[EM] Smith//MMPO

C.Benham cbenham at adam.com.au
Sun Sep 25 08:47:55 PDT 2016


In a recent earlier post you wrote:
> Plurality is a positional criterion. A positional standard won't give 
> the desired properties. 

C: A pairwise version is possible, "Pairwise Plurality" (PP):

*If X's smallest pairwise score is bigger than Y's largest pairwise 
score, then Y can't win.*

(I would favour the "above-bottom equal-ranking whole" version of 
"pairwise score").

The Plurality criterion is also akin to a stronger part-pairwise, 
part-positional criterion I like
that says that if  X both pairwise-beats Y and positionally dominates Y, 
then Y can't win.

(IRV  and Benham fail this, but they meet normal Plurality).

35 A>B
25 B
40 C
21 D

> Yes, that's a problem for MMPO. Maybe it's just offensive strategy by 
> A voters taking advantage of LNHe failure.
> It's a cycle. It's unknowable who, if anyone, is CWs, or who's 
> strategizing.
> But doesn't that mean that one interpretation is as good as another?

C: No.  I think meeting Condorcet is nice, and consistent with that 
standard is Smith and Condorcet Loser and Smith Loser.

But some Condorcet advocates think that one of the members of the Smith 
set might be (or likely is)  the  (centrist) "sincere CW",
and that the algorithm's most important task is to (perhaps with the 
help of wise and heroic "defensive" strategists) guess who
that candidate might be and elect hir.

I'm not on board with that philosophy.  There are other important 
"representative" criteria which can make distinctions among
the members of the Smith set.

> Maybe allowing that possible offensive strategy by A voters is as bad 
> as the Chicken-Dilemma. Is it?

C: No, it's much worse.  Failing Chicken-Dilemma allows the method to 
meet Minimal Defense, whereas allowing that
"possible offensive strategy" to succeed is related to the method's 
failure of Plurality.

> It requires order-reversal. 

C: Not if sincere is just A (i.e. A>C=B=D).

> Isn't it more of an assumption, to assume order reversal instead of 
> mere refusal to help?
> Which is easier & more likely?

C: If the method has a random-fill incentive then it is more logical to 
assume that truncators are more sincere than those
who rank more candidates.

The chicken strategists are taking some risk, whereas the offensive 
buriers may not be.

> Weak CD, FBC, & MAM strategy...That's a lot of important advantages.
> It would take a really _bad_ problem to rule out a method like that.

C: The "Smith" in Smith//MMPO  kills FBC.   And I'm not clear on the 
definition of  "Weak CD".

> C: What is "MAM-like strategy" and what do you think is so good  
> ("optimally unproblematic")  about it?
> M: Truncation by 1 faction can't defeat a  CWs & elect the truncators' 
> candidate.
> ...as it often can with other pairwise-count methods.
> Defensive truncation, plumping, by the CWs's voters thwarts & 
> penalizes burial.

C: What if the "defensive truncators"  don't know (or guess wrong)  who 
the (sincere) "CW" is?

Could that be a debacle?

I'd be interested in seeing one or two examples of  "MAM-like strategy" 
in operation.

Chris Benham

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