[EM] STV and weighted positional methods

Raph Frank raphfrk at gmail.com
Sat Jan 31 16:15:29 PST 2009

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


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
-- 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

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