Proportional Representation Election for
Schoolboys c. 1820
from "Your vote -
effective or wasted?"
ISBN 0 9598728 2 5 © Proportional
Representation Society of Australia 1980)
form of the Single
Transferable Vote in
multi-member electorates (PR-STV) that is
also known in Australia
as the quota-preferential method of
was first suggested in about 1820 by Thomas
Wright Hill, a Birmingham
schoolmaster. Thomas Hill
encouraged the boys in his school to use
his method to elect a committee. Although
there is no detailed account of this
election, it could have been somewhat as
in the diagrams below.
son Rowland, knighted after his major
reform of the UK postal
system, had earlier been the Secretary of
the Colonization Commission of South
Australia, in which position he is
understood to have been instrumental in
the adoption of PR-STV for the first election of councillors
for the City of Adelaide,
in 1840. That was the first PR-STV
election for public offices in the world,
and also the first election for public
offices in Australia. A large oil portrait
of Rowland Hill
hung in Ayers House,
the residence of a former Premier of South
Australia, after whom Ayers Rock (Uluru)
was named. The late Dr
David Hill, a direct descendant of Thomas Hill,
had been the Secretary of the Royal
Statistical Society, and he had convinced
it to use PR-STV for its elections.
He was also
a member of the Electoral
Reform Society of the UK.
With 17 boys voting to appoint a committee
of 5 from 7 candidates, we can imagine the
schoolmaster pointing out that any
candidate supported by three or more boys
should be elected. Not more than five
could each have three or more supporters
and this means that anyone with 3 or more
supporters must be among the 5 finally
elected. This number of votes necessary
for election is known as the 'quota'.
At the end of the election, 15 of the boys
are grouped into 5 quotas and there are 2
boys left over. In fact, one of these is
one who had originally supported the first
candidate elected. The result then is that
15 of the 17 boys see their first
preference candidates elected and only one
print the graphic below at the right size
to fill an A4 page, click on it with your
mouse button and save the
file, tom_hill.gif, to your hard drive.
Then open it and print it.
this case, every boy could see how the
others voted. It was shown later by Thomas
Hare in England and Carl Andrae in Denmark
that the same method could be used with
secret voting. Voters can show by
preference markings on ballot papers which
candidates they support and where they
would transfer their support is it was not
needed by their first-preference
candidates. Instead of the boys grouping themselves in
support of candidates and eventually
arranging themselves in quotas, the ballot
papers would be examined and the counting
carried out as shown above.
Each stage of counting corresponds exactly
to one stage in the schoolboys' election.
Each voter had a wide choice of candidates
and bodies of opinion are represented by spokesment in
numbers proportional to the numbers
supporting them, since each candidate
elected is supported by a quota of voters.
This method has been developed for use in
elections of all sizes, and several
refinements have been introduced to make
it as accurate and effective as possible.
For example in transferring Adam's
surplus, it is not necessary to make an
arbitrary selection of 3 of the ballot
papers showing Adam as first preference.
It is better to examine all of them and to
find which candidates the voters have
shown as second preferences. The surplus
of 3 will be carried by the 6 papers so
each is given a 'transfer value' of ½.
Each of the unelected candidates is then credted with the
papers showing him as second preference,
each with a value of ½.
The method can be used to fill any number
of vacancies. In each instance, the quota
is calculated so that it is possible to
form a number of quotas equal to the
number of vacancies but no more than this.
It is found by dividing the number of
formal votes by the next whole number
above the number of vacancies, and taking
the next whole number above the result of
the division. For example, in an election
with 40,000 votes to fill 7 vacancies, the
result of dividing 40,000 by 8 is 5,000
and the quota is 5,001. If 7 candidates
each have 5,001 votes, totalling 35,007,
there are only 4,993 votes remaining. So
only 7 quotas of 5,001 can be formed and
this is the smallest number that gives
this result. It can be left to the voters
to decide how many preferences they wish
to indicate. There is no need to compel
them to indicate preferences for all