[EM] Smith, FPP fails Minimal Defense and Clone-Winner (was "Burlington Vermont repeals IRV 52% to 48%")

Wed Mar 10 00:46:11 PST 2010

On Mar 10, 2010, at 7:08 AM, robert bristow-johnson wrote:

>
> thanks, Chris. i will ponder this.  i understand RP and (i think)  
> Schulze, at least how the mechanisms go, but i'll admit i haven't  
> been as invested in *how* to resolve cycles or *which* Condorcet  
> method is best as much as i am invested in (some) Condorcet vs. IRV  
> vs. FPP or two-round runoff.  the reason is that i am skeptical of  
> the likelihood of a real election with thousands of voters going  
> into a cycle.
>
> considering both the objective advantages of Schulze and the  
> simplicity of Ranked Pairs, i think that if Condorcet would ever be  
> sold to the general population as a method to decide elections for  
> government, i would suggest Ranked Pairs.  but maybe it should be  
> IRV (if a cycle) or something wild-assed.  whatever will be needed  
> politically to get people to buy into Condorcet.
>
> maybe it is, but i don't think that is the same mistake as, when the  
> Ranked Ballot is introduced to folks in Vermont or Minnesota or San  
> Francisco or North Carolina, attaching that ranked ballot to the IRV  
> method of tabulation.  that was a mistake and it doesn't serve as a  
> stepping stone to better elections with Condorcet (because of  
> entrenchment of IRV supporters and, i believe, a near certainty of  
> IRV displaying anomalies that turn everyone off of IRV and, by  
> association, the Ranked Ballot).
>
> so, keeping RP, Schulze in mind for later, what would be a "good"  
> scheme for resolving cycles by use of elimination of candidates?   
> what would be a "good" (that is resistant to more anomalies) and  
> simple method to identify the "weakest candidate" (in the Smith set)  
> to eliminate and run the beats-all tabulation again? i'm not saying  
> elimination is a good way to do it, but it might be easier to sell  
> to neanderthal voters.

All methods have some weaknesses that can be used against them in the  
marketing battle. So maybe the challenge is to build a solid campaign  
that is convincing enough to neutralize all emerging fears and failure  
examples.

Schulze method is quite convincing since it is already in use in many  
places. (I'm not sure it is objectively better than ranked pairs and  
others although it is certainly a good method.) Ranked pairs can be  
easily described as a method that sequentially confirms pairwise wins,  
so it is almost as natural and straight forward sequential algorithm  
based as IRV (although it is a bit more complex in the sense that it  
compares pairs instead of single candidates when making the sequential  
decisions). And there are also simpler Condorcet methods like  
minmax(margins) that simply counts the number of additional votes each  
candidate would need to beat all others.

I'm not aware of any sequential candidate elimination based method  
that I'd be happy to recommend. One can however describe e.g.  
minmax(margins) in that way. Eliminate the candidate that is worst in  
the sense that it would need most additional votes to win others, then  
the next etc. In the elimination process one would consider also  
losses to candidates that have already been eliminated (I wonder if  
this approach makes it less "natural looking" than the elimination  
process of IRV).

But as said, maybe the key is to arrange a solid campaign. You can  
surely e.g. find lots of election method experts that are happy to  
agree that Condorcet methods are the best for some city for some need  
and best single winner methods (for competitive elections) in general.  
But quite certainly there will be also experts that think otherwise.  
And there is certainly a risk that all the Condorcet friendly experts  
will use different argumentation, may disagree on details and as a  
result will confuse the audience. Maybe one should start from  
Scientific American etc. to first firmly establish the idea that  
Condorcet methods indeed are the de facto state of art methods (and  
practical too). IRV campaigns have been successful, so I wonder why  
Condorcet campaigns could not follow (maybe Burlington needs a timeout  
now but not much more, and other cities could take steps forward  
already now and support Burlington that way).

(I have to add that if people want to keep the USA as it mostly is, a  
two party based system, then I must recommend FPTP :-). And if not,  
then maybe also some additional (maybe proportionality related)  
reforms are needed.)

Juho

>
> r b-j
>
>
> On Mar 9, 2010, at 11:45 PM, C.Benham wrote:
>
>>
>> Robert Bristow-Johnson wrote (5 March 2010):
>>
>>> i like Ranked Pairs best, too. and if the Smith Set are three  
>>> candidates, it and Schulze pick the same winner.
>>>
>>> > Bringing Plurality in would be a distraction, since we have no  
>>> need
>>> > to go near this method and risk a worse answer.
>>>
>>> it's a "worse answer" in a weird circumstance where an argument  
>>> could be made that any in the Smith set have
>>> some reasonable claim or legitimacy to be elected. why not the guy  
>>> with the most votes?
>>
>> Interpreting "most votes" as  'top-ranked on the greatest number of  
>> ballots', the answer is that the resulting method
>> fails the Clone-Winner and  Minimal Defense criteria.
>>
>> 49: A
>> 24: B
>> 27: C>B
>>
>> A>C 49-27,  C>B 27-24,  B>A 51-49
>>
>> More than half the voters have ranked B above A and A no higher  
>> than equal bottom, and yet Smith,FPP elects A.
>>
>> The Ranked Pairs and  River and Smith//MinMax and Schulze  
>> algorithms, using Margins as the measure of defeat
>> strength (referred to collectively as "Margins")  and  IRV  also  
>> elect  A.
>>
>> Say we replace A with a set of clones,  A1 and A2.
>>
>> 26: A1>A2
>> 23: A2>A1
>> 24: B
>> 27: C>B
>>
>> (A2 > C > B > A1 > A2)
>>
>> Now Smith,FPP elects C violating Clone-Winner. Those other methods  
>> I mentioned meet Clone-Winner  and so
>> elect one of the clones (A1).
>>
>> The number of people (ballots)  that voted for (ranked above equal- 
>> bottom) the clones and not C exceeds the number
>> that voted for C, and yet C wins violating my suggested  "Strong  
>> Minimal Defense" criterion.
>>
>> Chris Benham
>>
>>
>> http://wiki.electorama.com/wiki/Minimal_Defense_criterion
>>
>> http://nodesiege.tripod.com/elections/#critmd
>>
>> http://nodesiege.tripod.com/elections/#critclone
>>
>> Douglas Woodall splits Clone Independence into "Clone-Winner" and  
>> "Clone-Loser".
>> Clone-Winner says that if winning candidate X is replaced by a set  
>> of clones than the winner must come from that
>> set.  Clone-Loser says that the winner shouldn't change if one (or  
>> more)  losers are replaced  by a set (or sets) of clones.
>>
>>
>>
>>
>>
>>
>>
>>
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>
> --
>
> r b-j                  rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
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