PROPORTIONAL REPRESENTATION SOCIETY OF AUSTRALIA

Tel +613 9589 1802

Tel +61429176725

18 Anita Street

BEAUMARIS VIC 3193

 

info@prsa.org.au

www.prsa.org.au

2012-08-01

 

Electoral Reform

 

AN EXPOSITION OF THE THEORY AND PRACTICE

OF PROPORTIONAL REPRESENTATION

 

An 1899 booklet written by Professor Edward Nanson, Professor of Mathematics, University of Melbourne, 1875-1922

 

Professor Nanson was, in the first half of the 20th Century, Secretary of the forerunner of the PRSA’s Victoria-Tasmania Branch
and a leading proponent of electoral reform in Australia in that formative period.

 

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.

 

COLOUR

35 votes

FORM

44 votes

PLACE

20 votes

QUALITIES

14 votes

PURSUITS

12 votes

 

White

Black

Yellow

Red

Square

Round

Oblong

Oval

City

Town

Village

Justice

Mercy

Science

Art

I

24

6

3

2

32

-16

5

10

4

3

3

3

9

7

4

11

3

10

2

II

24

-8

6

2

3

3

2

3

16

15

7

6

9

7

4

11

3

10

2

III

16

8

3

6

2

5

-5

16

15

3

7

3

6

-6

9

2

7

2

4

-4

11

3

3

-3

10

2

2

-2

IV

16

11

8

 

16

18

-2

10

2

 

11

9

 

14

 

12

 

V

16

11

6

8

-8

 

16

16

12

 

11

9

 

14

2

 

12

 

VI

16

17

-1

 

 

16

16

12

 

11

9

 

16

 

12

1

 

VII

16

16

 

 

16

16

12

 2

 

11

7

9

-9  

 

16

 

13

 

VIII

16

16

 

 

16

16

14

2

 

18

-2

 

 

16

 

13

 

IX

16

16

 

 

16

16

16

 

16

 

 

16

 

13

 

 

White

Black

 

 

Square

Round

Oblong

 

City

 

 

Justice

 

Science

 

 

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.

__________________________

 

 

Click here to go to the VICTORIA page of A Brief History of the PRSA and its Purpose.