[EM] Summable 3RD (non-partisan proportional) method

[Jameson Quinn]

I've written several posts here about my favorite methods for single-winner
<http://wiki.electorama.com/wiki/3-2-1_voting> and for partisan
proportional FPTP replacement
<http://wiki.electorama.com/wiki/Geographic_Open_List/Delegated_(GOLD)_voting>.
The missing third use case is for nonpartisan proportional use — things
like a city council.

For that, I support 3RD voting
<http://wiki.electorama.com/wiki/3-2-1_voting> — 3-rating delegated. I've
just revised this system so that it will be summable at O(N^2), essentially
by consolidating all ballots which top-rate a given candidate into an
overall average. (Ballots which top-rate multiple candidates are
effectively split into one equal fraction which top-rates each and
middle-rates the others).

It is, in theory, possible to take strategic advantage of this, but I think
it's not practical. For instance, say that X and Y had 0.75 quotas each of
hard support, and there was a strategic bloc of 0.3 quotas of XY
supporters. That should not be enough to get both X and Y elected, but if
the XY suporters found a candidate Z with 0.4 quotas of Z>W support, with
no other votes for Z and few for W, they could vote Z>XY. When Z was
eliminated, around .15 quotas would flow to each of X and Y. When W was
eliminated, another .2 quotas each would flow to X and Y, thus putting both
of them over the top — 1.8 quotas was strategically turned into 2.2 quotas.

But, as I said, this is not practical. It relies on the fact that Z and W
are both eliminated before X and Y. In practice, pre-election polling would
not be anywhere close to precise enough to allow planning a strategy like
this.

I think that 3RD would be a good method for nonpartisan or weakly-partisan
situations such as city council elections. It's proportional in purely
partisan scenarios (partisan-Droop-proportional; that is,
Droop-proportional in cases where each voter top-rates one of several
non-overlapping "party lists" and bottom-rates all others); it has the
capacity to give voters some voting power at the level of intraparty
factions (that is, more than a single candidate, but less than a full
party); it's simple enough for voters (substantially more so than STV); and
it's summable.
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