PROPORTIONAL REPRESENTATION SOCIETY OF AUSTRALIA (VICTORIA-TASMANIA) INC.
A0048538N Victoria ABN 31 010 090 247	Tel +613 9589 1802		18 Anita Street
	Mobile +61429176725	www.prsa.org.au/	BEAUMARIS VIC 3193
	Fax +613 9589 1680	ggd@netspace.net.au	20th June 2006

THOMAS HILL’S PROPORTIONAL REPRESENTATION ELECTION FOR SCHOOLBOYS c. 1820

(An extract from "Your vote - effective or wasted?  " ISBN 0 9598728 2 5   © Proportional Representation Society of Australia 1980)

The form of the Single Transferable Vote in multi-member electorates that is now known in Australia as the quota-preferential method of proportional representation was first suggested in about 1820 by Thomas Wright Hill, a Birmingham schoolmaster whose son Rowland became Secretary of the Colonization Commission of South Australia and later reformed the British postal system. We are told that Hill Senior encouraged the boys in his school to use his method in the election of a committee. Although there is no detailed account of this election, it could have been somewhat as in the diagrams below.

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 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 is disappointed.

To print the graphic below at the right size to fill an A4 page, click on it with your right hand mouse button & save the file, tom_hill.gif, to your hard drive. Then open it & print it.

In 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 and 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 foundby 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 candidates.