[EM] St. Louis and Pushover (Re: Reply to Rob regarding RCV)

[Rob Lanphier]

Thanks Kristofer!  Your analysis is really helpful for me as I try to
explain this to a broader audience than the folks on this mailing list.  I
strongly suspect that 99.999% of people who aren't on this mailing list
have no idea what the term "pushover" means, and now I suspect that most
people on this mailing list can't define it unambiguously.  I've started a
stub article here:
https://electowiki.org/wiki/Pushover

I'm hoping all y'all on this mailing list help improve the new "Pushover"
article.

I found the part in the "Tactical voting" page's changelog where pushover
was defined relative to monotonicity on electowiki:
https://electowiki.org/w/index.php?title=Tactical_voting&diff=prev&oldid=3014

It would seem that James Green-Armytage (or someone assuming that name)
defined "pushover" in terms of monotonicity back in 2005.

A prior definition that was briefly on electowiki shortly after it was
copied over from English Wikipedia states the following:

> '''Push-over''' or '''turkey-raising''' is a type of strategic voting in
> which a voter ranks a perceived weak alternative higher, but not in the
> hopes of getting it elected.  For example, in a [[bloc voting|bloc vote]]
> where multiple votes are required, a voter may insincerely vote for a
> candidate they perceive as unlikely to win, in order to help their
> preferred candidate win.
>

See <
https://en.wikipedia.org/w/index.php?title=Strategic_voting&oldid=10141683>
to see the version on English Wikipedia at the time it was copied.  I fear
it was a mistake to define "pushover" in terms of monotonicity on
electowiki, since it seems the "pushover" term is used for "turkey-raising"
in some contexts (as I'm assuming based on Chris Benham's email and the
contents of English Wikipedia in 2004 and 2005).

Rob

On Sun, Oct 1, 2023 at 6:08 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

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