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Proportional
Representation Society of Australia |
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Tel
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2021-02-01 |
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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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