Strategy-free criterion
It doesn't talk about just any "Condorcet winner". It says that if A is
the sincere CW and more than half the voters vote A above B, then the
voters who prefer B to A can't make B win just by truncating.
But maybe they can if less than half the voters vote A over B (with A
still being the sincere CW and pairwise-beating B) and maybe they can by
order-reversal Burial.
Sincere Defense says that if more than half the voters prefer A to B,
they can stop B from winning by voting A over B and truncating against
B. From a Kevin Venzke webpage:
*Minimal Defense*./(Due to Steve Eppley.)/
/If more than half of the voters rank candidate A above candidate B,
and don't rank candidate B above anyone, then candidate B must be
elected with 0% probability./
Steve Eppley has defined and discussed Minimal Defensehere [broken
link] http://alumnus.caltech.edu/~seppley/andhere [broken link]
http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm.
Satisfaction of this criterion implies compliance with Mike
Ossipoff's/strong defensive strategy criterion/, although the reverse
is not necessarily true. That criterion can be foundhere [broken link]
http://www.barnsdle.demon.co.uk/vote/stfree.html.
Note that the ballot must accept all preference orders; in particular,
the voter must be able to rank multiple candidates above no one
(usually by truncation), and to/strictly/rank any number of
candidates. If the word "strictly" were dropped, thenApproval
https://votingmethods.net/em2005#methapprwould satisfy, as could
other methods using a "limited slot" ballot. (Approval
https://votingmethods.net/em2005#methapprsatisfies Mike
Ossipoff's/weak defensive strategy criterion/for this reason.) In my
opinion, the word "strictly" should be dropped, sinceApproval
https://votingmethods.net/em2005#methapprcan already be made to
satisfy Minimal Defense just by allowing the voter to number his
approved candidates, without analyzing the ballot any differently.
Minimal Defense deals with the issue of what a majority need to do to
get their opinion counted. Specifically, if they are united in
preferring candidate A to candidate B, all they have to do is not rank
B. They need not do anything special regarding A. For instance, on
these ballots:
49 B
13 C>A
13 D>A
13 E>A
12 F>A
The A>B voters (i.e., the voters preferring A to B) are a majority,
and do not rank B at all, so that Minimal Defense guarantees that B
won't win. However, candidate B is the winner in e.g.Plurality
https://votingmethods.net/em2005#methfpp,Instant Runoff
https://votingmethods.net/em2005#methirv, andDescending Solid
Coalitions https://votingmethods.net/em2005#methdsc. Under these
methods, if the A>B majority want to prevent B from being elected,
they need to insincerely raise candidate A in their rankings.
A more general way to view this problem is by noting that this
election is primarily a contest between A and B. In that light, it
would be very undesirable for the election method to elect the/wrong
one/of these two. Minimal Defense ensures that the method can't be
"confused" by the introduction of weaker candidates preferred to the
major candidates.
As for the methods which satisfy Minimal Defense,Schulze
https://votingmethods.net/em2005#methschelects A in the above
scenario (as would anyCondorcet method
https://votingmethods.net/em2005#methcond), andEqual Majorities
https://votingmethods.net/em2005#methcdttelects either C, D, E, or
F. (This is because all candidates besides B are in the CDTT;
whenRandom Ballot https://votingmethods.net/em2005#methrbis used to
break the tie, only these four candidates have any first
preferences.Minimum Opposition
https://votingmethods.net/em2005#methmmpogives the same result,
incidentally, although it doesn't satisfy Minimal Defense when there
are more than three candidates.)
On 1/06/2024 8:38 am, Closed Limelike Curves wrote:
OK, so SFC prevents offensive truncation from defeating the Condorcet
winner, while minimal defense provides a simple way to stop
order-reversal?
On Fri, May 31, 2024 at 4:01 PM Michael Ossipoff
email9648742@gmail.com wrote:
Evidently, then, SFC merely says that the candidate can’t win
without order-reversal, while Minimal-Defense says he can’t win at
all if the minimal defensive-strategy is used.
It seems to me that Eppley’s Minimal-Defense was the votes-only
criterion based on SDSC.
…& that SDSC was the original, preference-&-sincerity version.
I preferred preference-&-sincerity because of its universal
applicability, where votes-only had to stipulate a balloting.
On Fri, May 31, 2024 at 12:33 Chris Benham
<cbenhamau@yahoo.com.au> wrote:
Why are we having a public discussion about a voting method
criterion without anyone giving its definition, and with
apparently most of the participants in the discussion knowing
nothing about it besides its name?
https://electowiki.org/wiki/Strategy-free_criterion
The*strategy-free criterion*is avoting system criterion
<https://electowiki.org/wiki/Voting_system_criterion>for
evaluatingvoting systems
<https://electowiki.org/wiki/Voting_system>.
Definitions
A sincere vote is one with no falsified preferences or
preferences left unspecified when the election method allows
them to be specified (in addition to the preferences already
specified).
One candidate is preferred over another candidate if, in a
one-on-one competition, more voters prefer the first
candidate than prefer the other candidate.
If one candidate is preferred over each of the other
candidates, that candidate is called "Condorcet candidate" or
"Condorcet winner".
Statement of criterion
If a Condorcet candidate exists, and if a majority
prefers this candidate to another candidate, then the
other candidate should not win if that majority votes
sincerely and no other voter falsifies any preferences.
In a ranked method, it is nearly equivalent to say:
If more than half of the voters rank/x/above/y/, and
there is no candidate/z/whom more than half of the voters
rank above/x/, then/y/must not be elected.
I think this evolved into the Minimal Defense criterion, the
"votes-only version" of which says that if more than half the
voters vote A over B and B no higher than equal-bottom then B
can't win.
On 31/05/2024 9:46 pm, Michael Ossipoff wrote:
Some time ago, I wrote a criterion that I called
Strategy-Free-Criterion (SFC).
Is that what you were referring to?
It was about a circumstance in which wv Condorcet is
strategy-free. At that time, autodeterence hadn’t been
considered.
SFC didn’t catch-on, & I haven’t heard mention of it lately,
& so I don’t know it’s definition. But wv Condorcet is
strategy-free in a meaningful sense.
On Fri, May 31, 2024 at 05:07 Michael Ossipoff
<email9648742@gmail.com> wrote:
On Wed, May 29, 2024 at 14:15 Closed Limelike Curves
<closed.limelike.curves@gmail.com>
Ppwrote:
I'm trying to work out how the strategy-free
criterion actually relates to strategy, because it
just sounds like it means the majority-Condorcet
criterion ("if a candidate majority-beats every
other, they have to win if everyone is honest").
@Michael Ossipoff ?
Closed, isn’t “Strategy-Free Criterion” your new name
for FBC.
It’s a very inaccurate name. FBC-complying methods aren’t
strategy-free in any sense.
But they’re free of any need for *drastic* defensive
strategy (favorite-burial or any defensive order-reversal).
You want strategy-free? The wv Condorcet methods, such as
RP(wv) & MinMax(wv), are strategy-free in a meaningful
sense…effectively free of need for any defensive
strategy…due to their autodeterence.
----
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----
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list info
On Fri, May 31, 2024 at 19:04 Chris Benham cbenhamau@yahoo.com.au wrote:
It [SDC] doesn't talk about just any "Condorcet winner". It says that if
A is the sincere CW and more than half the voters vote A above B, then the
voters who prefer B to A can't make B win just by truncating.
Exactly. That was what I meant to say. Forgive me if I didn’t say it.
But maybe they can if less than half the voters vote A over B (with A still
being the sincere CW and pairwise-beating B) and maybe they can by
order-reversal Burial.
Of course.
Sincere Defense [Minimal Defense (MDC)] says that if more than half the
voters prefer A to B, they can stop B from winning by voting A over B and
truncating against B. From a Kevin Venzke webpage:
https://votingmethods.net/em2005
Minimal Defense. (Due to Steve Eppley.)
If more than half of the voters rank candidate A above candidate B, and
don't rank candidate B above anyone, then candidate B must be elected with
0% probability.
Yes.
Steve Eppley has defined and discussed Minimal Defense here [broken link]
http://alumnus.caltech.edu/~seppley/ and here [broken link]
http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm.
Satisfaction of this criterion implies compliance with Mike Ossipoff's strong
defensive strategy criterion, although the reverse is not necessarily
true. That criterion can be found here [broken link]
http://www.barnsdle.demon.co.uk/vote/stfree.html.
Yes, it’s true that they aren’t the same, because MDC requires stipulation
of a balloting (usually ranked)…but SDSC is universally applicable, because
it’s a preference-&-sincere
criterion.
Note that the ballot must accept all preference orders; in particular, the
voter must be able to rank multiple candidates above no one (usually by
truncation), and to strictly rank any number of candidates. If the word
"strictly" were dropped, then Approval
https://votingmethods.net/em2005#methappr would satisfy, as could other
methods using a "limited slot" ballot
Yes, Approval doesn’t pass SDSC, due to the definition of “sincere” for
the preference-sincere criteria, though SDSC applies to Approval. …& I
didn’t apply MDC to Approval.
Because I prefer preference-sincere criteria, I didn’t define a version of
MDC for Approval-balloting.
Anyway, MDC was Eppley’s version. …& the version that was
generally-accepted. …& therefore the one that I usually refer to. …which
is fine, because we only use it for comparison of rank-methods.
. (Approval https://votingmethods.net/em2005#methappr satisfies Mike
Ossipoff's weak defensive strategy criterion for this reason.) In my
opinion, the word "strictly" should be dropped, since Approval
https://votingmethods.net/em2005#methappr can already be made to
satisfy Minimal Defense just by allowing the voter to number his approved
candidates, without analyzing the ballot any differently.
Sure, if that would make the votes-only criteria apply to Approval, Score
& STAR.
Minimal Defense deals with the issue of what a majority need to do to get
their opinion counted. Specifically, if they are united in preferring
candidate A to candidate B, all they have to do is not rank B. They need
not do anything special regarding A. For instance, on these ballots:
49 B
13 C>A
13 D>A
13 E>A
12 F>A
The A>B voters (i.e., the voters preferring A to B) are a majority, and do
not rank B at all, so that Minimal Defense guarantees that B won't win.
However, candidate B is the winner in e.g. Plurality
https://votingmethods.net/em2005#methfpp, Instant Runoff
https://votingmethods.net/em2005#methirv, and Descending Solid
Coalitions https://votingmethods.net/em2005#methdsc. Under these
methods, if the A>B majority want to prevent B from being elected, they
need to insincerely raise candidate A in their rankings.
—& that problem remains to some significant degree with any Condorcet
version that isn’t autodeterent.
A more general way to view this problem is by noting that this election is
primarily a contest between A and B. In that light, it would be very
undesirable for the election method to elect the wrong one of these
two. Minimal Defense ensures that the method can't be "confused" by the
introduction of weaker candidates preferred to the major candidates.
As for the methods which satisfy Minimal Defense, Schulze
https://votingmethods.net/em2005#methsch elects A in the above scenario
(as would any Condorcet method https://votingmethods.net/em2005#methcond),
and Equal Majorities https://votingmethods.net/em2005#methcdtt elects
either C, D, E, or F. (This is because all candidates besides B are in the
CDTT; when Random Ballot https://votingmethods.net/em2005#methrb is
used to break the tie, only these four candidates have any first
preferences. Minimum Opposition
https://votingmethods.net/em2005#methmmpo gives the same result,
incidentally, although it doesn't satisfy Minimal Defense when there are
more than three candidates.)
On 1/06/2024 8:38 am, Closed Limelike Curves wrote:
OK, so SFC prevents offensive truncation from defeating the Condorcet
winner, while minimal defense provides a simple way to stop order-reversal?
On Fri, May 31, 2024 at 4:01 PM Michael Ossipoff email9648742@gmail.com
wrote:
Evidently, then, SFC merely says that the candidate can’t win without
order-reversal, while Minimal-Defense says he can’t win at all if the
minimal defensive-strategy is used.
It seems to me that Eppley’s Minimal-Defense was the votes-only criterion
based on SDSC.
…& that SDSC was the original, preference-&-sincerity version.
I preferred preference-&-sincerity because of its universal
applicability, where votes-only had to stipulate a balloting.
On Fri, May 31, 2024 at 12:33 Chris Benham cbenhamau@yahoo.com.au
wrote:
Why are we having a public discussion about a voting method criterion
without anyone giving its definition, and with apparently most of the
participants in the discussion knowing nothing about it besides its name?
https://electowiki.org/wiki/Strategy-free_criterion
The strategy-free criterion is a voting system criterion
https://electowiki.org/wiki/Voting_system_criterion for evaluating voting
systems https://electowiki.org/wiki/Voting_system.
Definitions
A sincere vote is one with no falsified preferences or preferences left
unspecified when the election method allows them to be specified (in
addition to the preferences already specified).
One candidate is preferred over another candidate if, in a one-on-one
competition, more voters prefer the first candidate than prefer the other
candidate.
If one candidate is preferred over each of the other candidates, that
candidate is called "Condorcet candidate" or "Condorcet winner".
Statement of criterion
If a Condorcet candidate exists, and if a majority prefers this
candidate to another candidate, then the other candidate should not win if
that majority votes sincerely and no other voter falsifies any preferences.
In a ranked method, it is nearly equivalent to say:
If more than half of the voters rank x above y, and there is no
candidate z whom more than half of the voters rank above x, then y
must not be elected.
I think this evolved into the Minimal Defense criterion, the "votes-only
version" of which says that if more than half the voters vote A over B and
B no higher than equal-bottom then B can't win.
On 31/05/2024 9:46 pm, Michael Ossipoff wrote:
Some time ago, I wrote a criterion that I called Strategy-Free-Criterion
(SFC).
Is that what you were referring to?
It was about a circumstance in which wv Condorcet is strategy-free. At
that time, autodeterence hadn’t been considered.
SFC didn’t catch-on, & I haven’t heard mention of it lately, & so I
don’t know it’s definition. But wv Condorcet is strategy-free in a
meaningful sense.
On Fri, May 31, 2024 at 05:07 Michael Ossipoff email9648742@gmail.com
wrote:
On Wed, May 29, 2024 at 14:15 Closed Limelike Curves <
closed.limelike.curves@gmail.com>
Ppwrote:
I'm trying to work out how the strategy-free criterion actually
relates to strategy, because it just sounds like it means the
majority-Condorcet criterion ("if a candidate majority-beats every other,
they have to win if everyone is honest"). @Michael Ossipoff ?
Closed, isn’t “Strategy-Free Criterion” your new name for FBC.
It’s a very inaccurate name. FBC-complying methods aren’t strategy-free
in any sense.
But they’re free of any need for drastic defensive strategy
(favorite-burial or any defensive order-reversal).
You want strategy-free? The wv Condorcet methods, such as RP(wv) &
MinMax(wv), are strategy-free in a meaningful sense…effectively free of
need for any defensive strategy…due to their autodeterence.
Election-Methods mailing list - see https://electorama.com/em for list
info
Yes, I don't know where my "Sincere Defense" brain-fart came from. I
meant Minimal Defense. (I corrected it below).
Chris B.
On 1/06/2024 11:34 am, Chris Benham wrote:
It doesn't talk about just any "Condorcet winner". It says that if A
is the sincere CW and more than half the voters vote A above B, then
the voters who prefer B to A can't make B win just by truncating.
But maybe they can if less than half the voters vote A over B (with A
still being the sincere CW and pairwise-beating B) and maybe they can
by order-reversal Burial.
Minimal Defense says that if more than half the voters prefer A to B,
they can stop B from winning by voting A over B and truncating against
B. From a Kevin Venzke webpage:
*Minimal Defense*./(Due to Steve Eppley.)/
/If more than half of the voters rank candidate A above candidate B,
and don't rank candidate B above anyone, then candidate B must be
elected with 0% probability./
Steve Eppley has defined and discussed Minimal Defensehere [broken
link] http://alumnus.caltech.edu/~seppley/andhere [broken link]
http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm.
Satisfaction of this criterion implies compliance with Mike
Ossipoff's/strong defensive strategy criterion/, although the reverse
is not necessarily true. That criterion can be foundhere [broken
link] http://www.barnsdle.demon.co.uk/vote/stfree.html.
Note that the ballot must accept all preference orders; in
particular, the voter must be able to rank multiple candidates above
no one (usually by truncation), and to/strictly/rank any number of
candidates. If the word "strictly" were dropped, thenApproval
https://votingmethods.net/em2005#methapprwould satisfy, as could
other methods using a "limited slot" ballot. (Approval
https://votingmethods.net/em2005#methapprsatisfies Mike
Ossipoff's/weak defensive strategy criterion/for this reason.) In my
opinion, the word "strictly" should be dropped, sinceApproval
https://votingmethods.net/em2005#methapprcan already be made to
satisfy Minimal Defense just by allowing the voter to number his
approved candidates, without analyzing the ballot any differently.
Minimal Defense deals with the issue of what a majority need to do to
get their opinion counted. Specifically, if they are united in
preferring candidate A to candidate B, all they have to do is not
rank B. They need not do anything special regarding A. For instance,
on these ballots:
49 B
13 C>A
13 D>A
13 E>A
12 F>A
The A>B voters (i.e., the voters preferring A to B) are a majority,
and do not rank B at all, so that Minimal Defense guarantees that B
won't win. However, candidate B is the winner in e.g.Plurality
https://votingmethods.net/em2005#methfpp,Instant Runoff
https://votingmethods.net/em2005#methirv, andDescending Solid
Coalitions https://votingmethods.net/em2005#methdsc. Under these
methods, if the A>B majority want to prevent B from being elected,
they need to insincerely raise candidate A in their rankings.
A more general way to view this problem is by noting that this
election is primarily a contest between A and B. In that light, it
would be very undesirable for the election method to elect the/wrong
one/of these two. Minimal Defense ensures that the method can't be
"confused" by the introduction of weaker candidates preferred to the
major candidates.
As for the methods which satisfy Minimal Defense,Schulze
https://votingmethods.net/em2005#methschelects A in the above
scenario (as would anyCondorcet method
https://votingmethods.net/em2005#methcond), andEqual Majorities
https://votingmethods.net/em2005#methcdttelects either C, D, E, or
F. (This is because all candidates besides B are in the CDTT;
whenRandom Ballot https://votingmethods.net/em2005#methrbis used to
break the tie, only these four candidates have any first
preferences.Minimum Opposition
https://votingmethods.net/em2005#methmmpogives the same result,
incidentally, although it doesn't satisfy Minimal Defense when there
are more than three candidates.)
On 1/06/2024 8:38 am, Closed Limelike Curves wrote:
OK, so SFC prevents offensive truncation from defeating the Condorcet
winner, while minimal defense provides a simple way to stop
order-reversal?
On Fri, May 31, 2024 at 4:01 PM Michael Ossipoff
email9648742@gmail.com wrote:
Evidently, then, SFC merely says that the candidate can’t win
without order-reversal, while Minimal-Defense says he can’t win
at all if the minimal defensive-strategy is used.
It seems to me that Eppley’s Minimal-Defense was the votes-only
criterion based on SDSC.
…& that SDSC was the original, preference-&-sincerity version.
I preferred preference-&-sincerity because of its universal
applicability, where votes-only had to stipulate a balloting.
On Fri, May 31, 2024 at 12:33 Chris Benham
<cbenhamau@yahoo.com.au> wrote:
Why are we having a public discussion about a voting method
criterion without anyone giving its definition, and with
apparently most of the participants in the discussion knowing
nothing about it besides its name?
https://electowiki.org/wiki/Strategy-free_criterion
The*strategy-free criterion*is avoting system criterion
<https://electowiki.org/wiki/Voting_system_criterion>for
evaluatingvoting systems
<https://electowiki.org/wiki/Voting_system>.
Definitions
A sincere vote is one with no falsified preferences or
preferences left unspecified when the election method allows
them to be specified (in addition to the preferences already
specified).
One candidate is preferred over another candidate if, in a
one-on-one competition, more voters prefer the first
candidate than prefer the other candidate.
If one candidate is preferred over each of the other
candidates, that candidate is called "Condorcet candidate"
or "Condorcet winner".
Statement of criterion
If a Condorcet candidate exists, and if a majority
prefers this candidate to another candidate, then the
other candidate should not win if that majority votes
sincerely and no other voter falsifies any preferences.
In a ranked method, it is nearly equivalent to say:
If more than half of the voters rank/x/above/y/, and
there is no candidate/z/whom more than half of the
voters rank above/x/, then/y/must not be elected.
I think this evolved into the Minimal Defense criterion, the
"votes-only version" of which says that if more than half the
voters vote A over B and B no higher than equal-bottom then B
can't win.
On 31/05/2024 9:46 pm, Michael Ossipoff wrote:
Some time ago, I wrote a criterion that I called
Strategy-Free-Criterion (SFC).
Is that what you were referring to?
It was about a circumstance in which wv Condorcet is
strategy-free. At that time, autodeterence hadn’t been
considered.
SFC didn’t catch-on, & I haven’t heard mention of it lately,
& so I don’t know it’s definition. But wv Condorcet is
strategy-free in a meaningful sense.
On Fri, May 31, 2024 at 05:07 Michael Ossipoff
<email9648742@gmail.com> wrote:
On Wed, May 29, 2024 at 14:15 Closed Limelike Curves
<closed.limelike.curves@gmail.com>
Ppwrote:
I'm trying to work out how the strategy-free
criterion actually relates to strategy, because it
just sounds like it means the majority-Condorcet
criterion ("if a candidate majority-beats every
other, they have to win if everyone is honest").
@Michael Ossipoff ?
Closed, isn’t “Strategy-Free Criterion” your new name
for FBC.
It’s a very inaccurate name. FBC-complying methods
aren’t strategy-free in any sense.
But they’re free of any need for *drastic* defensive
strategy (favorite-burial or any defensive order-reversal).
You want strategy-free? The wv Condorcet methods, such
as RP(wv) & MinMax(wv), are strategy-free in a
meaningful sense…effectively free of need for any
defensive strategy…due to their autodeterence.
----
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----
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list info
Hi all,
When I test for SFC compliance the rule on cast votes is that if there is no
majority over A, and A has a majority over B, then B can't win.
This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
in terms of a graph of majority-strength defeats, it would say that if A has a
majority over B and B doesn't have a majority over anyone, then B can't win.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner. So MD is mostly about compromise incentive.
SFC is probably going to be about truncation. When a method fails it, most likely
it's because the majority gave the election away to a less liked compromise choice.
For example:
20 C>A>B
35 A>B
5 B
40 D
Here B is the implicit approval winner, but by SFC B should not win, because it
means it was not safe for the A voters to rank B.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Kevin
votingmethods.net
I think Minimal Defense can be justified as strongly desirable without any
reference to strategy at all: it's just the majority loser criterion with
truncation. In other words, if a majority of voters refuse to rank a
candidate at all, that candidate cannot win (unless all candidates are
rejected by a majority).
On Fri, May 31, 2024 at 7:57 PM Michael Ossipoff email9648742@gmail.com
wrote:
On Fri, May 31, 2024 at 19:04 Chris Benham cbenhamau@yahoo.com.au wrote:
It [SDC] doesn't talk about just any "Condorcet winner". It says that if
A is the sincere CW and more than half the voters vote A above B, then the
voters who prefer B to A can't make B win just by truncating.
Exactly. That was what I meant to say. Forgive me if I didn’t say it.
But maybe they can if less than half the voters vote A over B (with A
still being the sincere CW and pairwise-beating B) and maybe they can by
order-reversal Burial.
Of course.
Sincere Defense [Minimal Defense (MDC)] says that if more than half the
voters prefer A to B, they can stop B from winning by voting A over B and
truncating against B. From a Kevin Venzke webpage:
https://votingmethods.net/em2005
Minimal Defense. (Due to Steve Eppley.)
If more than half of the voters rank candidate A above candidate B, and
don't rank candidate B above anyone, then candidate B must be elected with
0% probability.
Yes.
Steve Eppley has defined and discussed Minimal Defense here [broken link]
http://alumnus.caltech.edu/~seppley/ and here [broken link]
http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm.
Satisfaction of this criterion implies compliance with Mike Ossipoff's strong
defensive strategy criterion, although the reverse is not necessarily
true. That criterion can be found here [broken link]
http://www.barnsdle.demon.co.uk/vote/stfree.html.
Yes, it’s true that they aren’t the same, because MDC requires
stipulation of a balloting (usually ranked)…but SDSC is universally
applicable, because it’s a preference-&-sincere
criterion.
Note that the ballot must accept all preference orders; in particular, the
voter must be able to rank multiple candidates above no one (usually by
truncation), and to strictly rank any number of candidates. If the
word "strictly" were dropped, then Approval
https://votingmethods.net/em2005#methappr would satisfy, as could
other methods using a "limited slot" ballot
Yes, Approval doesn’t pass SDSC, due to the definition of “sincere” for
the preference-sincere criteria, though SDSC applies to Approval. …& I
didn’t apply MDC to Approval.
Because I prefer preference-sincere criteria, I didn’t define a version of
MDC for Approval-balloting.
Anyway, MDC was Eppley’s version. …& the version that was
generally-accepted. …& therefore the one that I usually refer to. …which
is fine, because we only use it for comparison of rank-methods.
. (Approval https://votingmethods.net/em2005#methappr satisfies Mike
Ossipoff's weak defensive strategy criterion for this reason.) In my
opinion, the word "strictly" should be dropped, since Approval
https://votingmethods.net/em2005#methappr can already be made to
satisfy Minimal Defense just by allowing the voter to number his approved
candidates, without analyzing the ballot any differently.
Sure, if that would make the votes-only criteria apply to Approval, Score
& STAR.
Minimal Defense deals with the issue of what a majority need to do to get
their opinion counted. Specifically, if they are united in preferring
candidate A to candidate B, all they have to do is not rank B. They need
not do anything special regarding A. For instance, on these ballots:
49 B
13 C>A
13 D>A
13 E>A
12 F>A
The A>B voters (i.e., the voters preferring A to B) are a majority, and
do not rank B at all, so that Minimal Defense guarantees that B won't win.
However, candidate B is the winner in e.g. Plurality
https://votingmethods.net/em2005#methfpp, Instant Runoff
https://votingmethods.net/em2005#methirv, and Descending Solid
Coalitions https://votingmethods.net/em2005#methdsc. Under these
methods, if the A>B majority want to prevent B from being elected, they
need to insincerely raise candidate A in their rankings.
—& that problem remains to some significant degree with any Condorcet
version that isn’t autodeterent.
A more general way to view this problem is by noting that this election
is primarily a contest between A and B. In that light, it would be very
undesirable for the election method to elect the wrong one of these
two. Minimal Defense ensures that the method can't be "confused" by the
introduction of weaker candidates preferred to the major candidates.
As for the methods which satisfy Minimal Defense, Schulze
https://votingmethods.net/em2005#methsch elects A in the above
scenario (as would any Condorcet method
https://votingmethods.net/em2005#methcond), and Equal Majorities
https://votingmethods.net/em2005#methcdtt elects either C, D, E, or F.
(This is because all candidates besides B are in the CDTT; when Random
Ballot https://votingmethods.net/em2005#methrb is used to break the
tie, only these four candidates have any first preferences. Minimum
Opposition https://votingmethods.net/em2005#methmmpo gives the same
result, incidentally, although it doesn't satisfy Minimal Defense when
there are more than three candidates.)
On 1/06/2024 8:38 am, Closed Limelike Curves wrote:
OK, so SFC prevents offensive truncation from defeating the Condorcet
winner, while minimal defense provides a simple way to stop order-reversal?
On Fri, May 31, 2024 at 4:01 PM Michael Ossipoff email9648742@gmail.com
wrote:
Evidently, then, SFC merely says that the candidate can’t win without
order-reversal, while Minimal-Defense says he can’t win at all if the
minimal defensive-strategy is used.
It seems to me that Eppley’s Minimal-Defense was the votes-only
criterion based on SDSC.
…& that SDSC was the original, preference-&-sincerity version.
I preferred preference-&-sincerity because of its universal
applicability, where votes-only had to stipulate a balloting.
On Fri, May 31, 2024 at 12:33 Chris Benham cbenhamau@yahoo.com.au
wrote:
Why are we having a public discussion about a voting method criterion
without anyone giving its definition, and with apparently most of the
participants in the discussion knowing nothing about it besides its name?
https://electowiki.org/wiki/Strategy-free_criterion
The strategy-free criterion is a voting system criterion
https://electowiki.org/wiki/Voting_system_criterion for evaluating voting
systems https://electowiki.org/wiki/Voting_system.
Definitions
A sincere vote is one with no falsified preferences or preferences left
unspecified when the election method allows them to be specified (in
addition to the preferences already specified).
One candidate is preferred over another candidate if, in a one-on-one
competition, more voters prefer the first candidate than prefer the other
candidate.
If one candidate is preferred over each of the other candidates, that
candidate is called "Condorcet candidate" or "Condorcet winner".
Statement of criterion
If a Condorcet candidate exists, and if a majority prefers this
candidate to another candidate, then the other candidate should not win if
that majority votes sincerely and no other voter falsifies any preferences.
In a ranked method, it is nearly equivalent to say:
If more than half of the voters rank x above y, and there is no
candidate z whom more than half of the voters rank above x, then
y must not be elected.
I think this evolved into the Minimal Defense criterion, the
"votes-only version" of which says that if more than half the voters vote A
over B and B no higher than equal-bottom then B can't win.
On 31/05/2024 9:46 pm, Michael Ossipoff wrote:
Some time ago, I wrote a criterion that I called
Strategy-Free-Criterion (SFC).
Is that what you were referring to?
It was about a circumstance in which wv Condorcet is strategy-free. At
that time, autodeterence hadn’t been considered.
SFC didn’t catch-on, & I haven’t heard mention of it lately, & so I
don’t know it’s definition. But wv Condorcet is strategy-free in a
meaningful sense.
On Fri, May 31, 2024 at 05:07 Michael Ossipoff email9648742@gmail.com
wrote:
On Wed, May 29, 2024 at 14:15 Closed Limelike Curves <
closed.limelike.curves@gmail.com>
Ppwrote:
I'm trying to work out how the strategy-free criterion actually
relates to strategy, because it just sounds like it means the
majority-Condorcet criterion ("if a candidate majority-beats every other,
they have to win if everyone is honest"). @Michael Ossipoff ?
Closed, isn’t “Strategy-Free Criterion” your new name for FBC.
It’s a very inaccurate name. FBC-complying methods aren’t
strategy-free in any sense.
But they’re free of any need for drastic defensive strategy
(favorite-burial or any defensive order-reversal).
You want strategy-free? The wv Condorcet methods, such as RP(wv) &
MinMax(wv), are strategy-free in a meaningful sense…effectively free of
need for any defensive strategy…due to their autodeterence.
Election-Methods mailing list - see https://electorama.com/em for list
info
Kevin,
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner.
Instead of "above the preferred frontrunner" don't you mean below the
less-liked frontrunner?
The classic example used by people who like Winning Votes and Approval
to flout those method's compliance with MD (versus the MD failures of
Margins and IRV):
49 A (sincere might be A>B)
24 B (sincere might be B>C)
27 C>B (sincere)
A>C 49-27 (=23) C>B 27-24 (=3) B>A 51-49 (=2)
By Margins A's defeat is the weakest and MinMax (and methods that are
equivalent to it with only 3 candidates, such as Ranked Pairs and
Schulze) using margins elects A.
But Minimal Defense says "not A" because more than half the voters voted
B above A and A not above equal-bottom. MD has no problem with the 27
C>B voters who ranked a candidate above their preferred (presumably
perceived) "frontrunner."
What you wrote seems to better apply to another criterion about voters
"defending the (presumed) sincere CW", Steve Eppley's "Non-Drastic
Defense" that says that if more than half the voters rank X above Y and
X no lower than equal-top then Y can't win.
I think this was his example:
46 A>C (sincere is A>B)
17 B>A (sincere)
17 B>C (sincere)
20 C=B (sincere is C>B)
A>C 63-37 (=26) C>B 46-34 (=12) B>A 54-46 (=8)
More than half the voters have voted B above A and B no lower than
equal-top and so NDD says that A can't win, but Margins elects A.
Winning Votes meets NDD and elects B.
Chris B.
On 2/06/2024 7:23 am, Kevin Venzke wrote:
Hi all,
When I test for SFC compliance the rule on cast votes is that if there is no
majority over A, and A has a majority over B, then B can't win.
This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
in terms of a graph of majority-strength defeats, it would say that if A has a
majority over B and B doesn't have a majority over anyone, then B can't win.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner. So MD is mostly about compromise incentive.
SFC is probably going to be about truncation. When a method fails it, most likely
it's because the majority gave the election away to a less liked compromise choice.
For example:
20 C>A>B
35 A>B
5 B
40 D
Here B is the implicit approval winner, but by SFC B should not win, because it
means it was not safe for the A voters to rank B.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Kevin
votingmethods.net
Kevin,
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Inventing those methods was some achievement as a thought experiment to
demonstrate that certain criteria are mutually compatible.
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on its
electowiki page.
https://electowiki.org/wiki/Majority_Defeat_Disqualification_Approval
Procedure
The voter submits a ranking of the candidates. The candidates
explicitly ranked are considered/approved/by that voter.
A candidate is/dominated/if more than half of the voters rank some
other candidate strictly above him.
All dominated candidates are eliminated, unless this would eliminate
all the candidates.
Of remaining candidates, the one approved by the most voters is elected.
Criteria
MDDAsatisfies theFavorite Betrayal criterion
https://electowiki.org/wiki/Favorite_Betrayal_criterion,Strategy-Free
criterion https://electowiki.org/wiki/Strategy-Free_criterion,
theStrong Defensive Strategy criterion
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion(andMinimal
Defense criterion
https://electowiki.org/wiki/Minimal_Defense_criterion),
andmonotonicity https://electowiki.org/wiki/Monotonicity_criterion.
It failsClone-Winner
https://electowiki.org/wiki/Strategic_nomination, thePlurality
criterion https://electowiki.org/wiki/Plurality_criterion,
theGeneralized Strategy-Free criterion
https://electowiki.org/wiki/Generalized_Strategy-Free_criterion,
theCondorcet criterion
https://electowiki.org/wiki/Condorcet_criterion, theSmith criterion
https://electowiki.org/wiki/Smith_set,Participation
https://electowiki.org/wiki/Participation_criterion, theMajority
criterion for solid coalitions
https://electowiki.org/wiki/Majority_criterion, andLater-no-harm
https://electowiki.org/wiki/Later-no-harm_criterion.
25: A>B
26: B>C
23: C>A
04: C
78 ballots (majority threshold = 40)
B>C 51-27, C>A 53-25, A>B 48-26. Implicit Approval scores: C 53, B 51, A 48.
All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.
Say we now add 22 ballots that all plump (i.e. bullet vote) for C:
25: A>B
26: B>C
23: C>A
26: C
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 48-26. Implicit Approval scores: C 75, B 51, A 48.
Now only B is without a "majority-strength defeat", so the winner changes from C to B.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method would also fail Irrelevant Ballots Independence. It may be far less bad.
https://electowiki.org/wiki/Majority_Approval,_Minimum_Pairwise_Opposition
Procedure
The voter submits a ranking of the candidates. The candidates
explicitly ranked are considered/approved/by that voter.
The/score/for candidate/X/against candidate/Y/is equal to the number
of voters ranking/X/above/Y/. The/max score/of candidate/X/is the
largest score of any other candidate against/X/.
If nobody is approved by more than half of the voters, then the
candidate approved by the most voters is elected.
Otherwise, the candidate with the lowest max score, who is approved by
more than half of the voters, is elected.
Chris B.
On 2/06/2024 7:23 am, Kevin Venzke wrote:
Hi all,
When I test for SFC compliance the rule on cast votes is that if there is no
majority over A, and A has a majority over B, then B can't win.
This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
in terms of a graph of majority-strength defeats, it would say that if A has a
majority over B and B doesn't have a majority over anyone, then B can't win.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner. So MD is mostly about compromise incentive.
SFC is probably going to be about truncation. When a method fails it, most likely
it's because the majority gave the election away to a less liked compromise choice.
For example:
20 C>A>B
35 A>B
5 B
40 D
Here B is the implicit approval winner, but by SFC B should not win, because it
means it was not safe for the A voters to rank B.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Kevin
votingmethods.net
Yeah, MAMPO seems like it might behave more sensibly there.
IIB doesn’t make sense to me outside of positional voting systems (which
trivially satisfy it). If an empty ballot was genuinely intended to be
irrelevant, the voter wouldn’t have cast it in the first place. An
equal-ranking isn’t a way to express indifference (or else equal-ranks
would never happen); it’s a way of pleading the fifth. Learning that a
voter refuses to say whether they prefer Bob or Bill provides an important
piece of information.
Learning a voter has cast a completely blank ballot is an extreme case,
where the ballot provides a very important piece of information: it means
the voter expects a participation failure, because a nonempty ballot will
hurt them.
A rational response to this is to raise the threshold for a defeat, because
setting the bar for a defeat closer to 50% prevents cycles (and therefore
participation failures). In other words, these ballots are very relevant.
On Thu, Jun 6, 2024 at 7:40 AM Chris Benham cbenhamau@yahoo.com.au wrote:
Kevin,
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Inventing those methods was some achievement as a thought experiment to
demonstrate that certain criteria are mutually compatible.
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on its
electowiki page.
https://electowiki.org/wiki/Majority_Defeat_Disqualification_Approval
Procedure
The voter submits a ranking of the candidates. The candidates explicitly
ranked are considered approved by that voter.
A candidate is dominated if more than half of the voters rank some
other candidate strictly above him.
All dominated candidates are eliminated, unless this would eliminate all
the candidates.
Of remaining candidates, the one approved by the most voters is elected.
Criteria
MDDA satisfies the Favorite Betrayal criterion
https://electowiki.org/wiki/Favorite_Betrayal_criterion, Strategy-Free
criterion https://electowiki.org/wiki/Strategy-Free_criterion, the Strong
Defensive Strategy criterion
https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion (and Minimal
Defense criterion https://electowiki.org/wiki/Minimal_Defense_criterion),
and monotonicity https://electowiki.org/wiki/Monotonicity_criterion.
It fails Clone-Winner https://electowiki.org/wiki/Strategic_nomination,
the Plurality criterion https://electowiki.org/wiki/Plurality_criterion,
the Generalized Strategy-Free criterion
https://electowiki.org/wiki/Generalized_Strategy-Free_criterion, the Condorcet
criterion https://electowiki.org/wiki/Condorcet_criterion, the Smith
criterion https://electowiki.org/wiki/Smith_set, Participation
https://electowiki.org/wiki/Participation_criterion, the Majority
criterion for solid coalitions
https://electowiki.org/wiki/Majority_criterion, and Later-no-harm
https://electowiki.org/wiki/Later-no-harm_criterion.
25: A>B
26: B>C
23: C>A
04: C
78 ballots (majority threshold = 40)
B>C 51-27, C>A 53-25, A>B 48-26. Implicit Approval scores: C 53, B 51, A 48.
All the candidates have a majority-strength defeat, so none are eliminated and the most approved candidate, C, wins.
Say we now add 22 ballots that all plump (i.e. bullet vote) for C:
25: A>B
26: B>C
23: C>A
26: C
100 ballots (majority threshold = 51)
B>C 51-49, C>A 75-25, A>B 48-26. Implicit Approval scores: C 75, B 51, A 48.
Now only B is without a "majority-strength defeat", so the winner changes from C to B.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3 ballots that plump for X, the majority threshold rises to 52 and so C's majority-strength defeat goes away and C wins again by being the most approved candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method would also fail Irrelevant Ballots Independence. It may be far less bad.
https://electowiki.org/wiki/Majority_Approval,_Minimum_Pairwise_Opposition
Procedure
The voter submits a ranking of the candidates. The candidates explicitly ranked are considered approved by that voter.
The score for candidate X against candidate Y is equal to the number of voters ranking X above Y. The max score of candidate X is the largest score of any other candidate against X.
If nobody is approved by more than half of the voters, then the candidate approved by the most voters is elected.
Otherwise, the candidate with the lowest max score, who is approved by more than half of the voters, is elected.
Chris B.
On 2/06/2024 7:23 am, Kevin Venzke wrote:
Hi all,
When I test for SFC compliance the rule on cast votes is that if there is no
majority over A, and A has a majority over B, then B can't win.
This is kind of a flip side of MD / SDSC because, if you were forced to explain MD
in terms of a graph of majority-strength defeats, it would say that if A has a
majority over B and B doesn't have a majority over anyone, then B can't win.
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner. So MD is mostly about compromise incentive.
SFC is probably going to be about truncation. When a method fails it, most likely
it's because the majority gave the election away to a less liked compromise choice.
For example:
20 C>A>B
35 A>B
5 B
40 D
Here B is the implicit approval winner, but by SFC B should not win, because it
means it was not safe for the A voters to rank B.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Kevinvotingmethods.net
Hi Chris,
MD basically says that if there are two frontrunners and everyone truncates their
less liked frontrunner, then the worse frontrunner won't win. If this property
doesn't hold, it means the majority has done something to stop the method from
"seeing" their majority, which is surely that they ranked other candidates above
the preferred frontrunner.
Instead of "above the preferred frontrunner" don't you mean below the
less-liked frontrunner?
I don't mean that, and I am not sure how "below the less-liked frontrunner" would
apply? Who in 49/24/27 ranks a candidate below the less-liked frontrunner?
The classic example used by people who like Winning Votes and Approval
to flout those method's compliance with MD (versus the MD failures of
Margins and IRV):
49 A (sincere might be A>B)
24 B (sincere might be B>C)
27 C>B (sincere)
A>C 49-27 (=23) C>B 27-24 (=3) B>A 51-49 (=2)
By Margins A's defeat is the weakest and MinMax (and methods that are
equivalent to it with only 3 candidates, such as Ranked Pairs and
Schulze) using margins elects A.
But Minimal Defense says "not A" because more than half the voters voted
B above A and A not above equal-bottom. MD has no problem with the 27
C>B voters who ranked a candidate above their preferred (presumably
perceived) "frontrunner."
What I'm saying is that if a method fails MD in this scenario, the likely issue
is that the C>B voters ranked C above B, and if they didn't do that, then A
could've been defeated. In this scenario, that is fairly obvious, but it's true
in general, that MD failures are almost always instances of a majority (or part of
one) facing compromise incentive.
In practice you can liken MD / SDSC to a weak form of the strong FBC, and liken SFC
to a weak form of Later-no-harm.
Incidentally I agree with what CLC seems to suggest, that you don't have to discuss
burial to find merit in MD. There are methods with no burial incentive that satisfy
MD and it is certainly not meaningless in those contexts, because it addresses
compromise.
I would not like to see SFC as totally obsolete, since it was one of the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Inventing those methods was some achievement as a thought experiment to
demonstrate that certain criteria are mutually compatible.
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on its
electowiki page.
I can hardly advocate MDDA now due to the Plurality failure. However, it performs
very well in my truncation simulation, as does a method with very similar results,
which I call RMPA (River Majority Pass Approval). However, RMPA doesn't actually
satisfy FBC, so I can't list it in the same breath as the other two.
In RMPA we go down the list of candidates in order of descending implicit approval,
and process each candidate's full majority pairwise wins River-style (using the
"bins" conception, I would suggest). There is no need to sort the propositions; it's
enough to treat each candidate's wins in a batch with arbitrary order. Elect the
owner of the "bin" that the approval winner ends up in.
Of course the method also fails Irrelevant Ballots Independence. If we now add 3
ballots that plump for X, the majority threshold rises to 52 and so C's
majority-strength defeat goes away and C wins again by being the most approved
candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but that method
would also fail Irrelevant Ballots Independence. It may be far less bad.
Something I will have to post about at some point is what a game-changer it is if we
take it as an assumption that elections will have two frontrunners and all voters
use frontrunner truncation strategy. Arbitrary-looking majority rules prove very
useful in maximizing performance.
In such a setting I find that MAMPO is usually not as good as MDDA or RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
It's a different approach from what I usually use, to say "let's just assume voters
act in this way regardless of what the method is." We may not be standing on firm
ground there. But I find it a bit intuitive to think voters will mainly truncate
worse frontrunners. Compromise incentive isn't even completely ignored: By having
voters refuse to compromise, methods that depend on it this to work well (such as
FPP) are penalized in the analysis.
Kevin
votingmethods.net
Something I will have to post about at some point is what a game-changer
it is if we
take it as an assumption that elections will have two frontrunners and all
voters
use frontrunner truncation strategy. Arbitrary-looking majority rules
prove very
useful in maximizing performance.
I think there's a big issue with assuming two frontrunners because A) in
that case, it's just a majority vote between them and B) you can have
situations where multiple candidates have strongly correlated scores, e.g.
if they're all from the same party.
This is why I previously suggested that, ideally, a system should satisfy
both zero-info honesty and LNHe+FBC. This seems like the maximally-honest
combination of properties, because it handles low-information elections
honestly, and high-information elections "as sincerely as possible" (i.e.
no order-reversal, which is enough to guarantee the Condorcet winner is
visible from the ballots).
STAR works off of a very similar principle. The hope is the first stage
will find two similar frontrunners, and then the second stage is
strategyproof (since it's a majority vote). This combination fails both
criteria in theory, but might satisfy them in practice. That's especially
true if you combine it with other improvements: countbacks, a master lever
for straight-ticket voting, and skipping the runoff if the top-two
finishers are from different parties could maximize the chances of STAR
working as it should.
I think the best hope for a system that formally satisfies both criteria is
probably somewhere in the generalized median family of voting methods.
On Sat, Jun 8, 2024 at 3:44 PM Kevin Venzke stepjak@yahoo.fr wrote:
Hi Chris,
MD basically says that if there are two frontrunners and everyone
truncates their
less liked frontrunner, then the worse frontrunner won't win. If this
property
doesn't hold, it means the majority has done something to stop the
method from
"seeing" their majority, which is surely that they ranked other
candidates above
the preferred frontrunner.
Instead of "above the preferred frontrunner" don't you mean below the
less-liked frontrunner?
I don't mean that, and I am not sure how "below the less-liked
frontrunner" would
apply? Who in 49/24/27 ranks a candidate below the less-liked frontrunner?
The classic example used by people who like Winning Votes and Approval
to flout those method's compliance with MD (versus the MD failures of
Margins and IRV):
49 A (sincere might be A>B)
24 B (sincere might be B>C)
27 C>B (sincere)
A>C 49-27 (=23) C>B 27-24 (=3) B>A 51-49 (=2)
By Margins A's defeat is the weakest and MinMax (and methods that are
equivalent to it with only 3 candidates, such as Ranked Pairs and
Schulze) using margins elects A.
But Minimal Defense says "not A" because more than half the voters voted
B above A and A not above equal-bottom. MD has no problem with the 27
C>B voters who ranked a candidate above their preferred (presumably
perceived) "frontrunner."
What I'm saying is that if a method fails MD in this scenario, the likely
issue
is that the C>B voters ranked C above B, and if they didn't do that, then A
could've been defeated. In this scenario, that is fairly obvious, but it's
true
in general, that MD failures are almost always instances of a majority (or
part of
one) facing compromise incentive.
In practice you can liken MD / SDSC to a weak form of the strong FBC, and
liken SFC
to a weak form of Later-no-harm.
Incidentally I agree with what CLC seems to suggest, that you don't have
to discuss
burial to find merit in MD. There are methods with no burial incentive
that satisfy
MD and it is certainly not meaningless in those contexts, because it
addresses
compromise.
I would not like to see SFC as totally obsolete, since it was one of
the motivating
criteria (along with MD and weak FBC) for my methods MDDA and MAMPO :)
Inventing those methods was some achievement as a thought experiment to
demonstrate that certain criteria are mutually compatible.
But MDDA spectacularly fails the maximum-absurdity criterion
Mono-add-Plump, a very interesting fact that isn't mentioned on its
electowiki page.
I can hardly advocate MDDA now due to the Plurality failure. However, it
performs
very well in my truncation simulation, as does a method with very similar
results,
which I call RMPA (River Majority Pass Approval). However, RMPA doesn't
actually
satisfy FBC, so I can't list it in the same breath as the other two.
In RMPA we go down the list of candidates in order of descending implicit
approval,
and process each candidate's full majority pairwise wins River-style
(using the
"bins" conception, I would suggest). There is no need to sort the
propositions; it's
enough to treat each candidate's wins in a batch with arbitrary order.
Elect the
owner of the "bin" that the approval winner ends up in.
Of course the method also fails Irrelevant Ballots Independence. If we
now add 3
ballots that plump for X, the majority threshold rises to 52 and so C's
majority-strength defeat goes away and C wins again by being the most
approved
candidate.
This demonstration of Mono-add-Plump failure doesn't apply to MAMPO, but
that method
would also fail Irrelevant Ballots Independence. It may be far less bad.
Something I will have to post about at some point is what a game-changer
it is if we
take it as an assumption that elections will have two frontrunners and all
voters
use frontrunner truncation strategy. Arbitrary-looking majority rules
prove very
useful in maximizing performance.
In such a setting I find that MAMPO is usually not as good as MDDA or
RMPA, but all
of them outperform all Condorcet methods at sincere Condorcet efficiency.
It's a different approach from what I usually use, to say "let's just
assume voters
act in this way regardless of what the method is." We may not be standing
on firm
ground there. But I find it a bit intuitive to think voters will mainly
truncate
worse frontrunners. Compromise incentive isn't even completely ignored: By
having
voters refuse to compromise, methods that depend on it this to work well
(such as
FPP) are penalized in the analysis.
Kevin
votingmethods.net