[EM] Another PR-STV method for national proportionality

[Raph Frank]

I may have posted something similar previously.

The idea is to allow national level proportionality with district
based PR-STV.  However, it doesn't assume that a first preference vote
is the same thing as a party vote.

The voter gets to specifically choose which party to transfer his vote
to and when in the count.  Also, if the voter's vote is used to elect
a candidate, then only the surplus part of the vote can be transferred
to the party.

The assumption is that the country is split into multi-seat districts
and PR-STV is used to fill the the seats.  It doesn't require central
counting of all the ballots.  In principle, the districts could be
have as few seats as desired.  Though, obviously, the more seats the
better.  Very small districts would hurt independents, but shouldn't
have much of a negative effect on small parties, as they can recover
proportionality at the national level.  4-5 seats would probably be
enough to give a reasonable result.

The same quota is used nationwide.  This means that some seats won't
be filled.  Fair Majority Voting is then used to decide which party
gets which non-filled seat to restore national proportionality.  Each
party's vote total is used to decide where they are stronger for that
purpose.

If there were no members of a party standing locally, the voter could
give the party their first choice.

Ballots contain a list of all the local candidates in the district and
also all national parties.

When voting the voter ranks the parties and candidates.

A voter might vote

Candidates
A1:
A2: 1
B1:
C1: 2
C2: 3
D1:
E1:

Parties
A: 5
B:
C: 4
D:
E:

Note: ranking 2 parties is normally a waste of time

The count process works as follows:

Step 1: Count all the valid ballots

Each district announces how many valid votes were cast

The central office then calculates the total valid poll

The quota is determined as the Droop quota but at the national level

Q = floor [ (sum of all the votes)/(legislature size + 1) ] + 1

Note: This effectively gives a quota that is nearly equal to the Hare
quota in each district.

(It might be better to just use the Hare quota directly, and accept a
slight inaccuracy, in the interests of the local count being
localised)

Step 2: Filling local seats

This uses a PR-STV method.  The only exceptions are
- the national quota is used
- the parties count as uneliminatable/unelectable candidates
- candidates must reach the quota to be elected.

Each district announces who has won seats and how many are left unfilled.

It also announces how many votes were received for each national party.

Note: Party vote totals don't include votes for candidates who are
elected, it is just votes transferred to the party.  They are the
votes that correspond to the unfilled seats.

Step 3: Sharing the remaining seats

Based on the each party's vote sum, the unfilled seats are shared at
the national level using d'Hondt or Websters.

(It might be worth having a rule that if a party gets no seats (or
fails to hit a threshold), then the districts are asked to transfer
any votes for that party to the next choice, and the seats are
distributed again.)

(Also, it might be worth recalculating the quota and allowing one
final transfer to the national party totals)

Fair Majority Voting is used to decide how many seats each party gets
in each district.

Basically, each party gets a multiplier, and its vote total in every
district is multiplied by that amount.

In each district, the unfilled seats are split between the parties
using d'Hondt and their modified party vote total.

There is always a unique set of multipliers that give the correct
national vote share (or at least I think this conditions in the Fair
Majority Voting paper are still present for that to work).

This is calculated by the central office and the result can be easily
verified by looking at the district announcements.

Step 4: Select candidates to fill the remaining seats

In each district the votes that went to each party are used to fill
the party's seats in that district.

If the party gets 1 seat, a condorcet method is used.  Otherwise,
PR-STV is used.

Only party members are eligible to be elected to party seats.