[EM] Proportional election method needed for the Czech Green party - Council elections

[Jameson Quinn]

2010/4/26 Juho <juho4880 at yahoo.co.uk>

>
> Draft of a method:
>
> - collect ranked votes
> - use Condorcet to determine P (Condorcet tends to elect a compromise
> candidate that all voters find reasonably good)
> - use STV (using the same ballots) to elect the group of P and VPs (some
> special rules are needed to guarantee that the already named P will not be
> eliminated in the process but will be elected)
> - use STV (using the same ballots) to elect members of the board (some
> special rules are needed to guarantee that the already named P and VPs will
> not be eliminated in the process but will be elected)
>

Why not:
- ranked votes
- STV for council. Keep track of which members are elected first and second,
one of them will be VP.
- Condorcet winner among the councilmembers is P. (You could use original
ballots or have the council revote.)
- VP is first councilmember, or, if that person is P, second councilmember.


....

As to my own method which I mentioned earlier (RBV for "Reweighted Bucklin
Voting"): it's actually pretty simple if you don't need it to be
precinct-summable. (For precinct-summability, you need to keep two 3D
matrices, one for each level of approval, and do heavy algebra.)

Here's the non-precinct-summable version. *Voters vote into three
categories: preferred, approved, and unapproved/unvoted*. If there are
organized factions, they can publish lists for people to use in the
"approved" category, or there could even be some way to make a single mark
to approve a given list. (If you want to guarantee full Droop quotas, you
need to make people approve at least half the candidates plus half the
council size. If they vote almost that number, you almost have a guarantee.
As a practical matter, I'd require approving at least a quarter of the
candidates, or as many as seats on the council, whichever is greater.)

Start by counting only the preferred votes. *Elect the highest score greater
than a droop quota, then discount all those ballots* so that they add up to
one droop quota less. (ie, if there were three droop quotas of ballots
preferring the elected candidate, weight them all at 2/3). *Continue until
no candidate has a droop quota.*

*Now start again counting all approvals, ignoring "preferred".* Start with
all ballots fully-weighted again, and go through the already-elected
candidates in order and re-discount their ballots (they will probably have
more ballots getting a smaller discount each). Then elect & discount, as
above, until you fill the council. (If you didn't guarantee enough approvals
for full droop quotas, you may elect some candidates with less than that. Of
course, at that point, you can't discount a full droop quota from their
votes anymore. That is not a big problem.)

The 3D summable matrices are only used so that you can keep track of who to
discount at each step. (Technically, the summable version SRBV is not quite
identical to the non-summable version after the 2nd candidate is elected,
but they're highly probable to be the same - provably over 50% probable,
over all possible ballot combos -; they're only different for voters who get
at least 2 of their approved candidates elected - that is, one voter might
get 4 favorites elected while another voter FROM THE SAME PARTY might get
only 2 favorites -; there is really no way for the voters to tell when a
difference has occurred; and, when there is a difference, the summable
version's results are actually arguably a hair superior - more
Condorcet-like.)

Both versions are monotonic, unlike STV (because RBV is all top-down,
there's no bottom-up elimination. This also means it tends to start with
slightly more centrist candidates, though the PR properties mean that this
system moves on to the fringes after covering the center while STV moves to
the center after covering the fringes, so RBV might not be any more centrist
overall). Like any PR system, RBV and SRBV do not obey the participation
criterion - by getting one of your favorites elected earlier, you can
displace your other preferences. Because of that, like STV, there's a small
possibility of the same "free rider" strategy; but the risk is that your
preferred candidate is not elected, so candidates will encourage their
voters not to "free ride", and those candidates who fail to do so risk
losing (deservedly, IMO).

Probably the biggest advantage over STV is that it's much easier to vote -
you don't have to require full rankings. Ballot design is also simple and
it's tough to spoil a ballot. But, as I said in the previous email, the
disadvantage is that it's not (nearly) as field-proven.

I'd be happy to code a program for either version (open source, simple
inspectable code) if you're interested.

If you used this method, the president would be the highest second-round
approval on the council, and the VP would be the highest first-round
approval on the council besides the President. Simple and clear.

Jameson Quinn
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