[EM] Meek style STV - Part One of Two

[David Catchpole]

On Wed, 13 Oct 1999, Donald E Davison wrote:

> (a)     Votes are transferred to the next preference in the exact order
> indicated by the voter on the voting paper, unless the candidate has
> already been excluded:

OK, that qualifies it as an STV method...

> (b)     The total value of the surplus is shared equally across both
> transferable and non-transferable voting papers:

Which is where the major divergence occurs with many STV systems in
practice, and it's an good divergence.

> (c)     If a candidate is elected later in the count, or an elected
> candidate receives further votes, the surplus to be transferred is
> shared across all voting papers credited to that candidate in
> appropriate proportions, not just across the voting papers which gave
> immediate rise to the surplus:

Again, more of a divergence. In some systems (such as the system for
preselections in the Queensland ALP) only the preferences of the last
transfer are used (advantages bloc votes?).

> (d)     As votes are credited to the non-transferable total, the quota
> is recalculated to reflect the smaller total of votes remaining active.
>    The processing of votes exactly in accordance with the wishes of the
> voters means that in a Meek count votes are, in effect, being recounted
> again and again.  The iterative nature of a Meek count is derived from
> two simply-stated principles-

Actually, this is where it may be useful to turn to Craig Carey, who
criticised an immediate-quota system I suggested a few weeks ago because
it was "curved."

> (a)     The number of wasted votes in an election, i.e. votes which do
> not contribute to the election of any candidate, is kept to a minimum;
> 
> Donald: Meek Droop STV will have more wasted votes than Normal Droop STV,
> because the last Droop Quota will be larger. It is larger because Meek will
> balance up all the final vote totals including the vote total of the last
> Droop Quota, thereby making the last Droop Quota larger than it would
> otherwise be if normal Droop STV were used. Because the last Droop quota is
> larger, Meek will have more wasted votes when the last Droop Quota is
> wasted. This is not the fault of Meek, it is the fault of Droop.
>     If Meek really wanted to keep wasted votes down to a minimum, it would
> use Hare Quota in place of Droop. Meek would work better with Hare, then it
> could truthfully say that it is keeping wasted votes down to a minimum.

Well, the principles actually lead to the implication that the quota
becomes smaller, by taking into account reductions in the total
number of continuing votes (and therefore the quota) by exhaustion. I
think Meek is similar to my idea of an "instantaneous quota," in that all
transfers are instantaneously recalculated simultaneously with the
recalculation of the quota.

Hare sucks and has no justification, but Donald is so insistent on what to
him is its apparent worth that it's no use getting into an argument about
it.

> (b)     As far as possible, the opinions of each voter are taken equally
> into account; and
> 
> Donald: Except for the voters in the last Droop Quota. Steve does not like
> my harping on the Droop Quota, but I think it's silly for anyone to claim
> the "superiority of the Meek rules" while at the same time the system
> contains this big flaw, this flaw of disqualifying a quota of votes, which
> is the same as not allowing these people the right to vote.

OK, here we go- What the hell is the Hare quota? If a candidate has more
than the Droop quota, she will also win a Hare election, as no more than
n-1 candidates can recieve more votes than her. It is therefore rewarding
to give your favourite candidate a Droop quota in a Hare election, but no
more, as anything more simply gets sponged up into the Hare quota.
Therefore, to start with, there is a "loss" of the votes of
candidates with more than a Hare quota of
(n-1)(1/n - 1/(n+1))=(n-1)/n(n+1). All this compared with the lucky
bastard who gets the final half-Hare (more like half-arse) quota to
actually make the number of candidates, whose advantage over these guys is
1/2n votes. There is a "wastage," then, of (n-1)/n(n+1) + 1/2n of the
vote, which you'll find is significantly larger than the "wastage" caused
by Droop, which has an _equal_ quota which reflects the _minimum
conditions for winning_. Donald insists that we "drop the Droop." I say we
shoot the Hare- even Hare did the same.

> (c)     There is no incentive for voters to vote in any way other than
> according to their actual preference.
>    Whenever the quota is recalculated, based on the reducing number of
> valid votes remaining in the election, a reduced value for the quota is
> obtained.  This means candidates who are already elected, again have new
> surpluses which must also be transferred.  To complicate matters
> further, surpluses of elected candidates will often be transferred in
> part to other elected candidates, involving the transfer of
> progressively smaller surpluses between two candidates in a seemingly
> infinite regression.  Furthermore, some of the transfer will usually go
> to non-transferable, thus causing a further quota reduction and new
> surpluses.

All of this is in direct contradiction to what Donald insisted above about
quotas increasing.

>    Although these processes seem to be impossibly convoluted, as indeed
> they would be for elections where the counting of votes is carried out
> manually, they can be handled very easily by computers.  The
> never-ending transfer of surpluses can even be carried out to
> completion, or at least to a point where the surpluses remaining to be
> transferred are less than, say, 1/10000 of a vote.

It's a nice instantaneous system of equations that can be calculated
exactly.