Rob,

Blake Cretney (who used to be active here) had a web-page
("condorcet.org" I think it was called)
that is unfortunately now extinct. I regret not copying and storing the
definitions/explanations that
were there.

On 10/1/23 10:44, Rob Lanphier wrote:

I think this problem is about how to interpret pushover. Mono-raise IIRC
comes in these two forms:

1. If you raise A and A goes from winning to losing, that's a failure.
2. If you lower A and A goes from losing to winning, that's a failure.

Suppose A is the winner in STAR. Then raising A can't bump him off the
top two who advance to the final, nor can it reverse A's pairwise
victory over the other finalist B.

Similarly, lowering A's score can't get A into the top two if he wasn't
already, nor can it turn B>A into A>B. So STAR is monotone.

I can see two ways to interpret pushover. The definition from Electowiki
is:

"Push-over is a type of tactical voting that is only useful in methods
that violate monotonicity. It may involve a voter ranking or rating an
alternative lower in the hope of getting it elected, or ranking or
rating an alternative higher in the hope of defeating it."

A strict interpretation considers "defeating it" to mean "turn the
candidate from winning to no longer winning". That interpretation thus is:

1. If you prefer B to A, A is winning, and you raise your ranking/rating
   of A with the intent of having the result change from A to B, then
   that's pushover strategy.

2. If you prefer B to A, A is winning, and you lower your ranking/rating
   of B with the intent of having the result change from A to B, then
   that's also pushover strategy.

I.e. the candidate you're altering the position of must be either the
candidate who's winning or the candidate you want to win. By this
interpretation, pushover implies monotonicity failure, because if
raising A made A lose, that's a failure of the first kind, and if
lowering B made B win, that's a failure of the second kind.

STAR does not have this particular type of pushover.

But here's a looser type of pushover:

1. If you prefer B to A, A is winning, and you raise your ranking/rating
   of some other candidate X with the intent of having the result change
   from A to B...

2. (same as #2 above)

then STAR does fail. Suppose B beats X pairwise but A beats B
pairwise, and the finalist set before strategizing is {A, B} so that A
wins... then by increasing your rating of X, you might bump A off the
set so that it's {B, X} instead, after which B beats X and wins.

The "pied piper" strategy seems to be closer to this type than the
strict interpretation. A is the mainstream Republican, B is the
mainstream Democrat, and X is the outrageous Republican. By supporting
X, the Democrats intend to induce some Republican voters to "rank or
rate X higher", i.e vote for X rather than A in the primary. The
intended effect is to knock A out, which leads to the general being
between B and X, where B then (presumably) wins.

(But not if X is Trump: then you get a backfire.)

Strictly speaking, a monotone ranked method could also have this type of
pushover strategy, e.g. a voter voting:

B>A>C>D>E>F>X

leads A to win, but

B>A>X>C>D>E>F

leads B to win. But because the strict version implies nonmonotonicity
and ranking X higher is often accompanied by A being ranked lower, it's
associated with nonmonotonicity for ranked methods. I'm not aware of any
monotone methods with this kind of failure.

-km

Hi Chris,

I'm going to reply to your original email (and quote it on the
bottom).  I'm going to replace "SCORE" with "[STAR]" in your email,
because you agreed in an earlier mail that's what you meant

I have a lot clearer idea of what the "pushover" strategy is now,
thanks (at least partially) to your email (thank you!).  My hunch is
that the pushover strategy may not be as well-studied, but it may be
that there's different terminology used in academic circles (perhaps
"pied piper"...see below).  I'm assuming from your email address that
you're Australian.  Is "pushover" strategy common in Australian
elections, and commonly named by that name?   My hunch is that
pushover is a bigger problem in IRV/RCV/STV than it is in more
consensus-oriented election methods (like approval, any Condorcet
system, STAR).  I ask this because we don't talk about "pushover" here
in the United States, but it wouldn't surprise me if Australians talk
about it a lot.  We don't have very many places using STV/IRV/RCV, and
the politics of those places (e.g. San Francisco, Cambridge Mass) are
treated like outliers in mainstream political conversation.  San
Francisco has weird politics (which I assert from my office in San
Francisco)

There are more places that use "top-two open primary" (like California
and Washington state). "Pushover" hasn't (yet) made it into the
mainstream political lexicon in either place (that I know of), but I
do know that in 2022, the Democratic Party here made a point of trying
pushover against the Republicans in regular first-past-the-post
primaries :
https://www.washingtonpost.com/politics/2022/09/12/democrats-interfere-republican-primaries/

It was a risky strategy, but (I'm sad to say) it probably worked in
2022.  It failed for Hillary Clinton in 2016 though (see this 2016
article about Clinton's "pied-piper strategy"):
https://www.salon.com/2016/11/09/the-hillary-clinton-campaign-intentionally-created-donald-trump-with-its-pied-piper-strategy/

This claim you make is interesting:
 "[STAR] somehow doesn't 'violate monotonicity' and yet [...] is more
vulnerable to Pushover than RCV (aka IRV) which does.".

Is that true?  It seems to me that RCV's series of runoffs lead to
many opportunities for weak candidates to snowball via transfers from
eliminated candidates.  The snowball effect in RCV usually snowballs
to the center of public opinion, but can sometimes roll toward the
outskirts as candidates get eliminated and their ballots get
transferred to a stronger and stronger candidate on the outskirts. 
With STAR (and Score), I believe the candidate needs to have strong
support from all voters to get a high enough score to advance (since
all ballots are considered in the runoff round), but perhaps similar
polarization can occur under STAR over time.  It's truly an
interesting question which method is more susceptible to pushover.

As for the monotonicity of STAR, I'll need to leave it as an exercise
for the reader.  I'm not sure anyone has proven that STAR is
monotonic, though I suspect that an example of non-monotonic STAR
would be a really weird edge-case.

Rob
p.s. I've replaced "SCORE" with "[STAR]", but won't correct your
spelling of "maximising" nor "favourite", even though my spell checker
really wants me to. English-speaking people are one people, separated
by common language.  :-)

On Sat, Sep 30, 2023 at 1:07 AM C.Benham cbenham@adam.com.au wrote:

 Rob,

 Blake Cretney (who used to be active here) had a web-page
 ("condorcet.org <http://condorcet.org>" I think it was called)
 that is unfortunately now extinct. I regret not copying and
 storing the definitions/explanations that
 were there.

 That is where "Push-over" strategy was defined.  As I recall it
 said something simple like
 "the strategy of promoting a weak alternative for it to be beaten
 by a preferred stronger one".

 But really I think we are in the realm of common-sense and the
 bleeding obvious rather than being
 in awe of and deferring to academic authority.  Whatever it is
 exactly called, in the US political system it must be commonplace.

 Because (at least in some states) you have open public party
 primaries. Suppose you are a supporter of party A, and either you
 are happy with all the candidates running in A's primary election
 (or you are confidant that your favourite can win that primary
 without your help, or something in between) and so you decide to
 instead vote in main rival party B's primary to vote not for your
 sincere lesser evil but for the candidate you think would have the
 smallest chance of beating the A candidate in the general election.

 You would be using a Push-over strategy.

 Likewise suppose the method is plurality Top-Two Runoff.  If you
 are confident that your favorite can make it into the top two
 without your help then in the first round you might vote for a
 candidate (of course preferably among the other front-runners for
 the second spot) that you think most likely to lose in the runoff
 against your favourite. Then in the final you can vote sincerely.

 If the method is approval TTR, things are much easier for the
 pushover strategists because they don't have to rely on on other
 voters to get their favourite into the final two, and also they
 don't have to limit themselves to promoting just one weak candidate.

 If you only care about electing your favourite, the obvious
 strategy is to approve your favourite and all the candidates that
 you are confident can neither displace your favourite out of the
 top two or pairwise beat your favourite in the final.

 [STAR] is similar.  There one can choose between maximising the
 chance that a weak candidate will get in to the final two, or
 weakening your vote for the weak candidate to just below maximum
 (4 instead of 5) so as to help your favourite win the top-two
 pairwise comparison.

 In comparison with the methods I've so far mentioned in RCV (fka
 IRV) the would-be pushover strategists face the greatest problems
 and risks. They have to rely entirely on other voters to both get
 their sincere favourite into the final top two and also to
 overcome the strategists' own votes, for the strategists' sincere
 favourite to win the final two comparison.

 That electowiki entry you linked to:

 The first sentence looks like something I recall from that extinct
 page. It is correct in the universe of pure ranking methods. But
 according to apparent consensus here (and a wikipedia page you
 linked to)  [STAR] somehow doesn't "violate monotonicity" and yet
 (as I've discussed) is more vulnerable to Pushover than RCV (aka
 IRV) which does.

 Regarding the last bit, I've no idea how the author would know
 that it "often backfires", or have any idea how "often" it is
 attempted.

 Chris Benham

 ----
 Election-Methods mailing list - see https://electorama.com/em for
 list info

Rob,

Is "pushover" strategy common in Australian elections, and commonly named
by that name?

No and no.  I've only ever come across the term here, and from that Blake
Cretney page.

Seats/districts where that would even be a theoretical possibility would
rare. I did read a report in a newspaper
some time in the 1980s that the conservative Liberal Party toyed with the
idea of doing that in one seat, but rejected
the idea on the grounds that it would undermine the perceived integrity of
the election process and so the legitimacy
of the winner. Bear in mind that we have "compulsory voting" which is
popular, because it is widely accepted that
voting is a civic duty.

In that district the highly predictable FPP order was Right > Centre-Right

Liberal > Australian Democrats > Labor.

It was also highly predictable that nearly all of the Labor voters would
give their second preference to the Democrat and
that a big majority of the Democrat voters would give their second
preference vote to the Liberal.  (Bear in mind that truncation
isn't allowed).

In that circumstance the Liberals could have organised for some of their
supporters to vote Labor to "rescue" that candidate
from being eliminated, so that instead the Democrat will be eliminated and
then the Liberal will win in the pairwise contest
with Labor.  BTW, the Democrat was the sitting member (and it may have
been that party's only seat in the state parliament,
Labor and Liberal are the two major parties).  Of course the Democrat was
the Condorcet winner, but no-one  even had that
concept.

This claim you make is interesting:
"[STAR] somehow doesn't 'violate monotonicity' and yet [...] is more
vulnerable to Pushover than RCV (aka IRV) which does.".

Is that true?

Yes.

It seems to me that RCV's series of runoffs lead to many opportunities for
weak candidates to snowball via transfers from eliminated candidates.  The
snowball effect in RCV usually snowballs to the center of public opinion,
but can sometimes roll toward the outskirts as candidates get eliminated
and their ballots get transferred to a stronger and stronger candidate on
the outskirts.

Now you are just talking about things connected with RCV's clone
independence and slight "extremist bias". Nothing to do with Pushover.

With STAR (and Score), I believe the candidate needs to have strong
support from all voters to get a high enough score to advance (since all
ballots are considered in the runoff round), but perhaps similar
polarization can occur under STAR over time.

This is also completely irrelevant to Pushover strategy (which doesn't
necessarily have anything to do with polarization).

It's truly an interesting question which method is more susceptible to
pushover.

As a matter of simple logic STAR is much more susceptible.  The aim of the
Pushover strategist is create a two-candidate final consisting of his
favourite plus a "turkey".
(I've come across the term "turkey-raising" from a US source about voting
methods. Maybe it means the same thing as pushover.)

One of the dangers for the strategist is that his favourite won't make it
into the final, perhaps being displaced out of it by the turkey.  This
danger is obviously much lower
for the STAR strategist because (unlike the RCV strategist) he can fully
vote to help his favourite into the final as well as the turkey.  The RCV
strategist has to fully rely
on other voters to get his favourite into the final.

The second danger for the Pushover strategist is that in the final the
"turkey" might win. In that final the RCV strategist has to actually vote
for the turkey and hope that
his vote is overwhelmed by others.  The STAR strategist doesn't have that
problem. He can choose between "pushover-lite" where he gives the turkey
the second-highest
possible score so that his vote still helps his favourite beat the turkey
in the final,  and "full" pushover to maximise his help for the turkey into
the final in which case in the
final his vote merely has no effect.

Chris Benham

On 1/10/2023 7:14 pm, Rob Lanphier wrote:

Hi Chris,

I'm going to reply to your original email (and quote it on the bottom).
I'm going to replace "SCORE" with "[STAR]" in your email, because you
agreed in an earlier mail that's what you meant

I have a lot clearer idea of what the "pushover" strategy is now, thanks
(at least partially) to your email (thank you!).  My hunch is that the
pushover strategy may not be as well-studied, but it may be that there's
different terminology used in academic circles (perhaps "pied piper"...see
below).  I'm assuming from your email address that you're Australian.  Is
"pushover" strategy common in Australian elections, and commonly named by
that name?  My hunch is that pushover is a bigger problem in IRV/RCV/STV
than it is in more consensus-oriented election methods (like approval, any
Condorcet system, STAR).  I ask this because we don't talk about "pushover"
here in the United States, but it wouldn't surprise me if Australians talk
about it a lot.  We don't have very many places using STV/IRV/RCV, and the
politics of those places (e.g. San Francisco, Cambridge Mass) are treated
like outliers in mainstream political conversation.  San Francisco has
weird politics (which I assert from my office in San Francisco)

There are more places that use "top-two open primary" (like California and
Washington state).  "Pushover" hasn't (yet) made it into the mainstream
political lexicon in either place (that I know of), but I do know that in
2022, the Democratic Party here made a point of trying pushover against the
Republicans in regular first-past-the-post primaries :

https://www.washingtonpost.com/politics/2022/09/12/democrats-interfere-republican-primaries/

It was a risky strategy, but (I'm sad to say) it probably worked in 2022.
It failed for Hillary Clinton in 2016 though (see this 2016 article about
Clinton's "pied-piper strategy"):

https://www.salon.com/2016/11/09/the-hillary-clinton-campaign-intentionally-created-donald-trump-with-its-pied-piper-strategy/

This claim you make is interesting:
"[STAR] somehow doesn't 'violate monotonicity' and yet [...] is more
vulnerable to Pushover than RCV (aka IRV) which does.".

Is that true?  It seems to me that RCV's series of runoffs lead to many
opportunities for weak candidates to snowball via transfers from eliminated
candidates.  The snowball effect in RCV usually snowballs to the center of
public opinion, but can sometimes roll toward the outskirts as candidates
get eliminated and their ballots get transferred to a stronger and stronger
candidate on the outskirts.  With STAR (and Score), I believe the candidate
needs to have strong support from all voters to get a high enough score to
advance (since all ballots are considered in the runoff round), but perhaps
similar polarization can occur under STAR over time.  It's truly an
interesting question which method is more susceptible to pushover.

As for the monotonicity of STAR, I'll need to leave it as an exercise for
the reader.  I'm not sure anyone has proven that STAR is monotonic, though
I suspect that an example of non-monotonic STAR would be a really weird
edge-case.

Rob
p.s. I've replaced "SCORE" with "[STAR]", but won't correct your spelling
of "maximising" nor "favourite", even though my spell checker really wants
me to.  English-speaking people are one people, separated by common
language.  :-)

On Sat, Sep 30, 2023 at 1:07 AM C.Benham cbenham@adam.com.au wrote:

On 10/1/23 10:44, Rob Lanphier wrote:

I think this problem is about how to interpret pushover. Mono-raise
IIRC comes in these two forms:

1. If you raise A and A goes from winning to losing, that's a failure.
2. If you lower A and A goes from losing to winning, that's a failure.

Suppose A is the winner in STAR. Then raising A can't bump him off the
top two who advance to the final, nor can it reverse A's pairwise
victory over the other finalist B.

Similarly, lowering A's score can't get A into the top two if he
wasn't already, nor can it turn B>A into A>B. So STAR is monotone.

I can see two ways to interpret pushover. The definition from
Electowiki is:

"Push-over is a type of tactical voting that is only useful in methods
that violate monotonicity. It may involve a voter ranking or rating an
alternative lower in the hope of getting it elected, or ranking or
rating an alternative higher in the hope of defeating it."

A strict interpretation considers "defeating it" to mean "turn the
candidate from winning to no longer winning". That interpretation thus
is:

1. If you prefer B to A, A is winning, and you raise your
   ranking/rating of A with the intent of having the result change from A
   to B, then that's pushover strategy.

2. If you prefer B to A, A is winning, and you lower your
   ranking/rating of B with the intent of having the result change from A
   to B, then that's also pushover strategy.

I.e. the candidate you're altering the position of must be either the
candidate who's winning or the candidate you want to win. By this
interpretation, pushover implies monotonicity failure, because if
raising A made A lose, that's a failure of the first kind, and if
lowering B made B win, that's a failure of the second kind.

STAR does not have this particular type of pushover.

But here's a looser type of pushover:

1. If you prefer B to A, A is winning, and you raise your
   ranking/rating of some other candidate X with the intent of having the
   result change from A to B...

2. (same as #2 above)

then STAR does fail. Suppose B beats X pairwise but A beats B
pairwise, and the finalist set before strategizing is {A, B} so that A
wins... then by increasing your rating of X, you might bump A off the
set so that it's {B, X} instead, after which B beats X and wins.

The "pied piper" strategy seems to be closer to this type than the
strict interpretation. A is the mainstream Republican, B is the
mainstream Democrat, and X is the outrageous Republican. By supporting
X, the Democrats intend to induce some Republican voters to "rank or
rate X higher", i.e vote for X rather than A in the primary. The
intended effect is to knock A out, which leads to the general being
between B and X, where B then (presumably) wins.

(But not if X is Trump: then you get a backfire.)

Strictly speaking, a monotone ranked method could also have this type
of pushover strategy, e.g. a voter voting:

B>A>C>D>E>F>X

leads A to win, but

B>A>X>C>D>E>F

leads B to win. But because the strict version implies nonmonotonicity
and ranking X higher is often accompanied by A being ranked lower,
it's associated with nonmonotonicity for ranked methods. I'm not aware
of any monotone methods with this kind of failure.

-km

Courtesy of someone (I'm sure a promoter of STAR) Electowiki has been
made much worse (IMHO) than it used to be, and so is now not great.

The older definition you helpfully recovered from Condorcet.org :

I think this old Blake Cretney definition is right if we assume strict
ranking ballots (i.e. no above-bottom equal-ranking allowed).

No, I think it is about raising a "weak" candidate in order to "defeat
it" (and thereby win the election) instead of losing to a stronger
candidate in the final decisive part
of the election process.

You seem to be right about STAR meeting mono-raise.   I suspect that the
Electowiki entry is an attempt to define Push-over in such a way that it
can't be a problem for STAR.