[EM] more questions about PR allocation formulas

[James Green-Armytage]

Dear election methods fans,

	It is humbling to realize how little I know about proportional
representation. There are things that I thought I knew that now seem to be
wrong.
	One question I have is about the Droop quota. Is it always expressed as
(votes / (seats + 1)) + 1, or is (votes / (seats + 1)) also the Droop
quota? I thought that they both were, essentially, but I was reading some
of Nicolaus Tideman's work, and he says that only the former is the Droop
quota, whereas he calls the latter the Newland-Britton (NB) quota. What do
you guys think? Is there another name for the (votes / (seats + 1)) quota
besides NB?
	I must have got all confused. I thought that Newland-Britton was the
method of doing fractional transfers of surpluses rather than transferring
randomly selected ballots. He talks about a specific form of that, the
"senatorial rules," but he doesn't give it a general name. Does it have
one? (I'm not talking about Meek, but the one which only calculates the
fractional value of the votes once, that is at the time that a candidate
who holds them is elected.)
	Anyway, David Gamble's examples were great. Also, I got another message
that seemed to be saying that it is very uncommon for actual list systems
to use largest remainder forms of allocation such as Hare and Droop, and
it is far more common to use "highest average," divisor-based methods such
as D'Hondt and Saint-Legue. Can anyone confirm or deny this? Tideman
seemed to be saying the same thing, that quota systems come into play in
STV PR rather than party list PR. Woah. 
	Man, for a long time I've been wishing that I could find a chart of which
allocation formulas are used by the different countries that have party
list elections. But so far, I've found it hard to get that sort of data.
If anyone knows a source, please lay it on me.

	Well, I seem to be asking more questions then giving answers these days.
But what I'm doing is making it into a sort of introduction to voting
systems paper that is designed to bring a general reader step by step from
plurality to beatpath, ranked pairs, Meek, CPO-STV and the rest. 
	Basically, it is the sort of "what I have learned on the EM list" paper
that others have done, but everyone's take is a little different, and I
say the more accessible writing we produce at this point, the better.
Hopefully I will put it up on the web somewhere when I'm done, and then I
will post the address. My hope is that someone without any background
could read it straight through without getting confused, and come away
knowing how most of these methods work.
	So, I have to ask these questions to make sure I've got this stuff
straight before I try to explain it in writing. I hope that this can be
viewed as a sort of community teaching and learning effort and not some
sort of parasitism on my part.


my best,
James Green-Armytage