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PROPORTIONAL
REPRESENTATION SOCIETY OF AUSTRALIA |
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Tel
+613 9589 1802 |
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+61429176725 |
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BEAUMARIS
VIC 3193 |
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2012-08-01 |
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Electoral Reform AN EXPOSITION OF THE THEORY AND PRACTICE OF PROPORTIONAL REPRESENTATION |
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An 1899 booklet
written by Professor Edward Nanson,
Professor of Mathematics, Professor
Nanson was, in the
first half of the 20th
Century, Secretary of the forerunner of the PRSA’s Victoria-Tasmania Branch
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There
are two systems of election now in force
in Victoria. First, the block vote
which was used in the Federal Convention
election, and is now proposed for the
election of Federal Senators. Second,
the one-member
district system which is
in general use in English speaking
countries for political elections, and
is now proposed for the election of
Federal Representatives. Neither
of these systems ensures the rule of the
majority, and on this point we have the
teachings of experience as well as the reasons
of the scientist. In both systems the party
which is in a minority in the State may secure a
majority of the seats in the Elected House. But
in the block system this evil is aggravated by
the fact that a minority of the voters may elect
the whole of the members. It is not merely that
the will of the majority of the people may be
thwarted, that majority may be wholly excluded
from Parliament. This is what must inevitably
happen when the minority votes solidly on a
ticket, and the majority scatters its votes by
running too many candidates. The
object of reformers is to remedy this defect,
and to ensure that the party which is in a
majority in the State shall also be in a
majority in the Elected House. The reformers
also secure that the party which is in a
minority in the State is also represented in the
House, but by a minority as it ought to be, by a
minority proportional to its strength in the
State. This is but right and just, and that it
is right and just has always been recognised by
such Statesmen as Bright, Gladstone, and
Disraeli. These Statesmen always strongly
opposed the block vote
because they knew it was unjust, and they
supported the district system because they
believed it would produce equity. That these
Statesmen were mistaken in their belief has now
been abundantly proved by experience. Of
this experience the most notable example
occurred in 1871, at Newhaven U.S., when 42
Municipal Councillors were elected in 42
one-member districts. In the whole electoral
body the Republicans were to the Democrats as 26
to 16, but in the Council Chamber the
Republicans were to the Democrats as 14 to 28.
Thus, the votes cast were practically as 2 to 1,
whilst the members elected were as 1 to 2. A
striking example also occurred at Geneva in
1841. Here, the Liberals were in a majority, and
the Conservatives in a minority. But the
Conservatives carried three-fourths of the
seats, each by a narrow majority, whilst the
Liberals carried one-fourth of the seats each by
an overwhelming majority. Thus, the party which
was in a minority in the Canton had a majority
of 3 to 1 in the Elected House. The intense
dissatisfaction caused by this glaring injustice
had no little influence in bringing about the revolution
of 1846. The
object of the Statesmen mentioned was the rule of
the majority combined with a fair representation
of the minority. This object can be attained in
one way only. That way is the use of the
preferential or contingent vote and the use of the
principle of the quota. By these means, properly
applied, all votes can be made practically equal,
and the rule of the majority can be assured. All
the elector is concerned with is the method of
voting. It is an insult to say that a Victorian
cannot understand this, for the preferential or contingent vote is used all over
Queensland. To the uninitiated the
method of getting out the result of the election
is apparently complicated, but to the initiated it
is perfectly simple and straightforward. To the
elector this is a matter of little or no concern.
The citizen who drops a letter into the pillar-box
need not, and often does not, know the details of
the process by which that letter reaches its
destination. The passenger by the ocean greyhound
knows but little of all the vast mechanism by
which he is carried safely into port. The real
question, the essential point, is this. Is the
method true, does it do what it professes, is it
fair to all concerned? Such are the important
issues now before the intellectual and political
leaders of Victoria. To
ensure electoral freedom the preferential or
contingent vote must be used. Each elector has
one, and only one, vote. The voter is furnished
with a list of all the candidates. He marks the
candidate he likes best with the figure "one," the
candidate he likes second best with the figure
"two, " the next with the figure "three," and so
on, to just as many names as he pleases. But the
voter who fails to mark all the names runs the
risk of throwing away his vote. The object of the
preferential vote is to prevent waste of voting
power which may occur in two distinct ways. First,
by splitting which happens
when a party runs too many candidates and loses
through scattering its votes. Second, by
concentration which happens
when a party polls for a popular candidate,
votes far and away in excess of those necessary
to secure his election. Of concentration
a good example is furnished by the Convention
election, in which Sir George Turner polled twice
the number of votes necessary to secure his
election. Here was a great waste of voting power,
of power that might have elected to the Convention
a second Labour candidate or a representative of
the country party. By using the preferential vote
the individual elector secures freedom, freedom to
vote as he thinks right without risk of losing his
vote, freedom from the toils of the machine
politician without whose aid and guidance he is at
present like a mariner without a compass. To
secure electoral equality or one vote one value
the principle of the quota must be used. The quota
is the smallest number of votes which entitles a
candidate to election. It is found by dividing the
whole number of valid votes by one more than the
number of seats and increasing the quotient by
one. All votes polled
by a candidate in excess of the quota are of no
use to him. The principle of the quota asserts
that in a one member district any party with more
than half the votes is entitled to the seat. In a
two-member district it asserts that any party with
more than one-third of the votes is entitled to
one of the seats. In a three-member district it
asserts that any party with more than one-fourth
of the votes is entitled to one of the seats, and
so on. Thus, in a seven-member district a party
with more than one-eighth of the votes is entitled
to one of the seats; a party with more than
two-eighths or one-fourth of the votes is entitled
to two seats; a party with more than three-eighths
of the votes is entitled to three seats; and a
party with more than four-eighths or one-half of
the votes is entitled to four of the seats. The
principle of the quota then secures the direct
representation of all prominent parties in the
State, of each in proportion to its strength. It
means, therefore, the rule of the majority. It
means, practically, one vote one value throughout
the State. The quota is the true price in votes of
a seat in Parliament. The principle of the quota
practically secures the election of all members on
the same terms. In systems in which there is no
quota, members are elected on far different terms.
In the Convention election Sir George Turner paid
nearly twice the price in votes paid by Mr.
Higgins. At the general election in February,
1883, in Victoria, 813 votes sufficed, on the
average, to seat a Constitutionalist in the
one-member districts, but 2468 votes were
required, on the average, to seat a Radical. The
object of the preferential quota system is
to enable the voters to divide themselves into as
many absolutely equal unanimous electorates or
quotas as there are seats to be filled. The voters
begin by dividing themselves, by means of the
"ones" written on their voting papers, into as
many unanimous groups or electorates as there are
candidates. The groups so formed are in the first
place unequal in size, and in the second place,
they are too numerous. There are then two things
to be done. First, the groups which are too large
are to be cut down in size. Second, the number of
groups is to be diminished by weeding out the
weakest. Now, these two things are done by the
electors themselves by means of the preferential
vote. The Returning Officer is merely the agent of
the electors in this matter. He obeys the definite
written instructions of the voters, and by
carrying out those instructions he effects the requisite
cutting down and weeding out. There are two simple
principles which govern the whole process. First,
whenever any group exceeds the quota, that is,
whenever more than a quota of voters agree in
supporting the same candidate, then each member of
that group transfers an equitable portion of his
vote to the candidate he likes next best This is
the cutting down process. Second, when no group
exceeds the quota, that is, when no candidate has
more than a quota of supporters, then the
candidate with the smallest number of votes
retires, and his supporters transfer their votes
to the candidate they like next best. This is the
weeding-out process. It is the principle of the
exhaustive ballot in its simplest form. In
the cutting-down process Gregory's principle
is applied. Supposing that a candidate has two
quotas of votes it is clear that he only requires
half the vote of each of his supporters. Hence,
each of his supporters transfers half his vote to
the candidate he likes next best. Similarly,
if a candidate has a quota and a half, he
requires two-thirds of the vote of each of his
supporters. In this case then each of his
supporters transfers one-third of his vote to
the candidate he likes next best. The
weeding-out process is perfectly simple, both in
theory and practice. It is now partially in
force in Queensland. It is merely the principle
of the "Second Ballot" carried out in an
eminently practicable form to its logical
conclusion. In
each of these processes a parcel of voting
papers is divided into a number of smaller
parcels. Every step of the election is merely a
sub-division of this kind. The very first step
in an election is a case in point. The one
parcel of voting papers formed by the ballot box
is broken up into as many smaller parcels as
there are candidates, all the papers having the
same name marked "one" forming a smaller parcel
by themselves. When
a candidate is excluded or weeded out he may
have a number of parcels of voting papers. These
are broken up and distributed, one after the
other, in the order in which they came to him. When
several candidates have each more than a quota
of votes their surpluses are distributed in
succession, first the largest, then the next
largest, and so on. When
any surplus exists it is distributed before any
further exclusion or weeding out takes place.
But, nevertheless, any distribution of votes
once entered upon is completed, notwithstanding
that a surplus or surpluses may thereby be
created. When
by breaking up and distributing any parcel a
candidate is raised above the quota, no papers
are transferred to that candidate from any
subsequent parcel. The object of this simple
rule is to avoid all unnecessary handling and
rehandling of voting papers. For
a similar reason when a candidate with a surplus
has more than one parcel the Gregory principle is
applied, not to the whole of his parcels, but only
to the last parcel which came to him, to the
parcel which actually raised him above the quota.
Any votes that he has just before the receipt of
this last parcel are permanently retained as part
of his quota. In this way the number of papers
which have to be dealt with on the Gregory
principle is reduced to a minimum. Thus, a
candidate may have, say, half a dozen parcels and
be short of the quota by 20 votes. If a seventh
parcel of papers, equivalent to 30 votes, now
comes to him from any source he only needs
two-thirds of the strength of each of these
papers. Accordingly, the whole of the papers in
the seventh parcel are handed on, each to the next
name thereon, each with one-third of its previous
value. This previous value, be it observed, is
necessarily the same for all the papers in the
parcel. By
these two processes, the process of cutting down
and the process of weeding out, the electors build
up for themselves absolutely equal unanimous
groups, or quotas, each returning one member. That
they cannot build up more groups than are required
is obvious from the principle of the quota. They
will generally build up exactly the number of
groups required. But if many of the electors fail
to exercise all their preferences the required
number of groups may not be obtained. Should this
be the case the remaining seats are filled by a
different process. In
no circumstances is any candidate elected on less
than a quota of votes. The seats for which a quota
has not been obtained are filled one after the
other, each by a candidate elected by an absolute
majority of the whole of the voters. For the seats
to be filled in this way all candidates as yet
unelected enter into competition. The matter is
settled by a reference to the whole of the voting
papers. If any unelected candidate now stands
first on an absolute majority of all these papers
he is elected, But if not, then the weeding-out
process is applied until an absolute majority is
obtained. The candidate who gets the absolute
majority is elected. Should there be another seat,
the same process is repeated. If an absolute
majority of the whole of the voters cannot be
obtained for any candidate, then the candidate who
comes nearest to the absolute majority is elected. Those
who desire to test the proportional scheme for themselves, those who
desire to obtain a thorough grip of the subject,
cannot do better than go through the whole of the
details of an election, real or imaginary,
conducted by themselves. To all such persons, and
it is hoped that they, may be numerous, a few
practical suggestions may be offered. Voting
cards, not voting papers, should be used. Separate
boxes should be provided to hold, in their proper
order, the parcels of each candidate. Elastic
bands should be used to keep together all cards
belonging to the same parcel. The parcels are to
be dealt with one at a time. No two parcels are
even to be re-united into a single parcel. The
election is a process of disintegration all
through. Blank cards should be provided to be tied
up with each parcel shewing
(a) the owner of the parcel, (b) the common value
of each card in the parcel. A record should be
kept of every step which is taken. In commercial
language every transfer should be journalised and
the proper debit and credit entries made in the
ledger. There should be in the ledger an account
for (a) ballot box, (b) each candidate, (c) lost
votes. The ledger must balance at every stage of
the election. In making ledger entries all
fractions are to be omitted. Lost votes arise
through electors failing to express sufficient
preferences. When there is no next name to which a
paper can be transferred, the paper becomes
exhausted. On the exclusion of a candidate an
exhausted paper becomes a lost paper. On the
election of a candidate an exhausted paper is not
necessarily lost. The exhausted part of the parcel
which produces a surplus may, or may not, be less
than the surplus. In the former case all the unexhausted papers in the
parcel are handed on to the next name, and some
exhausted papers become lost. In the latter case
Gregory's principle is applied to the unexhausted part of the
parcel and no papers are lost. The
full details of an imaginary election are given
for the satisfaction of those who desire details.
They are given in order to show that the working
out is a mere piece of arithmetic in which every
step is taken in obedience to a simple and just
law, and that nothing is left to chance or to the
discretion of a Returning Officer who might
possibly wish to take a hand. The whole process
can be audited like the books of a commercial
institution, and, in fact, every intelligent
elector who looks carefully into the published
results is a possible auditor. It is to be
emphasised that a knowledge
of the various details is of no more practical
importance to the average elector than is a
knowledge of the mechanism of a locomotive engine
to the railway passenger. The passenger takes his
ticket in full confidence that he will be carried
safely to his destination. So the elector may cast
his preferential vote with full confidence that it
will travel unerringly to its final destination. To
show how the scheme may work out in practice
imagine an election to select 7 out of 15
candidates. Borrowing a nomenclature devised by
Miss Spence, let there be 5 parties, as shown in
the Table, constituted as follows: - COLOUR,
with 35 voters and 4 candidates, one of whom,
White, is popular, and polls 24 "ones." FORM,
with 44 voters and 4 candidates, one of whom,
Square, is strongest in popular favour and polls
32 "ones." PLACE,
with 20 voters and 3 candidates. QUALITIES,
with 14 voters and 2 candidates. PURSUITS,
with 12 voters and 2 candidates.
There
are in all 125 voters. As there are seven seats,
and each voter has one vote only, any candidate
who gets 16 votes is sure of election. For, when
seven candidates have each got 16 votes there are
only 13 left out of the 125 for an eighth man. This
number, 16, is found by dividing 125 by 8, that is by one more than the
number of seats, and increasing the
quotient by one. The number so found is called the
"quota." The
numbers of "ones" or votes polled by the various
candidates are shown in line I. of the Table,
which therefore shows the "first state of the
poll." In
an actual election in Victoria this "first state
of the poll" could be arrived at with the same
rapidity as was the result of the recent poll on
the Commonwealth Bill. In both cases but one fact
has to be gleaned from each voting paper. The
results from all parts of the colony would be
posted in Collins Street on election day. These
results would show exactly how the cat was going
to jump. The final results, as regards parties,
would be obvious to all observers, although the
results as regards individual candidates would be
far from clear. But this, although of vast
importance to the candidates themselves, would be
a matter of small concern to the great mass of the
people. Square and White
having both polled more than the quota are
elected. Each has a surplus or excess over the
quota. The former has a surplus of 16, and the
latter has a surplus of 8. These surpluses are now
to be distributed - first, the larger one, then
the smaller one. Square
has 32 votes, but only requires 16 to elect
him. He therefore needs exactly half a vote from
each of his 32 supporters. Therefore, each of
the 32 has half his vote left for the candidate
he likes next best. Accordingly, each one the 32
voting papers is handed on, each with the value
one-half, each to the next name thereon. It is
found, on looking at these 32 papers that on 20
of them Round
is
marked "two", on 6 Oblong
is marked "two", on 6 Oval
is marked "two". Thus, Round
receives from Square
20 voting papers, each valued at one-half.
This gives Round
10 more votes, and so Round
rises from 5 to 15. Similarly Oblong
rises from 4 to 7,
and Oval
from 3 to 6. Thus we get the "second state of the
poll" shown in line II. of
the Table. Next,
White's
surplus has to be distributed. White
has 24 votes, but only requires 16 to elect him. He
therefore needs exactly two-thirds of a vote from
each of his 24 supporters. Therefore, each of the 24
has one-third of his vote left for the candidate he
likes next best. Accordingly, each of the 24 voting
papers is handed on, each with the value one-third,
each to the next name thereon. It is found on
looking at these 24 papers that on 6 of them Black
is marked "two", on 9 Yellow
is marked "two", on 9 Red
is marked "two". Thus, Black
receives from White
6 voting papers each valued at one-third. This gives
Black
2 more votes, and so Black
rises from 6 to 8. Similarly Yellow
rises from 3 to 6, and Red
from 2 to 5. Thus, we get the "third state of the
poll" shown in line III of the Table. No
candidates except White
and Square have now
so much as the quota. Hence, the exhaustive ballot
now comes into play. The lowest on the poll retires.
Thus, Art
with
2 votes retires. These 2 votes are not wasted but
used to help PURSUITS,
the two voters having naturally given their second
preference to Science. Mercy
is now the lowest with 3 votes. He retires and the 3
votes are not wasted but used to help QUALITIES
to elect
Justice. Village
is now lowest with 4 votes, and therefore retires.
These 4 votes naturally help PLACE, and go, in accordance with
the instructions of the voters, 2 to Town and 2 to
City.
At this stage Red
is lowest with 5 votes. These go, 3 to Black,
2 to
Yellow. Oval
is now lowest with 6 votes and these pass, 3 to Round, and 3 to
Oblong.
In disposing of Red's
5 votes we distribute first the 2 votes he got from
the ballot box, then the 9 papers, each with the
value one-third, which he got from White,
and in disposing of
Oval's
6 votes we distribute first the 3 votes he got from
the ballot-box, then the 6 papers, each with the
value one-half, which he got from Square.
After these simple applications of the exhaustive
ballot, we get the "state of the poll" shown in line
IV of the Table. Round
is therefore elected with a surplus of 2 votes. We
have now to revert to the cutting-down process. Round
has
been raised above the quota by the receipt from Oval
of 3 votes. These 3 votes are found to be the 3
votes which Oval
originally got from the ballot-box. On examination
it is found, as might be expected, that Oblong
is marked "three" on the 3 voting papers in
question. As Round
wants only 1 of the 3, the 3 papers are passed on,
each with the value two-thirds, to Oblong.
This gives Oblong
2 more votes, and so we get the "state of the poll"
shown in line V. of the Table. No
candidates, except White,
Square,
and
Round,
have now so much as the quota. Once more, then, the
exhaustive ballot comes into play. Yellow
with 8 votes now retires. These 8 are made up of
three parcels - first, the 3 papers which came from
the ballot-box to Yellow;
second, the 9 papers with the value one-third which
passed from White to
Yellow;
third, the 2 papers -which passed with unit value
from Red
to
Yellow.
The first 3 papers raise Black
from 11 to I4. Then the 9 papers, each with the
value one-third, raise Black
from
14 to 17 and so elect him. Next, the third parcel of
2 votes or papers would pass from Yellow
to
Black;
but, as Black
is already elected, we look for the next names and
find them to be the same, viz., Justice, on the 2
papers. Thus 2 votes pass from Yellow
to
Justice,
and elect Justice.
Thus we have the "state of the poll" in line VI of
the Table. The
cutting-down process has now to be applied. Black has been
raised above the quota by the receipt from Yellow
of
a parcel of 9 papers each with the value one-third.
As Black
requires only two-thirds of each of these to elect
him, the whole 9 are passed on to Science,
each with one-third of the previous value, that is,
each paper is passed on with the value one-ninth.
Thus we get the "state of the poll" shown in line
VII of the Table. Once
again exhaustive ballot applies. Town with 9 votes
now retires. The 9 would naturally flow to City.
But we distribute first the 7 which Town
got from the ballot-box, then the 2 which Town
got from Village.
The 7 pass from Town
to City
and elect City.
Then the 2 pass, not to City,
who has now no need for them, but to Oblong.
We then get the "state of the poll" shown in line
VIII of the Table. Finally
the cutting-down process has once more to be
applied. City
has been raised above the quota by the receipt from
Town
of a parcel of 7 papers, each with unit value. As City
requires only 5 of the 7 to elect him, the whole 7
are passed on to Oblong by Gregory's principle,
each with the value two-sevenths. This .gives Oblong
two
more votes, and we have the final "state of the
poll" shown in line IX of the Table. Oblong
is elected to the seventh seat, Science
being
the runner-up with 13 votes. Thus,
the 7 seats are filled by candidates elected by
equal unanimous quotas or groups of electors. COLOUR,
with a trifle over two quotas, gets two seats; FORM,
with a little less than three quotas, gets, with the
help of PLACE,
three seats. PLACE,
with a trifle over one quota, gets one seat and
helps FORM. QUALITIES, with
a little less than one quota, gets,
with the help of COLOUR,
one of the seven seats. But the PURSUITS
party, which has less than a quota and receives
practically no help from any other party, gets no
representation. This,
surely, is electoral justice and fair play.
All voters are represented save the 12 who
support PURSUITS,
and these amount
to less than one-tenth of the whole. No votes are
lost or ineffective except the PURSUIT
votes. Contrast
with this the results of the block
system. With strict
party voting, which has been assumed throughout,
each of the five parties would put forward seven
candidates. The seven seats would all be secured
by FORM
with 44 votes out of a total of 125, and the
remaining 81, or more than two-thirds of the
voters, would be wholly unrepresented. This result
is attained by strict party organization which
means the utter extinction of' individual freedom. Tactic
and the party list are absolutely necessary in the
block vote. They enable the strongest party, which
may be a mere minority of the people, to crush all
opponents, to crush the real majority because that
majority may have the misfortune to be
disorganized and divided. But, with the
preferential vote and the quota, tactic and
organization are alike helpless and unnecessary.
With or without them the real majority can get
what it is justly entitled to, the supreme
control. But the minority also can get what it is
entitled to, and that is a fair hearing, not
merely in the turmoil of the hustings,
but in the calmer atmosphere of Parliament. It can
get all this, not as a mere crumb from the table
of the machine politician who runs the winning
ticket in the block vote system, but as a matter
of right and justice. In
the preferential system the members elected are
not merely the spokesmen of the dominant party.
They represent, so far as their numbers will
allow, all the principal opinions prevailing in
the State, each in its due proportion. This result
is attained, not by imposing an expensive
organization on parties, but by the automatic
action of machinery provided by the State, by
machinery which gives full and adequate effect to
the wishes of the whole of the electors in this
way, and in this way only, can the true will of
the people be ascertained and a substantial, and
necessary addition made to the edifice of
Democracy. __________________________ |
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