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

[C.Benham]

Kristofer,

What does "IIRC" mean?

> 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."

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 :
> *push-over*
> The strategy of ranking a weak alternative higher than one's preferred 
> alternative, which may be useful in a method that violates 
> monotonicity 
> <https://web.archive.org/web/20090713234702/http://www.condorcet.org:80/emr/defn.shtml#monotonicity>.
> *monotonicity*
> 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 "push-over 
> <https://web.archive.org/web/20090713234702/http://www.condorcet.org:80/emr/defn.shtml#push-over>" 
> strategy.

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

> A strict interpretation considers "defeating it" to mean "turn the 
> candidate from winning to no longer winning".

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.

Chris B.

On 1/10/2023 11:38 pm, Kristofer Munsterhjelm 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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