Re: [EM] Yee/B.Olson Diagram Remarks

2008-12-19 Thread fsimmons
Property (2) below is not always apparent in existing YBD's, because when sigma 
is small the notch 
that makes A's win region non-starlike will also be small and will be within 
sigma of the center of the 
circle that circumscribes the candidate triangle.  This center is (as often as 
not) outside the viewing 
window of the YBD when the triangle is obtuse.

To understand why this is so, contemplate the basic reason for the non-starlike 
effect:  

For each sigma, there is a point P in candidate C's win region for which there 
is a first place preference 
tie when the distribution of voters centered at P has standard deviation sigma. 
 If sigma is small P will be 
near the center of the circumscribed circle.   

When the center of the distribution is moved directly towards the long side of 
the triangle the first place 
preferences are in order of ABC, and A wins the runoff between A and B. 

But when the center moves directly from P towards any point A' sufficiently 
near A, the first place 
preferences change to the order order ACB, and C wins the runoff between A 
and C.  

This effect creates the notch that makes A's win region non-starlike.

 Here's the latest update on my investigation of squeeze out and 
 non-starlike effects in Yee/B.Olson 
diagrams (YBD's) of IRV.

 I'm still concentrating on the three candidate case,

 If the triangle of candidates is scalene, then ...

 (1) for all sufficiently large values of sigma (the standard deviation of the 
 voter distributions) candidate 
C (the one opposite the longest side of the triangle) will be excluded from her 
own win region.  The bigger 
sigma, the further outside her win region.  As sigma gets larger without bound 
the distance from C to the 
win region grows without bound.

 (2) for all sufficiently small values of sigma, the win region for candidate 
 A (the candidate opposite the 
smallest side of the triangle) is not starlike relative to A.

 I am working on mapping the size of the sigma gap between these two kinds of 
 pathologies.

Included in this investigation is a precise mapping of the set of triangles for 
which the two pathologies 
overlap, i.e. for which there exist values of sigma that are simultaneously 
large enough for (1) and small 
enough for (2).

Soon I will give details (pseudo code) of a procedure for determining the 
greatest lower bound for the 
values of sigma in (1) and the least upper bound for the values of sigma in 
(2).given any set of sides, 
vertices, and/or angles that determine the candidate triangle.

Forest

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Re: [EM] FairVote on Robert's Rules of Order and IRV

2008-12-19 Thread Dave Ketchum

Authors of RR have their own primary goals and properly avoid the election
methods wars that take place in EM, etc, - simply recommending that group's
rules authors should be careful as to what methods they choose to define
for their groups.

DWK

On Sun, 14 Dec 2008 21:27:40 -0500 Abd ul-Rahman Lomax wrote:
 At 12:49 PM 12/14/2008, Steve Eppley wrote:

 Hi,

 I think Mr. Lomax missed the big point (though I agree he is right to
 criticize Instant Runoff).  The big point is that the authors of books
 on Robert's Rules showed zero awareness of the existence of
 Condorcetian preferential voting methods--or perhaps they were aware
 but their analysis was made before the technological age made it easy
 to exhaustively tally all the voters' pairwise preferences--so their
 recommendation of single winner STV preferential voting was only
 relative to a few even worse methods.  Clearly, Condorcetian methods
 have properties that are much closer to the properties of the Single
 Elimination Pairwise method that RR advocates, because Condorcetian
 methods are not subject to the criticism they made of STV that it can
 easily defeat the best compromise.


 This analysis is incorrect. Yes, they show no specific awareness, but
 the language they used was quite precisely crafted, surprisingly so, if
 they were not aware that other preferential voting methods did not
 suffer from the failure of the STV method. That is, they make it a
 criticism of the *specific method they have described*, which is STV.
 They have also mentioned that there are many forms of preferential
 voting. That they spent precious words -- this is a manual of practice,
 not a dissertation -- to make it clear that center squeeze was a
 specific problem of this method, i.e., the one they describe,
 indicates to me that they were quite aware that this wasn't a universal
 problem with preferential voting.

 You have missed something else. RR does not recommend single elimination
 pairwise. They recommend, indeed *require* by default, repetition of the
 election, until a majority is found. There is no candidate elimination.
 It's true, though. The RR method -- election repetition -- together with
 associated rules, is an approximately Condorcet compliant method. The
 deviation is, in fact, a Range-like effect. When a proposed candidate is
 close enough, i.e., the general preference for the Condorcet winner is
 low enough, the process terminates. People would rather finish with the
 election than seek any more improvement in satisfaction with the result.
 If there is some group of voters who strongly oppose this, they will
 attempt to prevent it, they will attempt to wheel and deal to come up
 with some better compromise. It's when the remaining preference
 strength, possible improvement, is lower than the perceived cost of
 continuing the process, that it terminates. With the explicit consent of
 a majority for the result.

 I'm told that the reason they didn't describe other voting methods is
 that those other methods, at the time, were not in common use, and they
 still are not. They are a manual of actual practice, and it's remarkable
 that they said as much as they did. In any case, they clearly think that
 the practice of repeated elections is superior to IRV, and that using
 this *even with a majority requirement* is deficient compared to
 repeated elections. That's because, if voters do fully rank, a majority
 may be found which is *not* the compromise winner.

 But they don't seem to have realized that truncation is a reasonable
 voter strategy in Center Squeeze conditions. And when the election must
 be repeated, the top-two failure is irrelevant, or almost so.

 (Approval can easily defeat the best compromise too, because many
 voters will fail to approve compromise candidates out of fear of
 defeating preferred candidates, which in turn will deter potential
 candidates from competing.  If Mr. Lomax likes Approval due to its
 cheapness and simplicity, I'll point out that the family of voting
 methods known as Voting for a Published Ranking are as cheap as
 Approval, easier for the voters, some methods of the family are as
 simple, and if I'm right about how candidates would behave would tend
 to elect a good compromise.)


 Published ranking is interesting, for sure, but Approval is far, far
 simple and far less radical. Bucklin, in fact, addresses that
 reluctance. Unstated here was how the published rankings would be used.
 Condorcet? Bucklin is simpler, but when we are dealing with published
 rankings, we need only collect those votes en masse, and then applying
 them to a Condorcet matrix would be simple.

 However, politically, it's, shall we say, a step. Count All the Votes is
 a small step, *and* cheap. And quite surprisingly powerful, considering.
 Bucklin has been used, and this might make it easier to bring it back.

 The behavior of Published Rankings is unknown. There are a *lot* of
 questions, some of them quite difficult to