policy for membership in MOTU key teams

Cody A.W. Somerville cody-somerville at ubuntu.com
Wed Jul 2 23:31:52 BST 2008


On Wed, Jul 2, 2008 at 5:29 PM, Scott Kitterman <ubuntu at kitterman.com>
wrote:

> On Wednesday 02 July 2008 07:29, Cody A.W. Somerville wrote:
> > Hello,
>

<snip>


>
>
> >
> > This is probably the toughest part to figure out: "How the voting works".
>
> ...  snip
>
> Actuall I think it's not.   There is a lot of research supporting  the
> http://en.wikipedia.org/wiki/Condorcet_method and services that support
> it.
> It's a little complex in the theory, but actual voting is just ranking your
> preferences.
>
> Scott K
>

For those not familiar, the Condorcet method is the method used by Debian.
Personally, I'm not overly familiar myself but I've attempted to do some
research for the benefit of the crowd.

What benefits does the Condorcet method provide over Single Transferable
Vote? From what I see, both systems are preferential voting systems however
the Condorcet method is exceedingly more complex than STV and is classed as
a single member system (ie. engineered to elect one member) where STV is
classified as a multi-member system. Although STV suffers from the issue of
sequential exclusions (meaning that sometimes STV eliminates at an early
stage in the count a candidate who might have gone on to be elected later
had they been allowed to remain in the contest), there have been a number of
recent refinements to STV such as CPO-STV and Sequential STV which solve the
problem by incorporating elements of the Condorcet methods into STV.
Alternatively, a method known as BTR-STV deals with the problem with a
completely different (but exceedingly more simple than the other systems)
solution by simply making sure no candidate could possible be eliminated. On
the other hands, a neat feature of Condorcet is that it is possible for a
candidate to be the most preferred *overall* without being the first
preference of on any of the ballots yielding a compromise candidate whom the
largest majority will find to be the least disagreeable even if not their
top pick. This may or may not be desired (I'm not sure).

So what *is* the "Condorcet method", well it isn't actually *a* method but a
set of criteria. When people refer to the Condorcet method, they are talking
about any single-winner election method that meets the Condorcet criterion.
What is the criterion? Basically that the system has to always selects the
Condorcet winner. What is the Condorcet winner? It is he candidate who would
beat each of the other candidates in a run-off election (there is actually a
few different types of run-off elections to boot but in this context I would
describe it as the guy who gets the majority votes if everyone voted on only
those two people) . In modern examples, voters rank candidates in order of
preference but things get very tricky from there as there is need to resolve
circular ambiguities. This situation emerges when, once all votes have been
added up, the preferences of voters with respect to some candidates form a
circle in which every candidate is beaten by at least one other candidate.
An example borrowed from wikipedia is if there are three candidates, Alex,
Cody and David, there will be no Condorcet winner if voters prefer Alex to
Cody and Cody to David, but also David to Alex. Frustratingly, depending on
the context in which elections are held, circular ambiguities may or may not
be a common occurrence .

Now, if the Condorcett method is meant to elect a single member only how
would we use it? Well, it will actually produce a list and I'd suppose we'd
pick the number the highest ranking individuals? Erm... maybe? I suppose it
depends on the exact system used. Earlier I said that Debian uses the
Condorcet method but now you must be wondering which method they *really*
use now that you know what Condorcet is really all about. The name is "the
Schulze method", aka Schwartz Sequential Dropping (SSD), Cloneproof Schwartz
Sequential Dropping (CSSD), Beatpath Method, Beatpath Winner, Path Voting,
and Path Winner. In this system, each ballot contains a complete list of all
candidates and the individual voter ranks this list in order of preference.
Generally, ascending numbers are used, whereby the voter places a '1' beside
the most preferred candidate, a '2' beside the second-most preferred, and so
forth. Sounds like how one might vote on a Single Transferable Ballot, no?
Just wait... it isn't so simple. Voters may give the *same* preference to
more than one candidate and *may keep candidates unranked*. If the latter
occur (ie. doesn't rank all candidates) then it is assumed that all ranked
candidates are strictly preferred to those that he or she did not rank and
indifferent between the non-ranked candidates. Then to determine the actual
winner (this is a single-member system remember), it determines the
"strongest path". The following is from wikipedia:

*Procedure*
>
> Suppose d[V,W] is the number of voters who strictly prefer candidate V to
> candidate W.
>
> A *path* from candidate X to candidate Y of *strength* p is a sequence of
> candidates C(1),...,C(n) with the following properties:
>
>    1. C(1) = X and C(n) = Y.
>    2. For all i = 1,...,(n-1): d[C(i),C(i+1)] > d[C(i+1),C(i)].
>    3. For all i = 1,...,(n-1): d[C(i),C(i+1)] ≥ p.
>
> p[A,B], the *strength of the strongest path* from candidate A to candidate
> B, is the maximum value such that there is a path from candidate A to
> candidate B of that strength. If there is no path from candidate A to
> candidate B at all, then p[A,B] : = 0.
>
> Candidate D is *better* than candidate E if and only if p[D,E] > p[E,D].
>
> Candidate D is a *potential winner* if and only if p[D,E] ≥ p[E,D] for
> every other candidate E.
>
Confused? No worries. This system actually comes with a tutorial (albeit in
German).

I'll just stop here (lots on Wikipedia you can read though). So, why am I
still leaning in favor of the Single Transferable Vote (or a refined version
that sees that STV meets the monotonic criterion)? Because it is a
*multi-member*, proportional representative, preferential electoral system
and is *significantly simpler* then any of the Condorcet methods. Do we
really care that Schwartz Sequential Dropping meets Condorcet loser, clone
independence, reversal symmetry, polynomial time, and local independence of
irrelevant alternatives criterion when it is so complicated that a lengthy
manual is required to actual determine who is the winner not to mention
further complex circular ambiguity resolutions using yet another voting
system? Besides, according to Wikipedia, Condorcet methods are not currently
in use in government elections anywhere in the world - although a Condorcet
method known as Nanson's method was used in city elections in the U.S. town
of Marquette, Michigan in the 1920s, and today Condorcet methods are used by
a number of private organisations (Debian, Wikimedia Foundation, Gentoo
Foundation all use SSD) . If you've seen some of the vote pages for Debian,
you'll see all sorts of lovely matrices and graphs and what not and hey, it
might look nice but I think we'll get desired results with a much simpler to
understand system that is actually geared towards what we're dong. Maybe in
the future when our numbers are larger and we run into some of the electoral
corner cases SSD (or something else) would be more appropriate but for now
STV seems to serve the purpose rather well.

I should also note there is already software out there to calculate both STV
and SSD.

Just to clarify, this e-mail isn't a vote *against* SSD or anything like
that, just me expressing that SSD seems like overkill for now.

Cheers,

-- 
Cody A.W. Somerville
Software Engineer
Red Cow Marketing & Technologies, Inc.
Office: 506-458-1290
Toll Free: 1-877-733-2699
Fax: 506-453-9112
Cell: 506-449-5899
Email: cody at redcow.ca
http://www.redcow.ca
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