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

[Kristofer Munsterhjelm]

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