Back correspondence on Nanson method

[Steve Eppley]

Tom R posted comments from several people.  I've snipped a few 
to which I want to reply.  [I'm not sure if everyone in Tom's 
distribution list will receive this, since I'm using a distribution 
list I copied from one of Tom's old messages.]

Deane Crabb wrote:
>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.

It's not Nanson's method which allows majority overrepresentation. 
It's the *optional* "failure" to delete the ballots which elected
the winner of the previous iteration that makes their multiseat
version non-PR.  It could be made into a PR method by deleting
those ballots, in exactly the way that STV deletes ballots each
iteration.

When electing representatives, though, I think there's a fundamental
principle which needs to be considered.  The purpose of democratic
representation is to efficiently voice the views of the citizens and
make decisions which closely match what the citizens would say and
do in a well-functioning direct democracy.  This suggests that the
representatives elected should not be "compromise" candidates (which
pairwise methods would elect), but should instead be top choices of
some of the voters (as STV would elect, if the size of the
representative body is sufficiently large).

When the number of representative choices being elected (or
remaining to be elected, as at the tail end of an STV tally) is
small, that's when pairwise methods should take over.  

I'm not certain how to define small; small includes 1, for sure. 
Whether it includes 2, 3, etc. I haven't attempted to investigate;
perhaps there are properties of the voters' expressed preference
orders which can be used to distinguish, for a given number of
remaining seats, whether the next seat should be calculated pairwise
or STV-wise.

>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.

The more important consistency, in my view, is to consistently
advocate the best method for the given type of election.

Tom R wrote:
>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 don't think you should let the National Constitution hold you back.
At worst, there would be a debate over whether to terminate the
branch's affiliation, and this publicity would be helpful for
educating people about Condorcet's method.  (Maybe you can even
choreograph a "fight" which would gain significant media coverage.)  
If the National turns out to be irrational, the branch can always bow
to the whim of the National, and will have accomplished an important
educational mission.  The "civilized" alternative, asking the National 
for prior permission, might turn out to be far less educational with
far less publicity.

>Forgot to ask - do you mind if I cc your messages to the other
>mailing lists
-snip-
>Please let me know if this'll be okay - I think netiquette
>requires me to seek an affirmative response.

There's netiquette, but there's also the "fair use" doctrine.  
I'd delete personal information before forwarding, of course.

John Taplin wrote:
>Nanson showed that a Condorcet candidate (he assumed complete
>expression of preference) has a better than average Borda
>score and hence his method.

Nanson, like many academics, evidently made an assumption that no
voter misrepresents his/her preference order.

>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.
>Nevertheless, there are paradoxes possible with truncation
>and good reasons for stipulating the expression of a minimum
>number of preferences.

The last sentence in that paragraph seems to contradict the first
sentence.

Pre-election polls can provide rough info on how others will vote.
It's also possible that after the method is in widespread use, some
joker will publish a "strategist's cookbook" containing recipes for 
insincere voting given certain patterns of pre-election poll data.
Since there'd be no way to know who has read the cookbook, there'd be 
no reason to expect direct "retaliation" in that election, and maybe 
not even "delayed" retaliation in subsequent elections.

Is there some reason to prefer Nanson, or another pairwise method,
more than Smith-Condorcet or Condorcet?  The iterations in Nanson
make it more complex, and it violates majority rule criteria which 
seem to be significant (as Mike Ossipoff pointed out).

-snip-
>The reason for 1) is that most elections have such a Condorcet
>winner.

That statement makes untested assumptions.  Peter Ordeshook,
professor of political science at Caltech, stated the opposite
yesterday in a private conversation.

>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. 
-snip-

By "leading" I presume John means to compare them based on 
"plurality" (voters' first choices).  That's fine, but isn't 
necessarily the quickest way of finding the winner.

The algorithm John described seems to be nearly identical to the
Condorcet shortcut I posted some weeks back.  (By shortcut, I mean 
a way to avoid calculating every pairing.)  It's not necessary to 
compare the two "leading" candidates; random choice of those not 
yet compared with the provisional winner will also converge on the 
Condorcet winner.  (The shortcut I posted also converges on the 
candidate who would win according to the "opposition minimax" 
circular tie breaker.  I also posted a shortcut for determining 
the Smith set.)