom).
So C's approval would be its top (including equal top) count plus half of
the number of ballots where it is ranked strictly between top and bottom.
which has that manual DSV/Burr dilemma that I
really don't like.
-km
Kevin,
Otherwise elect the winner of the pairwise comparison between the IRV
winner and the candidate
with the most approval opposition to the IRV winner.*
Just a comment on this aspect. I'm concerned that on its face it may seem a little unfair
to choose two finalists, such that one finalist has some specific merit, and the other
finalist is someone specifically expected to have high odds of beating the first
finalist.
Do you think this method "seems a little unfair" to the IRV winner?
It could be that there is an Approval winner who is ranked above the IRV
winner on a lot of ballots that also
approve the IRV winner, but the IRV winner is spared that pairwise
comparison.
Chris
On 7/08/2023 5:58 am, Kevin Venzke wrote:
Hi Chris,
Le dimanche 6 août 2023 à 01:37:25 UTC−5, C.Benham cbenham@adam.com.au a écrit :
The MD criterion has gone a bit out of fashion because it directly contradicts the
Chicken Dilemma criterion.
I'm not sure if MD (even as SDSC) was ever in fashion exactly, but what it is, as you
know, is a special case of trying to minimize compromise incentive. If you say that has
gone out of fashion too, well, maybe you'd be right. I don't think CD is the reason for
that though. In any case I think it would be a mistake for a Condorcet advocate to omit
compromise incentive from their vocabulary.
CD doesn't seem like much of an alternative to me. It has a high cost, and the proposed
benefit is speculative, dependent on one set of its resulting incentives prevailing over
another.
Otherwise elect the winner of the pairwise comparison between the IRV
winner and the candidate
with the most approval opposition to the IRV winner.*
Just a comment on this aspect. I'm concerned that on its face it may seem a little unfair
to choose two finalists, such that one finalist has some specific merit, and the other
finalist is someone specifically expected to have high odds of beating the first
finalist. It makes one wonder if the merit of the first finalist is being penalized
sometimes.
This isn't to say I haven't proposed such designs myself.
Kevin
votingmethods.net