[EM] STV when applied to choosing pizza toppings

[James Gilmour]

Jonathan Lundell > Sent: 13 November 2006 16:27
> At 11:37 AM +0000 11/13/06, James Gilmour wrote:
> >Rather, STV-PR was devised to
> >ensure that each significant point of view within the electorate was
> >represented fairly (as expressed by the voters' responses to the
> >candidates who had offered themselves for election).  Originally, the
> >intent was to maximise the diversity of representation rather than
> >maximise the consensus of representation, but there has been some de
> >facto shift in that by changes made to the counting rules (for the
> >extremes, compare Dáil Éireann STV rules with Meek STV rules)..
> 
> Would you elaborate, please, on what you mean by 
> diversity vs. consensus of representation, and how 
> Meek maximizes the latter over the former? Or 
> point me to something I should be reading?

This analysis of 'diversity vs. consensus' has not been written up
anywhere, but it is on my "to do" list, as an article for 'Voting
matters'.  Meantime I have copied the text from a post last March to
another list in which I was concentrating on how consequential surpluses
are transferred, and have added a bit at the end.

There are currently five different methods (of transferring
consequential surpluses) for use in STV-PR elections (leaving aside the
Cambridge, MA, rules which have their own peculiarities).

In the Dáil Éireann rules the surplus votes are carried as integer votes
on the appropriate number of ballot papers (each ballot paper of value 1
vote).  These ballot papers are selected only from the last parcel
received by the newly elected candidate, i.e. from the parcel that
created the surplus.  To minimise chance effects, the last parcel is
sorted into sub-parcels according the next available preferences
(candidates not yet elected) and a due proportion of ballot papers is
then taken from each sub-parcel.  This process inevitably involves an
element of chance that may or may not affect the outcome of the
election.

To eliminate the element of chance, ballot papers can be transferred at
fractional values, as suggested by Gregory in Australia in 1880; hence
this is known as the Gregory Method (GM).  All the papers in the last
parcel received are sorted according to next available preferences.  Any
that are non-transferable are set aside and the votes carried on those
papers are retained as part of the newly elected candidate's quota.  If
the total value of the transferable papers does not exceed the surplus,
the papers are transferred at their current value.  If the total value
of the transferable papers exceeds the surplus, the value of each paper
(all of one value) is reduced: the new transfer value of each ballot
paper equals the surplus divided by the number of transferable papers.

Some consider that taking only the last parcel received as inherently
"unfair" or "defective" or just "a shortcut for manual counting" and so
have devised methods to transfer ALL of a candidates ballot papers when
that candidate is elected with a surplus. These are the "inclusive"
methods of handling consequential surpluses.

The Inclusive Gregory Method (IGM) is used in the STV-PR elections to
the Australian Federal Senate and to some Australian State legislatures.
In this method, all of the ballot papers of a newly elected candidate
are sorted according to the next available preference and an AVERAGE
transfer value is calculated by dividing the surplus by the total number
of ballot papers then held by the newly elected candidate.
Non-transferable papers are set aside as "non-transferable", taking with
them the proportionate share of the surplus.  This method (IGM) is
fundamentally flawed and should never be used because the process of
calculating an average transfer value for all ballot papers has the
effect of INCREASING the total contribution of some ballot papers to
more than 1 vote, and correspondingly decreasing the contribution of
some other ballot papers to less than 1 vote.  This violates the
principle of "one person, one vote" and should have been declared
unconstitutional.

The Weighted Inclusive Gregory Method (WIGM) overcomes the defect in IGM
described immediate above.  In this method, all of the ballot papers of
the newly elected candidate are sorted according to the next available
preference.  A 'surplus fraction' is first calculated: the 'surplus
fraction' equals the surplus divided by the candidate's total present
vote.  Then the 'continuing transfer value' of each paper is calculated:
equals the current value of the ballot paper multiplied by the surplus
fraction. Non-transferable papers are set aside as "non-transferable",
taking with them the proportionate share of the surplus.  This method
ensures that each ballot paper contributes in total 1 vote to the
election.  WIGM has not yet been implemented for public elections
anywhere in the world.  It was proposed for STV-PR elections to the
Western Australia Legislature, but the Electoral Reform Bill was
withdrawn (for reasons not related at all to WIGM) - since
re-introduced.  It was proposed for BC-STV in British Columbia.  It is
under consideration for use in the STV-PR local government elections in
Scotland in 2007, subject to e-counting (scanning paper ballots).

Meek STV uses the weighted inclusive calculation of WIGM but transfers
votes to already elected candidates.  This creates further surpluses
which then have to be transferred.  This is an iterative process that,
for more than a handful of votes, can be contemplated only in a fully
computerised count.  Meek STV also transfers votes on exclusion to
already elected candidates and reduces the quota every time
non-transferable ballot papers are encountered and then starts the whole
count again from the beginning with the reduced quota.  These add
further sets of iterations.  This is currently the ultimate in
"inclusive" STV-PR methods.


The differences between the "exclusive" and "inclusive" methods are also
reflected in the finer details of the way exclusions are handled (not
explained here).

There is much more to the difference between the "exclusive" and
"inclusive" methods of handling ballot papers than an apparent
"unfairness" or a "convenient shortcut" when a surplus has to be
transferred.  Overall the Dáil rules and the GM rules have the effect of
keeping the voters (via their ballot papers) in discrete groups that are
likely to be different from each other (in terms of the patterns of
preferences) and to involve the minimum possible number of voters
(ballot papers) when any decision has to be made.  In contrast, the WIGM
rules and the Meek rules involve the maximum possible number of voters
(ballot papers) on every occasion when a decision has to be made and
then take all those voters (ballot papers) together in one (inclusive)
group.

The effect of the "exclusive" methods of handling the ballot papers is
to maximise the diversity of representation.  The effect of the
"inclusive" methods is to maximise the consensus of representation.
These two "philosophies" of representation have quite different views
about what STV-PR elections should be trying to achieve, although this
philosophical difference has usually not been recognised (or at least,
not stated explicitly) by the protagonists of the "exclusive" and
"inclusive" methods in the debates about STV counting rules.

James Gilmour