[EM] Fw: Invitation to join politicians-and-polytopes

[Norman Petry]

Comments below:

-----Original Message-----
From: Craig Carey <research at ijs.co.nz>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Date: April 7, 2000 7:11 AM
Subject: Re: [EM] Fw: Invitation to join politicians-and-polytopes


>
>I apologize for the length of this, and I write in defence of
>  principle in voting theory. Once a method is derived from principle,
>  then the principles can be given instead of the method to the voters,
>  although the counters would always need the method (unless some
>  computer program handled the implicit form). So Mr Petry failed
>  to realize that it is very possibly ('probably', I presume) Condorcet
>  that would be the more complex. ....

No, this would not be sufficient.  Speaking for myself as a voter (and as
someone who does, in fact, have a reasonable grasp of mathematics), I would
not be satisfied with assurances from a mathematician that a particular
method was consistent with a prescribed set of axioms (assuming I understood
and accepted the axioms themselves).  I would want to be able to check that
fact for myself, and unless I had the necessary mathematical background to
follow the proofs, this would be impossible.  In most electorates, knowledge
of higher math is not widespread, and I think it is doubtful that you would
be able to persuade a majority to trust their democracy to the promises of a
mathematically inclined elite.

[...]
>
>Mr Lanphier wrote he did not tend to the discussions in the list. I have
>  no comment on that. I note to the list owner that I am defending
>  mathematics (again).
>

I don't consider it the list owner's responsibility to either participate in
debates or censor the content of other participants, so I fail to see a
problem here.  I assume that the latter opportunity is the advantage you
think may be gained by starting a new list.  On Monday you wrote:

>I would hint to the owner that the guidelines are not shaped to
>  stamp out a problem occurring: postings that do not contain ideas
>  that are real enough mathematically to allow them to be separated
>  from the person stating the ideas, are being posted. I would
>  say that false and/or badly defined information is being posted.

Thanks, but no thanks.  I have no desire to join a list where ideas that
aren't "real enough mathematically" are not allowed to be considered.
Perhaps censorship of alternate views is not your goal, and I have misread
your intent (I find that I often have difficulty understanding what you are
trying to say, in fact).  Still, the "Guidelines" for your new list
certainly give this impression:

"[B] Methods failing these 2 rules may not be advocated:
  (1) P4 ('one man one vote'), which approximately says that a paper's power
to get what it wants does not exceed that of all FPTP papers that it can be
decomposed into (ref. http://www.ijs.co.nz/ifpp.htm).
  (2) Truncation resistance, which says that a candidate's win-lose status
is unaffected by altering preferences after that preference (i.e. away from
the 1st). These are two properties held by STV/AV and SNTV/FPTP."

Of course, you are free to create a discussion list with such a narrow
scope.  I'm just not sure why anyone *but* you would be interested in being
bound by such limitations.

[...]
>
>This is the only mathematics mailing list I have been a subscriber
>  of where posters reject mathematics and refer vaguely to people.
>

You misread what I wrote.  I said:

1) "This is particularly true if the fixes you are attempting can ONLY be
described in mathematical terms.  Any method which cannot be described in a
natural language to an informed layman is also a dead-end."

-and-

2) "Only mathematical societies would be willing to adopt a method whose
rationale can ONLY be described in mathematical terms,..." (emphasis added)

I did not "reject mathematics", or criticize its use in the anlysis of
voting methods here on EM, or anywhere else.  Indeed, mathematics can be a
very useful tool in the analysis of many things, including voting methods.
Proofs that demonstrate unresolveable conflicts between seemingly reasonable
criteria (such as Arrow's theorem) are very useful.  The proofs I like best
are those that actually allow for simplification.  For example, a while ago,
Markus posted a proof that beatpaths cannot be cyclic.  This proof made it
possible to redefine the Schulze method without reference to the Schwartz
set, which I (at least) regarded as a simplification.  Mathematics like this
I appreciate greatly.  Also, if mathematicians find it easier to understand
a particular voting method when it is described in their language, I think
that's a perfectly reasonable thing to do, and it may be helpful by
revealing ambiguities/imprecision in the definition of the method that need
to be resolved.

What I actually said was that the *method itself*, if it is to be a
practical method that the public should/would be willing to adopt, must
(also) be explainable in NON-mathematical terms.  Voting methods that
*require* specialist knowledge in order to be understood are not democratic,
outside groups of such specialists.  Voters should not have to trust a
specialised elite with their decisionmaking apparatus; doing so is
effectively no different than entrusting that elite with the actual
decisions.  It is extremely important that the democratic process be
TRANSPARENT to those making the decisions, and not some black box that they
put ballots into, with the outcome a lottery as far as the voters are
concerned.

Unfortunately, this "transparency" standard I'm arguing for sets an upper
bound on complexity, which would vary from one electorate to another
depending on the sophistication of the voters.  Therefore, there is no such
thing as a "perfect" method.  What is perfect for one group will be overly
complex for another.  For the general public, the ideal method will probably
be pretty simple (and I do regard some pairwise methods, such as Mike's
Sequential Dropping (SD) to be simple enough).

It may be that the AV variant you are working on will satisfy all your
rigorous mathematical anlyses, as well as being easy to describe/justify to
voters.  If you do discover what you consider to be the perfect method on
your new list, I'd be interested in hearing about it.  Even at the outset,
though, I must say that I am doubtful that I would agree to the axioms that
underlie the method you are trying to develop.  Let's look at the example
you provide in your first message to politicians-and-polytopes:

>Candidate C should win this election:
>
>     3  AB
>     4  B
>     6  C
>
>STV picks candidate B.
>
>The first statement is controversial
>The author's IFFP method, has C win.

The Condorcet winner for this election is B.  STV, although it does not
satisfy the Condorcet Winner criterion generally, chooses the Condorcet
winner in this particular example.  Most social choice theorists consider
the Condorcet Winner criterion to be desireable, so that even for methods
such as Approval, which fail the criterion generally, an attempt is made to
estimate the "Condorcet Efficiency" of the method to try to justify it.

You however, have decided that the correct method must fail the Condorcet
criterion.  It's an interesting choice, but not one I agree with. I'm
curious whether or not David Catchpole, who also seems to have a strong
interest in both STV and mathematical analysis, will be assisting you in
developing a single-winner method with this constraint.  A while ago, David
showed that when there is a Condorcet Winner, it is possible for the method
to satisfy IIA without contradiction.  At the time, he regarded IIA as being
highly desireable, which would suggest that the Condorcet Winner criterion
might also be important to him.  Comments, David?

>I guess the key word is the word desire. Maybe the message I write is
>  a mistake. Still, this is likely no to be the last incident at this
>  list where mathematics is found to be a non-essential item in the
>  determinations on how to advance voting theory.
>
Again, you misread what I wrote -- this is a strawman argument.

>[I recall the computer methods you used and I recall having thought them
>  ratter arbitrary, with the results being close and emphasising the
>  low value of such a treatment. Also I recall controversial presumptions
>  about the worth of pairwise comparing.

In the simulation results I initially posted, I was comparing two pairwise
methods.  Under sincere voting assumptions, there is little difference in
the results produced by different pairwise methods, because they are all
constrained by the Condorcet Winner criterion (at least the ones we've
looked at).  Later, I provided data showing that there is a Condorcet winner
90-95% of the time, so different pairwise methods will only differ 5-10% of
the time.  However, this is not true of other, non-pairwise methods I have
analysed.  These differ dramatically in accuracy from the results I
presented for pairwise methods, and therefore the simulation is more useful
for comparing methods generally than the data you've seen would suggest.

>  I am not aware that a candidate
>  ought win when it pairwise beats all other candidates. It certainly
>  could be true. But methods can't exactly be rejected on presumptions.]

Perhaps if we defined the Condorcet Winner criterion as an axiom and
labelled it 'P5' we would be able to reject them :)


Norman Petry