[EM] STV and weighted positional methods

[Raph Frank]

On Sat, Jan 31, 2009 at 11:48 PM, Dave Ketchum <davek at clarityconnect.com> wrote:
> Eventually you get down to successfully running an election.  Among your
> choices:
>     Leave a slot in the ballot by each candidate for voter to write in the
> rank number.   Allows for lots of ranks, but a challenge to decipher what
> the voters write.
>     Provide a check off slot by each candidate for each possible rank. Three
> slots will satisfy most voters for most IRV races, provided they recognize
> needs vs abilities.
>     Of course, to elect a slate needs more ability.

In Ireland, there is a box by each candidate and you write in the rank
you want to give that candidate.

I would agree, in most cases, 3 ranks should be sufficient, as long as
voters are away that their last rank must go to one of the top-2
(unless they have already voted for one of them).

The London Mayoral election is pretty bad.  It is instant top-2
runoff, but it only provides 2 ranks.

If neither you first or second choice make it to round 2, you don't
get to vote in the 2nd round.

> Depends mostly what you want to accomplish as a voter:
>     Get in on top-2 - then rank your preference between these.
>     Get in on others such as your own preference - rank per your desire in
> available ranking.

Assuming you vote for one of the top 2, the remaining ballots are
purely for information purposes.  They show the candidates where their
support is coming from.

> Proving difficulty is tricky because it depends on understanding the
> problem.  What I see below sounds like simplifying the problem to make it
> solvable.

The simplification due to random ballots certainly makes the hand
count easier.

However, it isn't required.  You can just assign a weight to each pile.

This sub-pile is kept separate from the rest of the ballots for that
candidate.  The weight for that sub-pile could be written on a
page/sign beside the pile.

This weight gets updated for any surplus transfer.

So, it would be something like

Initialisation:

1) sort all the ballots into piles based on first choice
2) Place a sign with a 1 on it beside each pile
3) Count all the piles
4) work out quota

Processing (once per round)

If any candidate has more than the quota in his pile
-- declare that candidate elected.
-- multiply the weighting for each of the candidate's piles by
(surplus/candidate's vote)
-- update all the signs
-- Split the piles based on the next highest ranking and copy the sign
for all the sub-piles
-- assign those sub-piles to the other candidates
Otherwise
-- declare lowest candidate eliminated
-- redistribute all the votes in his pile

It can also be less efficiently accomplished by having 1 sign per ballot.

> Seems like I just read of collecting all the ballots for a race at a central
> counting site.

For PR-STV, it would be very helpful to have all the ballots in one
place, but not essential.  You could have the central office issue
instructions.