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<p>Kristofer,<br>
<br>
What does "IIRC" mean?<br>
<br>
<blockquote type="cite">I can see two ways to interpret pushover.
The definition from Electowiki is:
<br>
<br>
"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."
<br>
</blockquote>
<br>
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.<br>
<br>
The older definition you helpfully recovered from Condorcet.org :<br>
<blockquote type="cite"><b>push-over</b> <br>
The strategy of ranking a weak alternative higher than one's
preferred
alternative, which may be useful in a method that violates <a
href="https://web.archive.org/web/20090713234702/http://www.condorcet.org:80/emr/defn.shtml#monotonicity">monotonicity</a>.</blockquote>
<blockquote type="cite"><b>monotonicity</b> <br>
The property of a method where an alternative can never be made
to succeed by
being ranked lower on some ballots. Doing this is using the "<a
href="https://web.archive.org/web/20090713234702/http://www.condorcet.org:80/emr/defn.shtml#push-over">push-over</a>"
strategy.</blockquote>
<br>
I think this old Blake Cretney definition is right if we assume
strict ranking ballots (i.e. no above-bottom equal-ranking
allowed).<br>
<br>
<blockquote type="cite">A strict interpretation considers
"defeating it" to mean "turn the candidate from winning to no
longer winning".</blockquote>
</p>
<p>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<br>
of the election process.<br>
<br>
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.<br>
<br>
Chris B.<br>
<br>
</p>
<div class="moz-cite-prefix">On 1/10/2023 11:38 pm, Kristofer
Munsterhjelm wrote:<br>
</div>
<blockquote type="cite"
cite="mid:f4b46665-d77a-ee1a-cb99-b455c2b6adac@t-online.de">On
10/1/23 10:44, Rob Lanphier wrote:
<br>
<br>
<blockquote type="cite">This claim you make is interesting:
<br>
"[STAR] somehow doesn't 'violate monotonicity' and yet [...]
is more vulnerable to Pushover than RCV (aka IRV) which does.".
<br>
<br>
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.
<br>
</blockquote>
<br>
I think this problem is about how to interpret pushover.
Mono-raise IIRC comes in these two forms:
<br>
<br>
1. If you raise A and A goes from winning to losing, that's a
failure.
<br>
2. If you lower A and A goes from losing to winning, that's a
failure.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
I can see two ways to interpret pushover. The definition from
Electowiki is:
<br>
<br>
"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."
<br>
<br>
A strict interpretation considers "defeating it" to mean "turn the
candidate from winning to no longer winning". That interpretation
thus is:
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
STAR does not have this particular type of pushover.
<br>
<br>
But here's a looser type of pushover:
<br>
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...
<br>
<br>
2. (same as #2 above)
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
(But not if X is Trump: then you get a backfire.)
<br>
<br>
Strictly speaking, a monotone ranked method could also have this
type of pushover strategy, e.g. a voter voting:
<br>
<br>
B>A>C>D>E>F>X
<br>
<br>
leads A to win, but
<br>
<br>
B>A>X>C>D>E>F
<br>
<br>
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.
<br>
<br>
-km
<br>
</blockquote>
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