Back correspondence on Nanson method

[Tom Round]

The following is a record of discussion that people [Deane Crabb, John 
Taplin, Mike Ossipoff] sent to me (or I to them) concerning the Nanson 
method. I have either been asked, or have gotten consent, to forward these 
postings to the list at large now. Happy reading. Tom.

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From: crabb.deane To: Tom Round Subject: E J Nanson's method -
Reply Date: Thursday, January 09, 1997 2:48 PM

For the University of Adelaide, this method is used in
multi-seats. As I pointed out earlier (let me know if you did
not get my e-mail sometime towards the end of last year), this
method does not allow minority groupings to be represented
fairly. In effect the "block vote" allows the majority to be
over-represented or to even win all positions.

Regarding the Democrats' internal elections - for policy
ballots only, the Hallett method is used. You may like to
refer to Hoag and Hallett, "Proportional Representation",
1926, pages 496 - 503. It was Ed Haber who implemented this
system.

Basically where there are more than 2 options, each is
compared with each other. If one option is preferred to every
other, it is easy. Where there is a circular result, it gets
more difficult and it is necessary to compare the differences.
There is an example of this on page 502 which compares the
results under various methods.

Of course, John Taplin would argue for the Taplin method,
which as far as I know is used for CSIRO elections. John would
be able to give you more details when he returns from
overseas.

In the reference I gave you, it says that both Hanson [sci.
Hallett?] and Nanson satisfies the Condorcet criteria, but
that the Hallett method gives the better result!!

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From: crabb.deane To: Tom Round Subject: PS - Reply Date:
Friday, January 10, 1997 9:12AM

No problems from me about my comments, for what they are
worth, being passed on.

I assumed you meant Deane - not Lee in your message!! I had
briefly mentioned that the Democrats use the Hallett method (I
hope you can get the reference so that you can really see how
it works and then give your impression of it) and had also
sent some comments about the method used for the University of
Adelaide.

Re single-member elections, I know Geoffrey Goode argues that
for consistency that STV should continue to be used. But I
have been comfortable with the concept of a pairwise system.
In fact if we continue to have single-member parliamentary
elections I would like to see a pairwise system used - an
extension of the 2-party preferred vote concept. It could
hurry along the change to PR and multi-member electorates!!

Re PRSA, I don't think any one has looked closely at the
constitution!! And in any case our emphasis remains on
elections for several vacancies.

////////////////////////////////////////////////////////////
From: Tom Round To: 'Deane Crabb'; 'John Taplin' Subject:
Nanson Date: Thursday, January 09, 1997 9:30 PM

Dear John/ Deane,

A quick thanks for the info you sent me regarding the Nanson
method - very useful. I'll reply at more length later.

John, also, I have been reading the material you sent me a few
months ago (your conference papers from circa 1982 et al). My
brain rebels at more than a certain very primitive threshold
of mathematics so I am struggling through with highlighter pen
and notepad hand!

Lee, I did receive a few messages from you in late 1996, but
I'm not sure if there was one that gave details of the Hallett
method, although you did mention about how it's used for
internal AD ballots.

I am coming to agree that the PRSA should support a pairwise
system (Hallett, Nanson, Condorcet, Smith-Condorcet) for
single vacancies and decisions by majority,* in conjunction
with PR-STV for multiple vacancies. Or at least allow its
branches and members to support the pairwise alternative for
single vacancies. Unfortunately, at present I don't think the
National Constitution permits this: a Branch, to remain
affiliated, must endorse and use the method set out in the PR
Manual (ie, STV, AV) for all elections, whether for one seat
or several. I am curious whether the WA Branch was granted a
special exemption or waiver, or whether the matter has never
been challenged. (Not that I can really picture Bogey or Geoff
sending in federal marshals to enforce the national
constitution, of course!)

* [What about decisions by PR? - ie, not elections to fill
vacancies, but "referenda" in which more than one option must
be elected and the quota is lower than 50%+1? One could
conceivably imagine scenarios like this - eg, a polity might
decide by referendum which languages shall be the two official
languages, with an election by PR. Presumably if, say, English
won both "seats" it would be the sole official language. Maybe
for these situations "bottom-up" would be appropriate - for
once - with the lowest contenders excluded one by one until
all remaining are over a certain threshold, say 20%.]

Cheers, Tom Round

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From: Tom Round To: 'Deane Crabb'; 'John Taplin' Subject: PS
Date: Thursday, January 09, 1997 9:34 PM

Forgot to ask - do you mind if I cc your messages to the other
mailing lists that I cc'ed my original posting to? That is,
the PRSA list here in Aust, and the "voting-systems",
"election-methods", and "single-winner reform" lists in the
USA. Just so we can share the information and pool it further.
Please let me know if this'll be okay - I think netiquette
requires me to seek an affirmative response.

Cheers, TOM
//////////////////////////////////////////////////////////////

From: John Taplin To: Tom Round Subject: Re: E J Nanson's
method Date: Wednesday, January 08, 1997 7:16 PM

At 10:03 AM 8/01/97 +1000, you wrote:

>    Some weeks ago, it was asked on this list how Edward
     Nanson's method works. By coincidence, only a
     fortnight ago an article appeared discussing
     Nanson's contribution to the literature: Iain McLean
     (1996) "E J Nanson, Social Choice and Electoral
     Reform." 31(3) AUSTRALIAN JOURNAL OF POLITICAL
     SCIENCE 369- 385. On page 372, McLean gives a brief
     summary of what Nanson proposed:

Nanson' method was published in the Proceedings of the Royal
Society of Victoria vol 19 pages 197-240 (1883). Most of it
was reproduced in the British Blue paper "Methods of Election"
(3) cd 3501 of 1910. Be careful there are several
modifications that are passed off as Nanson but differ, I
think significantly. The Uni of Melbourne adopted a
modification in 1926 that only excludes one candidate at a
time and some US references treat this as Nanson.

The University of WA used Nanson for Convocation to elect one
Senator each year from 1920? until 1996. Unfortunately they
iterated the method when they had multiple vacancies at which
I assume Nanson turned in his grave. He advocated STV for
multiple vacancies. You are quite correct in that iterating
any single vacancy method gives a block vote effect.

I give you a simple description of Nanson's method without the
renumbering of ballots after each exclusion. 1 A candidate
with a majority of first preferences is elected 2 Otherwise
find the preference margins for each candidate 3 Exclude each
candidate with a non-positive sum of margins 4 If only one
candidate remains elect her 5 Recalculate the margins
considering only the continuing candidates 6 Go to step 3

Nanson showed that a Condorcet candidate (he assumed complete
expression of preference) has a better than average Borda
score and hence his method. I have some discussion of Nanson's
method and of Baldwin's modification (adopted by Melb uni) in
my paper "A Social Choice Function" Search vol 12 p 310-314
(1981. Unfortunately this paper was edited by an executive
editor between being approved by the referees and sending me
the galley proofs. I was not able to restore the meaning
completely. It also suffers from reversing the usual
convention for the direction of arrows on the directed graphs.

I do not take very seriously the notion that traditional
Condorcet methods can be manipulated by insincere truncation.
To do so you have to know how everyone else will vote and that
you and your faction can vote insincerely without retaliation.
Never-the-less there are paradoxes possible with truncation
and good reasons for stipulating the expression of a minimum
number of preferences.

John Taplin <jhtaplin at cygnus.uwa.edu.au>

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From: John Taplin To: Tom Round Subject: Re: Nanson Date:
Friday, January 10, 1997 2:30 PM

Dear Tom Round

I suppose I should write one letter and send it to both Deane
and you but I must confess I have not learnt to send to
several addresses simultaneously. I suspect my Eudora Light is
faulty for I cannot highlight or read attachments.

People sometimes wrongly assume that I advocate the method
described in my Search paper. In fact I usually advocate the
method adopted by the CSIRO Officers Association. (I re-invent
the wording) 1. Elect a candidate with a majority of first
preferences, if none such 2. Elect a candidate with only
positive margins, if none such 3. Exclude any set of
candidates that has only negative margins to each candidate
outside the set. 4. Elect the candidate who has the nearest to
zero sum of negative margins to the continuing candidates.

The reason for 1) is that most elections have such a Condorcet
winner I do not specify finding all the preference margins
because there is a systematic way of looking for a Condorcet
winner. There is a way of setting out the ballots on the
counting table which is more a guide to Returning Officers
than part of the method. First find the margin of the two
leading candidates. Consider the preferred candidate as a
provisional winner. Find the margin of the provisional winner
over the candidate with the next highest total of first
preferences and so on. Whenever a candidate is preferred (by a
majority) to the provisional winner that candidate becomes the
provisional winner. One of the leading candidates is probably
the Condorcet winner. If there is no Condorcet winner it will
be necessary to find all margins. You will recognise 3 as
finding the "Smith set". I got the idea from Dodgson who had
the idea a century before Smith. I defend this rule against
the minimum negative margin. In complex anarchic (cyclic)
Smith sets you may have to decide between candidates with a
number of small losses and candidates with fewer but larger
loses. Remember a Condorcet winner has no losses.

It is a long time since I studied the Hallett method but I
remember concluding that it was very complicated and either
inferior or no better than Nanson. I would therefore be
interested to learn of any example where it is claimed that
Hallett is better than the above method. I believe the ERSWA
adopted the Condorcet Criterion before we applied for
affiliation with the PRSA. Nobody ever suggested we should be
expelled. I was unaware that the Manual specified a method for
filling a single vacancy. We certainly support the use of
STV-PR to elect representative bodies.

> [What about decisions by PR? - ie, not elections to fill
vacancies, but "referenda" in which more than one option must
be elected and the quota is lower than 50%+1? One could
conceivably imagine scenarios like this - eg, a polity might
decide by referendum which languages shall be the two official
languages, with an election by PR. Presumably if, say, English
won both "seats" it would be the sole official language. Maybe
for these situations "bottom-up" would be appropriate - for
once - with the lowest contenders excluded one by one until
all remaining are over a certain threshold, say 20%.]

I think you will find anomalies in trying to make decisions of
this sort by PR. I suggest that if the decisions are linked
(e.g. If English is one official language I prefer French as
the other but if German is one then I prefer Italian as the
other.) then the best method is to let the voters choose a
single combination out of English-French, English-Italian,
English-German, French-Italian, French-German, Italian-German
etc. The number of combinations grows rapidly and there are
twice as many if the order matters. A more realistic example
would be voting on the title of the Qld Branch of the PRSA
e.g. PR Soc of Qld Qld PR Soc Electoral Reform Soc of Qld Qld
Soc for Electoral Reform JHT - John Taplin
<jhtaplin at cygnus.uwa.edu.au>

//////////////////////////////////////////////////////////

From: Mike Ossipoff To: election-methods-list Subject:
Nanson's Method Date: Friday, January 10, 1997 6:25 PM

First: This is only going to EM. I tried the group-reply
option to send it to the other recipients of Tom's method
[sci. message], but, again, I got
"distribution-list at eskimo.com", a nonexistent address that
would result in the entire transmission being cancelled, with
the loss of whatever I'd written.

So I'm just sending it to EM, and asking Tom to forward it to
the people on that distribution list.

***

Yes, the Nanson method was described in books I've found it
in, the Borda scores are re-calculated for the new rankings
created by the elimination.

And it's true that though Nanson always elects the BeatsAll
candidate if there is one, that isn't the same as electing the
Condorcet winner, as we use the term on this list, and as the
term is often defined by academics: The alternative that, when
compared separately to each one of the others, is ranked over
it by more voters than vice-versa.

Nanson _doesn't_ guarantee the election of the Condorcet
winner by that definition. No method does, absolutely,
guarantee that, but some do a much better job of it than does
Nanson.

For instance, Condorcet's method & Smith-Condorcet, having the
property of truncation-resistance, and meeting GMC, LO2E-1 &
LO2E-2, do a far better job of electing Condorcet winners. And
Condorcet, but not Nanson, honours that simple, obvious basic
democratic principle:

If a majority of the voters indicate that they'd rather have A
than B, then, if we choose A or B, it should be A.

***

By "honours that principle", I mean "never unnecessarily
violates that principle".

***

Manipulation? Yes, Nanson is more subject to manipulation,
offensive strategy. Creating a strategic circular tie by
truncation or order-reversal, you might be able to make your
favourite win that strategic circular tie. In fact, as I've
said, the truncation could be strategically-intended, or it
could be innocent, but could still have the same result as if
it had been strategically-intended.

This vulnerability to offensive strategy is a result of
Nanson's failure of the criteria mentioned above.

Mike Ossipoff <dfb at bbs.cruzio.com>

-------------------
Overflow-Cc: TomR at orgo.cad.gu.edu.au (Tom Round),
   100245.2440 at compuserve.com ('Geoff Powell'),
   afreeman at acslink.net.au ('Andrew Freeman'),
   bmusidla at email.dot.gov.au ('Bogey M'),
   c-p-r at netcom.com ('Citizens for Proportional Representation'),
   crabb.deane at pi.sa.gov.au ('Deane Crabb'),
   dunnmj at ozemail.com.au ('Martin Dunn'),
   GGoode at VTRLMEL1.TRL.OZ.AU (Goode, Geoff),
   j.pyke at qut.edu.au (John Pyke, QUT Law School),
   jhtaplin at cygnus.uwa.edu.au ('John Taplin'),
   lee at cs.mu.OZ.AU ('Lee Naish'),
   martinw at cse.unsw.edu.au ('Martin Willis'),
   mdt at ozemail.com.au ('Matthew Townsend'),
   voting-systems at netcom.com ('Voting-systems')