[EM] Fractional STV for PR

[James Green-Armytage]

Brian, you wrote:
>So, if there are 2 times the number of first-active-place votes as are 
>needed to elect a candidate, that candidate is elected and all of those 
>voters get their voting strength reduced to 1/2. Their next-place 
>candidates then gets a bunch of 1/2 weight votes added on.
>
>Just tell me "yes, people have thought of this" and "yes, we think it's 
>a good idea" and I'll go away and code it up for use in a forthcoming 
>multi-seat Election Calculator ( http://bolson.org/v/vote_form.html ).

	Yes, people have thought of this, and yes, we think it's a good idea. 
	Also, it wasn't an EM list person who thought of it... the idea has been
around since 1880, at least. But it's always fun to re-invent voting rules
before you learn about them. I reinvented approval, pairwise comparison,
the stable marriage problem, and I almost re-invented CPO-STV. 

	However, surprisingly, the fractional transfer issue doesn't end there.
Note that in STV-PR, candidate eliminations happen before surplus
transfers. So, a clever voter can cast their first choice vote for some
wacko who is sure to be eliminated, but before this wacko is eliminated,
the voter's sincere first choice might be elected. Everyone who voted for
them first will now have their votes reduced to a fractional value, but
once the wacko is eliminated, our clever friend's vote will hop along to
his second choice in whole. This is a foolproof strategy as long as you
don't get the wacko elected by accident... so you have to pick an
extra-wacky wacko, and you're fine.
	Anyway, this is why the Meek method was invented. Meek continually
re-calculates the "retention fractions" for elected candidates in each
successive round. I'm not sure that I totally understand Meek, but I
almost do. There's another one called Warren, which addresses the same
problem. The difference, I think, is that Warren emphasizes "candidate
prices" instead of a retention fraction, so that someone whose vote has
already been fractionally reduced is obligated to "pay" the same "price"
for the next candidate as anyone else before their vote moves on, rather
than "paying" the same fraction of the vote which went into that candidate
to begin with. Anyway, Tideman and Richardson explain it better than I
can. I guess I like Meek better so far, but I haven't really thought about
it to the utmost depths or anything.
	So yeah, there's this Tideman / Richardson paper which gives a great
history of STV. Highly recommended.
http://www.econ.vt.edu/tideman/rmt.pdf
	Also, I did my best to explain this stuff in my voting methods survey, so
the url with the bookmark is
http://fc.antioch.edu/~jarmyta@antioch-college.edu/voting_methods/survey.htm#surplus
	And, I think that James Gilmour is an expert on surplus transfer rules,
so he can probably tell you more than I can.

my best,
James