[EM] Smith, FPP fails Minimal Defense and Clone-Winner (was "Burlington Vermont repeals IRV 52% to 48%")
rbj at audioimagination.com
Tue Mar 9 21:08:21 PST 2010
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
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
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
>> > 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
> Douglas Woodall splits Clone Independence into "Clone-Winner" and
> 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
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