W'K/,^\ FOR THE PEOPLE FOR EDVCATION FOR SCIENCE LIBRARY OF THE AMERICAN MUSEUM OF NATURAL HISTORY ;^ 090 ROYAL SOCIETY OF TASMANIA PAPERS & PROCEEDINGS OF THE '^^.:d(3^(:>3Cl ROYAL SOCIETY °\ OF TASMANIA FOR TFiE YEAR 1913 With I Text.Figure. 22 Plates, and I Map. ISSUED 14th FEBRUARY', 1^14. PUBLISHED BY THE SOCIETY. The Tasmanian Museum, Argylc Street, Hobart, 1914. Pr-iae: Fifteen Shillings. The responsibility of the statements and opinions in trie following papers and discussions rests with the individual authors and speakers; the Society merely places them on record. Printed al "The Mciv-urv" 0£Fiv.£. Macyuatic 5tree-l. Hobart. THE ROYAL SOCIETY OF TASMANIA. The Royal Society of Tasniania was founded on the 14th Octo- ber, 1843,"^ by His Excellency Sir John Eardley Eardley AVilmot. Lieutenant Governoi- of Van Diemen's Land, as "The Botani- cal and Horticultural Society of Van Diemen's Land." The Botanical Gardens in the Queen's Domain, near Hobart, were shortly afterwards placed under its management, and a grant of £400 a year towards their maintenance was made by the Government. In 1844, His Excellercy announced to the Society that Her ]\[ajesty the Queen had signified her con- sent to become its patron ; and that its designation should thenceforAvard be ''The Royal Societv of Van Diemen's Land for Horticulture, Botany, and the Advancement of Science." In 1848 the Society established the Tasmanian Museum ; and in 1849 it commenced the publication of its -Papers and Proceedings." In 1854 the Legislative Council of Tasmania by "Tlie Roval Society Act" made provision for vesting the property of the Society in trustees, and for other matters connected with the management of its affairs. In 1855 the name of the Colony was changed to Tasmania, and the Society then became "Tlie Royal Societv of Tasmania for Horticulture, Botany and the Advancement of Science." In I860 a piece of ground at the corner of Argyle and Mac- quarie-streets, Hobart, was given by the Crown to the Society as a site for a Museum, and a grant of £3,000 was made foi* the erection of a building. The Society contributed £1.800 towards the cost, and the new Museum was finished in 1862. In 1885 the Society gave back to the Crown the Botanical Gardens and the Museum, A^hich, with the collections of the Museum, were vested in a body of trustees, of whom six are chosen from the Society. In consideration of the services it had rendered in the promotion of science, and in the for- mation and management of the ^Museum and Gardens, the right was reserved to the Society to have exclusive possession of sufficient and convenient rooms in the Museum, for the safe custody of its Library, and for its meetings, and for all other purposes connected with it. In 1911 the Parliament of Tasmania, by "Hie Royal Society Act 1911," created the Society a body corporate by the name of ''The Royal Society of Tasmania," with perpetual succession. ^ The objects of the Society are declared by its Rules to be ''the prosecution of the study of Science in its^ various branches, and more especially tlie development of a knowledge of the physical character and natural history of Tasmania and the neighbouring States." His Majesty the King is Patron of the Society; and His Excellency the Governor of Tasmania is President. CONTENTS. Page On the Relation between the Loss of Energy and the lonisation produced bv Cathode Ravs. Bv J. L. Glas.son. B.A., D.Sc ".. ... : 1 The Height of Ben Lomond. By L. F. Giblin, B.A., E. L. Piesse, B.Sc., and H. R. Hutchison, Authorised Surveyor 3 Tho Thoorv of tht^ Quota in Proportional Kopreseuta- tion— 11. liy E. L. Piesse, B.Sc., LL.B IT, Notes on Hi/inenophylluin peltatum (Poll) Dosr. By I.. Rodsvay .". :^S Bibliograpliv of Proiwrtional Representation in Tas- mania. By ' E. L. Piesse, B.Sc, LL.B 30 A Rectification in the Cartography of Xortli-Easl Tasmania. By Colonel W. V. Legge, F.R.G.S 7() List of Native A^'ords of the Oyster Bay Tribe. \ aw Diemen's Land. By J. W. Beattie. ... ' 79 Notes on the List of Native Words of tlie Oyster Bay Tribe, presented bv ]Mr. J. AV. Ik-attic Bv Hermann B. Ritz, M.A. ... : 82 Notes on the Section at One Tree Point, near Hobart. By Fritz Noetlmg, M.A., Ph.D 95 Note on Strzelecki's Determinations of Heiglits in Tas- n.ania 11- Some Australian Brachiopods. By F. Blochmann ... 113 The Foundation and Early Work of the Society : with some Account of Earlier Institutions and Societies in Tasmania. By E. L. Piesse 117 Notes on a Fossil Whal(^ tVoni Wvnyard. Bv H. H. Scott \ .". ' 167 Demography of Tasmania. By L. F. Giblin, B.A.... 173 Tasmanian Bryophyta. Part III. By L. Rodway. ... 177 New Australian Asilidae. By Artliur White 264 Abstract of Proceedings 281 Annual Report List of the Society 295 Report 304 Accounts 311 Obituary Notices 313 Institutions, etc., to which 'M*aper.s and Proceedings' are presented 320 Plates, i. - xxii. Index 325 :\Iap Errata. Page 33, line 21— for "/" (where it first oceui's), read " />/' Page 34. The third equation should rea In order to calculate the value of n we refer to a paper by Crowther (Prnc. Hoy. Soc, vol. 84, p. '226), in which he shows that ior the five elements C, Al, Cu, Ag, Pt, whicli have atomic weights varying from 12 to 195, the number of electrons in the atom is three times the atomic weight to within a iew per cent. Assuming that this holds also for the atoms of 0 and N, we find that the number of electrons per c.c. of air at 760 m.m. is v. = '2''d x l()*i. Putting this value in (ix) we get ^. = 5-5 (approx.) 'Thus the energy s^penf in ionisation is one- fifth o' the n'inde energy spent hi/ the ray. I am grateful to Professor Kerr Grant, of the University •of Adelaide, for valuable suggestions in connection with this paper. The University of Tasmania, 29th March, 1913. THE HEIGHT OF BEN LOMOND. By L. F. GiBLiN, B.A., E. L. Piesse, B.Sc, and H. R,. Hutchison, Authorised Surveyor. (Read 14th April, 1913.) Map In a paper read before the Society in 1907(^), two of ua gave an account of observations made with aneroids on Ben Lomond in 1906 and 1907 with the object of deter- mining the difference of height between Legge Peak(^), the highest summit in the northern part of the Ben Lomond range, and the trigonometrical station at the south- ern end of the range. The trigonometrical station is stated on the official maps of Tasmania to have a height of 5010 feet; Cradle Mountain is stated to be 5069 feet, and the Ben Lomond station comes next below it, being thus the second highest of the officially recorded summits. The observations in 1906 made Legge Peak 140 feet higher than the trigonometrical station; and in 1907, 160 feet. From the former, the height of Legge Peak was 5150 feet, from the latter 5170 feet, and the mean of the two results was 5160 feet. If this result were correct Legge Peak was nearly 100 feet higher than Cradle Mountain, and was the highest known summit in Tas- mania. But the result had been obtained with aneroids not of the best pattern for this purpose, and not used in the best conditions, and it was desirable that the difference of height should be ascertained by survey. An oppor- tunity to revisit the mountain did not occur until 1911. A survey was then made which in part confirmed the height obtained in 1906 and 1907, but the result was not conclusive, and another survey was accordingly made in 1912, and this placed the height of Legge Peak beyond doubt. (0 L. F. Giblin nnd E. L. Piesse, Note on the Height of Legge Tor {Proc. Boy. Soc. Tas. 1906-7, xxxvii.-xL). (*) The name Mt. Legge was proposed :n the paper just mentioned, but In the title of the paper the name was altered to Legge Tor as this was understood to be the form desired by the Department of Lands and Sur- veys. In the County chart Cornwall Xo. 3 the summit has been called Leg^e Peak. fi) THE HEIGHT OF BEN LOMOND, ■R.S. TAS. At Christmas, 1911, a party consisting of Messrs. W. F. D. Butler, J. A. Johnson, A. F. Weber, and two of the writers (L. F. Giblin and E. L. Piesse) spent several days at Ben Lomond. Leaving Hobart by the morning train, the party was met at Avoca station by Mr. C. E. Foster, who made all arrangements for the ascent of the mountain and enabled the party to reach before dark the old Ben Lomond Hotel, 11 miles from Avoca, and about 2400 feeb above sea-level. The " Hotel," it should be mentioned, is untenanted, and travellers will be wise to make their own camp. Next morning, Mr. Foster's horses helped the party to the Upper Camping Ground, about 3700 feet, and from there the loads were carried to the plateau. Arrived at the moor, the party went southwards to the Stacks Bluff, on which is the trigonometrical station. There a base rather more than a quarter of a mile long was measured, and with a 5 -inch Everest theodolite angles were taken to ascertain the distance and elevation of Legge Peak. Then the party went on to Youl's Lake, where a camp was made. The rcsu'ts of the day's observations were computed, and the height of Legge Peak was found to be 5158 feet. As the object of the expedition seemed to be attained, the next day, again a fine one, was spent in a visit to Legge Peak instead of in making a check survey. This was attempted on the following day, but the weather had iDroken and it was impossible to do more than measure a second base on the moor south of the Nile gorge, and move camp to a more sheltered spot, a little flat about 400 feet above the LTpper Camping Ground and at the foot of the talus slope from Wilmot Bluff. Three of the party had to return to Hobart next day, but Messrs. Giblin and Piesse remained, and were able to take the required angles at the second base. Satisfied with these, they returned to the flat, and moved camp to the old Hotel, in preparation for an easy stage next day into Avoca . But when the day's observations were examined that night at the camp fire, it was found that they did not confirm the first day's work at the Stacks Bluff. The observations from the two ends of the Nile gorge base made Legge Peak, from one end of the base, 13 feet lower than the trigonometrical station, and from the other end 6 feet. The apparent agreement of these two results BY L. F, GIBLIN, E. L. PIESSE, AND H. I\. HUTCHISON. 7 1913, averted suspicion from the instrument, and no other explanation could be imagined. The supply of food was almost exhausted, but there was just enough for another day's stay, so an early start was made with the theodolite next morning, and the site of the previous camp reached by eight o'clock. Then a cloud covered the summit, and did not lift for eight hours. At last, at nearly five o'clock, the fog lifted, and vertical angles were taken from the trigonometrical station to the ends of the Nile base (which, of course, had not been marked on the first day) and again to Legge Peak. The angles to the base agreed closely with the angles taken in the opposite direction from the ends of the base to the trigonometrical station, and the angles to Legge Peak w^ere also nearly the same as those taken on the first day, and so the mystery of the discordant results was still unsolved. However, it v/as not possible to do any more, and next day the party had to go in to Avoca. It was only after the return to Hobart that an examination of the instrument showed that some parts of it had w^orked slightly loose, so that it would sometimes give a correct vertical angle and sometimes a quite 'incor- rect one. Its vagaries had not been discovered in the field, because on each test made of it the reading confirmed the previous reading. It was tempting to disregard the results from the Nile gorge base, and to treat the height, 5158 feet, obtained from the Stacks Bluff base, agreeing so closely with the height given by the aneroids in 1906 and 1907, as correct. However, it was safer to wait for a confirmation, and the result was therefore not published. At Christmas, 1912, the writers and Messrs. Butler and Weber went again to Ben Lomond. Mr. Foster again made all arrangements for us, and at some inconvenience accompanied us as far as the Upper Camping Ground. This time we decided to avoid the labour of carrying our stores across the moor, and we made our camp at last year's site on the flat below Wilmot Bluff, a position quite convenient for our work. Relying on a little stream (the head of the Ben Lomond Rivulet) which we had found above this flat in 1911, we had no fears for a supply of water; but the supply was much scantier than in the pre- vious year, and this spot, otherwise a very pleasant camp site, might be without water in a dry season. In spite of the heavy rains during December, we found the moor 8 THE HEIGHT OF BEN LOMOND, r>.<5. TAS. much drier than usual. The beautiful pools which usually are found everywhere over the plateau were for the most part dry, and the bright vegetation which grows in and round them was withered. The blaze of colors which Ben Lomond show^s in summer was duller than in other years; the sage bush and the yellow bush had their usual tints, but there was scarcely a flower on the acres which are often covered with the white and red and orange blossoms of the richea. We first remeasured the base (TA) at Stacks Bluff. In 1911 this had been found to be 1554*42 feet and 1554'43 feet in two measurements, each made with a 300-foot J-inch steel band in the usual w^ay. When remeasured in 1912 with the same band, the length was found to be ISoS'O feet; but owing to a high wind the measurement was probably not as accurate as those made in 1911. We took the length to be 1554 feet. This base is of course a very short one. But it is to be remembered that our object was not to find the distance of Legge Peak (which was nearly seven miles) — an object for which the base would have been unsuitable, as any error of measurement would be exaggerated twenty times, and in addition there would bo an error in calculation result- ing from the smallness of the angle at Mt. Legge — but to determine a difference of height which was only about one- tenth of the length of the base. An error of a foot, then, in the measured length would give an error of only a little more than an inch in the difference of height, and from this point of view the base was long enough. Mr. Hutchison then measured the horizontal and ver- tical angles from the ends of the base to Legge Peak, and to the ends of a new base CD which another member of the party had marked meanwhile near last year's base at the Nile gorge. Owing to a high wind and other circum- stances the angles are not quite complete, but even apart from the angles taken at the second base, they give two determinations of the height of Mt. Legge, and with these angles they give an ample check. On the following day we measured the new base at the Nile gorge ( 1366*5 feet), and Mr. Hutchison took the necessary angles there. We also laid out two other bases, ^B, BE, and used these to determine the heights of the two summits of Ragged Mountain, an outlier to the north- west of Ben Lomond. BY L. F. GIBLIN, E. L. PIESSE, AND H. R. HUTCHISON. 9 1913. The instrument used was a 5 -inch Troughton and Simms transit theodolite reading on each circle by two verniers to 20". The angle obtained at each setting is given below. The degree of accuracy of the angles appears from the triangles ACD, CDT, in each of which all three angles were measured. The sum of the measured angles of the triangle ACD is 180^ 0' 17", and the sum of the measured angles of the triangle CDT is 179^ 59' 53". For the vertical angles, a test of accuracy is given by the angles between A and C and between A and Z>, which were measured in both directions. After applying the usual correction for curvature and refraction, the difference between the angles A to C and C to A is 51", and the difference between the angles A to D and D to A is 3". A test of the accuracy of the angles and measurements of length combined is obtained by calculating the distance from the trigonometrical station to Legge Peak, first from the Stacks Bluff base and the angles observed there, and second from the Nile gorge base and the angles observed at it. The results are 35,280 feet and 35,260 feet, whence it appears that the lengths required for determining the difference of height are known with sufficient accuracy. From the abstract given below of the calculations, it will be seen that the height of Legge Peak was deter- mined in four ways calculated in pairs from independent observations at the two bases. The results are: Height of Legge Peak. Hoio Obtained. Ca Iculatcd Height. Direct from T 5160-0 From A 5160-6 From D 5160-6 From C 5158-3 These results and the result (5158) feet obtained in 1911 justify the adoption of 5160 feet as the height of Legge Peak, which accordingly is the highest known summit in Tasmania, a satisfactory conclusion to the investigations of the height of Ben Lomond commenced by Col. W. V. Legge in 1906. The agreement between the results by aneroid and by the theodolite is remarkably close, and could not be expected to occur again in similar conditions. The claims of Barn Bluff to be higher than its neigh- bor, Cradle Mountain, have still to be tested by survey. 10 THE HEIGHT OF BEN LOITOND, R.S. TAS. Barn Bluff may prove to be liigher than Cradle Mountain, hut no one, so far as we know, has suggested that it is likely to be as much as 90 feet higher, and there is little probability that Legge Peak will be displaced from its position at the head of Tasmanian summits. The results of the calculations for X (the west-ern summit) and .S' (the eastern summit) of l^.lL"■.p'l Moun- tJiin ui-e also given below. The height of the northern sum- mit is about 4440 feet, and of the southern about 4490 feet. The mountain has thus a respectable place in the list of Tasmanian summits, although perhaps not quite as high a one as its prominent appearance from Launceston and elsewhere would suggest. (•'^) The map published with this paper is based on a rough survey made by Colonel Legge. We are indebted to Mr. A. F. Weber for preparing it for reproduction. The aneroid heights shown on the map depend for the most part on single unchecked observations. The topographical features of the map are shown on the county chart of Corn- wall (No. 3), issued by the Department of Lands and Surveys, which has also been drawn from Colonel Legge's survey. Most of the names given on our rnap are not, however, shown on the official chart. (^) (^) Ragged Mountain can be seen on a clem* day from Mt. Welling-ton. Legge Peak is also in view, between Rai?ge important surface characterisiics ol the plateau : alter governors, officials, surveyors, \-c. of the State. 3. Other features on the plateau : alter fellow-explorers and asjistanta in the purvey. 4. The remarkable eroded-down valley, dissect! g the plateau, at th*- upper entrance of the Speke Gorge : after our good Queen. 6. The lofty clift' buttress as seen from the Break-o'-Day Valley, often standing up alone against the cloud in the ' amphitheatre,' after the lonely and mysterious ' Sentinel of Egypt ' — the * Sphinx.' " BY L. F. GIBLIX, E. L. PIESSE, AND H. R. HUTCHISON. 11 1913. ABSTRACT OF OBSERVATIONS. T, a spot on the rock within the '"stockade" at the trigono- metrical station on the southern summit. We did not see any mark of the original station, and its position is some- what uncertain. A, the top of a flag at the eastern end of the Stacks Bluff base. B, C, D. E. tops of flags at the ends of the bases south of the Nile Gorge. L, the base of the cairn erected in 1907 on Mt. Legge. N, S, the highest points visible from B, G, E, of the wastern and eastern summits of Ragged Mountain. TA (W BC BE Lengths of Bases. (Reduced .to the horizontal.) Measured in 1911, 155442. 155443 feet. Measured in 1912, 15530 feet. Length adopted, 1554 feet. 1366-5 feet. 1369 feet. 1204 feet. HORIZONTAL ANGLES OBSERVED. Each entry in the columns *" Face Right," "Face Left," is the mean of the vernier-readings at one setting. Fac . R = g ht. ^"ace Le ft. Mean. Corrected Angle. (') o , o / '/ o / /» O / '. LTA 75 12 40 75 12 20 40 75 12 35 CTD 5 31 30 20 5 30 45 55 5 31 07 CAD 5 21 50 5 21 40 5 21 45 DAL 16 27 15 16 27 20 16 27 17 LA r 102 19 10 102 19 45 102 19 27 LCD 71 37 36 06 40 7i 37 36 20 35 71 36 55 LCA 144 20 20 40 16 144 21 20 10 55 144 20 45 LCT 150 34 33 00 40 150 34 10 10 1.50 34 CO CDL 104 59 58 25 50 104 58 58 55 5u 104 59 00 CDA 101 54 54 1" 55 101 54 54 o5 101 54 42 101 .54 32 CDV 95 31 32 25 00 95 31 31 45 35 95 31 41 95 31 45 (*) Corrected to make sum of ob.served angles of triangle 180' 12 THE HEIGHT OF BEN LOMOND, R.S. TAS. 09 fl ctf , .^'. € r: o — cr cr. ^ ic* CC O -H CO — . Oi c C X -^ X -* X o|. ee rH ■* f-i ■ii CO i^*> -rt^ CO CO ^i ^ CO ^ § * § o C o o O r^ — ^ rH + 1 + 1 i + 1 + +. + + + O lO lO >c o >c uo o o »o o '^^S^S o o o o o o ~ lO -^ -* CI CO CO lO >0 -H (M CO o o O CO o o Cu—i oi d ^ G^ C^ lO X •* o Ol O) O ?< CO o y^ ^ ^ be- - Ttl ^ CO CO O) ^ CO ^ CO CO CO rfi o as o O o o 1—t I— 1 rH r-- ^ — ^^ ,_, ^ ^^2,2- :^ + 1 + 1 1 4- ! + + + + + •o o n s -* § a a O »0 lO o »c c c c o o o uO O >0 O C: w "^ o D O O +5-r :^ tH CO CO CO lO ^ iTJ 1— 1 -IH ^ CO O 0< 0{ CO Tf CO -^ <:tH CO rH 'Sd . O C C^l '-' CO -H Ot (^ O t- o o. CO t> lll~^ s iO -^ •+ CO Ot (M 01 -t< CO .CO -tH 'CO "S /* a> a* SS — • ^>— ' ^— • "'-' o ■*^ ^ ^^ 'T^ -n t; t: '^ o^ c* OC5 ^ ^ •^ BY L. F. GIBLIN, E. L. PIESSE, AND H. R. HUTCHISON. VS 1913. CALCLLATION OF HEIGHTS. Point. How obtained. Calculated Height Height. Adopted. 1 feet. feet. T Trigonometrical Survey ot Tasmania ... 5010 A Direct Irom T 4992-4 4992-4 D Direct from T 4587-4 / 4588*1 From A 4588-8* C Direct from T 4607-6^ 4606-2 J 4606-6) From .4 4606-8 From I) L Direct from T 5160•0^ 5160-6 ( From ^4 5160 From D 6160-6 ( 5158-2 J From C N From C 4439 » 4444 > 4442) From B 4440 From E S From C 4491 ) 4492 > 4491 ) From B 4490 From E LIST OF PAPERS, &c., RELATING TO THE PHYSICAL GEOGRAPHY AND GEOLOGY OF BEN LOMOND. 1846. P. E. De Strzelecki. Physical Description of New South Wales and Van Diemen's Land. (London : Longmans, Brown, Green and Longmans, 1845. 8vo.) Count Strzelecki gives the following in his table of heights (p. 44) : — " Mount Ben Lomond, culminant point, 5002, , N.W. point, 4354, , South Bluff, 4500." There is nothing, however, to show where his '' cul- minant point " was. His " South Bluff " may have been Sphinx Bluff (4580 feet), but it is a name more suitable for the Stacks Bluff (5010). If South Bluff was the Stacks Bluff, Strzelecki's table shows that he observed a higher summit elsewhere on the mountain. Many of his heights in other parts of Tasmania were inaccurate, although he seems to have made the most of his apparatus. The instruments used were Gay Lussac's syphon mountain barometers and Wollaston's boiling point apparatus (p. 40). Count Strzelecki describes the scenery of Ben Lomond. Of the plateau he says (p. 67) : ^' The scene is here one of unbroken solitude, silence, and desolation." 14 THE HEIGHT OF BEN LOMOND. R.S. TA5.. 1892. A. Montgomery (Geological Surveyor). Report on the Ben Lomond District. (In Report of the Secretary of Mines (Tas- mania) for 1891-2, pp. 25-40. Journal and Papers of Parlia- ment, 1892, Vol. XXVI., No. 79.) Geological section from Avoca to Ben Lomond. 1901. George A. Waller (Assistant Government Geologist). Report on the Tin-mining District of Ben Lomond. (Issued with Report of the Secretary of Mines (Tasmania) for 1901-2, pp. 1-41. Government Printer, Hobart, 1908. 8vo.) Geological sketch-map oi the district. Ideal section from Ben Lomond Butts to Mt. Rex. 1907. Colonel AV. V. Legge. An Investigation into the Physio- graphy of the Ben Lomond Plateau, Tasmania. (In Report of the Eleventh Meeting of the Australasian Association for the Advancement of Science. Adelaide. 1907, pp. 521-5.) Colonel W. V. Legge. Note on the Ben Lomond Plateau, and the Discovery of High Land at the North End. (In Pro- ceedings of the Royal Society of Tasmania, 1906-7, pp. XXXIV. -XXXVI.) L. F. GiBLiN and E. L. Piesbe. Note on the Height of Legge Tor. (In Proceedings of the Royal Society of Tasmania, 1906-7,. pp. XXXVII. -XL.) THE THEORY OF THE QUOTA IN PROPOR TIONAL REPRESENTATION— II.- By E. L. PiESSE, B.Sc, LL.B. (Read 19tli May, 1913.) 64-65. — List ^Systems (continued). 54-60. M. Saint e-Layue's discussion by the method of least squares. 55. The problem stated. 56. The rule of least squares. 57. The D'Hondt rule. 58. The rule of the largest fractions. 59. The rule of Equer. 60. Other results. 61. Beferences to French and Belgian writers on the problem of the partition of seats. 62-65. The method of the uniform quota. 62. Rou- the problem of the partition of seats is avoided. 63. The method stated. 64. Example from the General Election of 23rd Junuiiry, 1913, 'in Ta.^inan'ia. 65. Incidental advantages; redistribution no longer required. 66-70. — Multiple Transferable Vote Systems. 66. The system defined. 67. lielation to other methods of voting. 68. In example of the Launceston voting system in a six-member constituency, showing how dispro- portionate representation may occur. 69. Table of possible elis proportionate representation. 70. Bules which would avoid this source of disproportion- ate representation. 71-77. — Notes. 71. Single transferable vote systems — Mr. Barford^s paper. 72. Close contests. 1^-11. Single-yi ember Constituencies. 73. Disproportionate representation may occur even with absolute-majority voting in equal constituencies. 74. The condition for a minority to obtain a majority of seats in a two-party contest. 75. An illustration. 76. Investigations of the exaggeration of the majority. 77. The election of 1910 for the Australian House of Bepresentatives. 78. — Bemarl: as to ^hr conclusions of the paper. * For Part I., .se^ Papers and fritcecdivgs of the Bmjal Society of Tastnan'iK. 191*2, pp. Ji)-77. 16 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. List Systems. 54. In §§ 22-25, I discussed, with the aid of the method of least squares, the problem of partitioning a given num- ber of seats among three parties in proportion to their strengths. I had not then seen any mathematical discus- sions of this problem ; but I have since obtained a copy of a paper published in 1910 by M. A. Sainte-Lague, Pro- fesseur de Mathematiques speciales au Lycee de Douai (and now of Besan9on), in which he gives a discussion of the problem for any number of parties by the same method. (-^) The volume in which this paper is published is not accessible to many students in this part of the world, and I have therefore made a summary of M. Sainte- Lague's results. I use the notation of § 25 of my own paper, as corrected in the erratum slip. 55. Each elector, says M. Sainte-Lague, has the right to be represented by a fraction of a deputy given by ml V = 1/ Q. If he belongs to the party A, he is repre- sented by the fraction x/]} of a deputy; whence the error in representation for him is seen to be x / jj — m/v. For the electors of the various parties, there are errors «i> ^2» ^3' •••^s. The various methods diverge from one another in the ways in which they endeavour to make these errors as small as possible. 56. To arrive at the best rule, M. Sainte-Lague applies the method of least squares. For each elector of party A the error in representation X m The sum of the squares of the errors for the p electors of this party is — '% - v) and the sum of the squares of the errors for all v electors (*") La irp resfi)itation J) rojwrtionnelle et la methode des moindres carres. Annates Scientifiques de rEcole Normale Sup«irieure, He. serie, tome 27, December, 1910, pp. 5:30-542. M. Sainte-Lague has given a more popular account of his results in the Revue Generale des Sciences pares et appliquees of 30th October, 1910, pp. 846-852 ; and the " rule of least squares " is stated in a communication made to the Academy of Sciences of Paris on 8th August, 1910. BY E. L. PIESSE, B.SC, LL.B. IT 1913. whence it can be shown that — ni- p V The quantity to be made a minimum is, then, S (^^'V/^). M, Sainte-Lague suggests a geometrical solution similar to the method used by me for three parties, but gives the- following practical solution for any number of parties. The identity — ^■- = 1 + 3 - 5 + ... -r (2a - 3) -f (2.r - 1) shows that the sum to be made a minimum is the sum of the X first numbers of (1), the y first numbers of (2), &c. ; X, y, z being chosen so that the m smallest numbers are- selected : — (i> (2). As the same result would be obtained by inverting all these numbers and choosing the m largest we have the following rule: — Rule of least squares: Divide p, q, r ... by the odd integers 1, 3, 5 ..., and in the various series of quotients, so obtained select the largest, until m have been obtained.. Party .4 receives as many members as the number of quotients taken from its series; and so with the other- parties. 57. Next, consider only positive errors {i.e., errors for electors who are over-represented). If the error for each elector of party A is positive, this party has at least X + 1 seats {X + 1 being the whole number next greater than X^^). According as the seats obtained are X + 1., X 4- 2, ..., the error for each elector of .4 is^ — JC + 1 m X + 2 m 1 3 5 p P P 1^ 3, 5 '1 7 n 1^ 3 5 r /• )' p V V V and so for the other parties; and the remaiaing seats have- to be allotted so that these errors may be as small as pos^- sible. If the parties have obtained X, 7, Z . seats, and 18 QUOTA IN PEOPORTIONAL REPRESENTATION, II., R.S. TAS. there are I seats left, these seats will be distributed according to the I smallest of these numbers, or according to the I largest of the numbers — X +1.' X ^ 2 r i- i' r + 2 ' z + 1 If we notice that the numbers — f^ i\ ^^ iL. V, (I, i, >% . . /•, 1 '2 3 • • X 1 2 ' • r 1 z • • ' each greater than those that follow in the same series, may be considered as corresponding to the seats already allotted, we are led to the rule of D'Hondt, of which the statement is the same as the rule of least squares, with the substitution of the consecutive integers 1, 2 3, 4 .. as divisors in place of the odd integers 1, 2, 3, ... 58. If we consider only negative errors {i.e., errors for electors who are under-represented), and limit ourselves to cases in which the parties have at least X, 7, Z ... members, negative errors will occur for such of the lists as do not get any more seats, and we have therefore to choose for the allotment of the remaining seats the smallest of the numbers }> V Y n, . - 7 ... q V Now if — P = A'.^^ + />, r^ Y.q + r„ . . . we have — X m. 1 rp w _ -Vp^ A-f J,-^~q^ pQ ^ pQ occ We must choose then the smallest of the numbers —rp/pQ (fee., or the largest of the numbers rp/p, &c., for the remaining seats. This is the rule of the largest fractions. This method, M. Sainte-Lague points out, is not to be confused with the rule of the largest remainders^ in which the remaining seats are allotted according to the largest of the remainders z-^^, /;^ . . . 59. Finally, the rtde of l^quer results from making as small as possible the difference between the largest positive error and the largest negative error. BY E. L. PIESSE, B.SC, LL.B. 19' 1913. 60. M. Sainte-Lague then passes to methods which are based on the consideration, not of the error for each elector, but of the error for each member ; a less valid basis, as he considers, for the apportionment of seats. A member should represent vl'tn = Q electors; if he has been elected by party A he represents pjx, whence the error for him is pIx — vjm,. Applying the method of least squares to these errors,. M. Sainte-Lague finds that if each party secures at least one member, the seats are to be allotted by using divisors whose approximate values are 3, 5, 7, 9, 11, 13, 15 ..., one seat having been allotted to the largest party before applying the rule. If, in place of considering the error for each member,, we consider the error for each party {x — jmijv), the method of least squares leads us to the rule of the largest remainders, also known as the Swiss rule. Finally, M. Sainte-Lague applies several tests to com- pare the rule of least squares with the rule of D'Hondf, and concludes that the former rule leads to fairer results than the rule of D'Hondt. 61. For the assistance of those who may wish to become acquainted with the views of French and Belgian writers on the principal rules proposed in recent years for par- titioning seats among parties district by district, I have compiled the following list of references to the various rules. These are the principal rules; but there are many others, and these may be found in the reports of MM. Benoist and Groussier. Systeme des moyennes, or rule of Dietz, adopted in the Projet de loi portant modificatiov aux lots organiques sur V election des Deputes, passed by the French Chamber of Deputies in July, 1912. (Each party gets, in the first place, as many seats as it has whole quotas of votes, the quota being the number of votes in the district divided by the number of seats. If there is a seat unallotted, th© number of votes for each list is divided by one more than the number of seats already allotted, and the seat is given to the list which gives the largest quotient, and so for any other unallotted seats.) Groussier, p. 27 et sqq. Lachapelle, pp. 114-6. D'Rondt rule (systeme du diviseur electoral). Benoist, pp. 19, 43 et sqq. Flandin, pp. 11 et sqq. Goblet d'Alviella, pp. 5-8. Lachapelle, pp. 94-98, 107-117,, 208-217. La Chesnais Ch. VII. and App. I. Macquart, pp. 548-551. Moch, passim. Sainte Lague, p. 534 et sqq. (see § 57 above). Van den Heuvel. '20 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. Hagenbach-Bischoff rule or systeme Genevois (used in the Canton of Geneva and in the town of Basel) (the Droop quota vl{m + 1) + 1 is used as divisor; if any seats remain unallotted, v/(m + 2) + 1 is used as divisor; if any still remain v/(m + 3) + 1 is the divisor; and so on). Macquart, pp. 551-4. Lachapefle, pp. 117-9. System of the electoral quota (quotient electoral), unal- lotted seats going to the largest parties. (The quota is the number of votes in the district divided by the number of seats). Groussier, p. 28 et sqq. This system was used in the Neuchatel electoral law of 1894, article 64 (Benoist, p. 126.) System of the electoral quota (quotient electoral), unal- lotted seats going to the parties with largest remainders. Groussier, p. 28 et sqq. Macquart, 546-9. Sainte-Lague, pp. 537-8 (see § 60 above). Lachapelle, pp. 103-107. Moch, §§ 5-13. System of the electoral quota (quotient electoral), unal- lotted seats going to the parties for which the ratio of the remainder to the strength of the party is largest (methode des phis fortes fractions). Sainte-Lague, p. 535 (see § 58 above). System of M. Maurice Equer (in which seats are par- titioned so that the difference between the greatest and least of the quantities xjp — see § 55 — may be as small as possible). Equer. Groussier, p. 33 et sqq. Sainte-Lague, p. 535 (see § 59 above). Methode des nioindres carres (see § 56 above). Sainte- Lague, p. 531 et sqq. Van de Walle's syste^n (system of the electoral quota ; remainders added together in a group of districts and remaining seats allotted by applying D'Hondt rule to the totals of the remainders). Lachapelle, pp. 221-230. Van de Walle, pp. 1-30. Goblet d'Alviella, pp. 13-15. Van den Heuvel. General discussions of the problem will be found in — Groussier, pp. 22-51. Sainte-Lague, pp. 529-542. Macquart, pp. 545-554. The works referred to above by authors' names are as follows : — Benoist, Charles (Depute). Rapport fait au nom de la commission du suffrage universel chargee d' examiner diverses propositions de loi tendant a. etahlir la repi'eseti- tation jM'oportio7inelle. Chambre des Deputes, Annexe au proces-verbal de la seance du 7 Avril, 1905. (Chamber of Deputies, No. 2376 of 1905.) BY E. L. PIESSE, B.SC, LL.B. 21 1913. Equer, Maurice. Arithmetique et rejyresentation 'pro- portions ell e. Supplement a la Grande Revue de 25 Juin, 1910. Flandin, Etienne (Depute). Rapport fait an nom de la comrnission du suffrage uiiiversel chargee d' examiner les propositions de loi : 1'^ de 31 . Dansefte; 2^ de 31 . Louis Martin ei plusieurs de ses coUegues; 3° de 31. 31assahuau; 4"^ de 31. Etienne FJandin (Tonne), tendant a l' etablisse- ment du scrutin de liste avec representation jJ^oportion- nelle dans les electio7is a la Chamhre des Deputes. Chambre des Deputes, Annexe au proces-verbal de la seance du 22 Mars, 1907. (Chamber of Deputies, No. 883 of 1907.) Goblet d'Alviella, M. le Comte Felix. Quelques con- siderations sur la representation proportionnelle. Extrait de la Revue de Belgique. (Bruxelles : Societe anonyme M. Weissenbrucli, Imprimeur du Roi, 1910.) Groussier, Arthur (Depute). Rapport fait du nom de la commission du suffrage universel chargee d' examiner le pro jet de loi et di verses propositions de loi portant modification aux lois organiques sur V election des deputes et tendant a etahlir le scrutin de liste avec reprtsentation proportionnelle. Chambre des Deputes, Annexe au proces- verbal de la Ire seance du 16 Mars, 1911. (Chamber of Deputies, No. 826 of 1911.) Lachapelle, Georges (Secretaire general du Comite repub]icain de la R.P.). La representation proportion- nelle en France et en Belgique. (Paris: Felix Alcan, 1911.) La Chesnais, P.-G. La representation pro port iotmelle et les partis politiques. (Paris: Georges Bellais, 1904.) Macquart, Emile (Secretaire general de la Ligue pour la Representation proportionnelle). Examen critique des divers procedes de repartition proportionnelle en matiere electorale. Revue Scientifique, 5e serie, tome iv., 28 Octo- bre, 1905, pp. 545-554. Moch, Gaston. La rejTresentation rraiment proportion- nelle. Collection de la Grande Revue. (Paris: Edouard Comely et Cie, 1910.) Sainte-Lague, A. (Professeur au Lycee de Douai). La representation proportionnelle et la methode des moindres carres. Annales scientifiques de I'Ecole Normale Superi- «ure, 3e. serie, tome 27, December, 1910, pp. 530-542. Van den Heuvel, Jules. Le mecanisme de la representa- tion proportionnelle. Extrait de la Revue Generale, fevrier, 1911. (Bruxelles: Goemaere. 1911.) 22 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. Van de Walle, Victor. La Re presentation proporfion- nelle integralement appliquee aux elections legislatives : Proposition de loi (avant-projet). (Bruxelles : Imprim- erie du Progres- V. Feron, 1910.) List Systems — The Method of the Uniform Quota. 62. Finally, it remains to ])oint out that the problem of apportioning seats among parties arises from fixing before the election the number of seats for each constituency. The problem can be avoided, and a partition of seats among parties as exact as the size of the legislature allows can be secured, if the number of seats in the legislature is fixed, but the number of seat& for each constituency is determined after the polling by the number of votes polled in it. On this idea is based the system of le nombre imique, or the uniform quota — a system supported by the late Professor Ilenri Poincare and other French mathematicians as the only exact method of proportional representation, i"^*^'^) 63. Hare proposed to use for the quota the number obtained by dividing the total of the votes throughout the country by the number of members in the House of Com- mons. He also proposed that the whole country should be one constituency ; a proposal which, with other notions contained in his works, is usually thought to have kept back for a generation the progress of pro- portional representation in England. The same quota is used in the system of le nombre unique; but the country is divided into districts, as in other systems of proportional representation, and these may be equal or unequal, as may be convenient. The system assumes that the same parties will contest the election in many districts or throughout the country ; it would break down if there were many iso- lated candidatures, but these are not to be expected when the party system has become established. The votes for all the candidates of each party through- out the country are totalled, and then the total number of votes for all parties is obtained. This total is divided by the number of members to be elected, and the result is le nombre unique, or the uniform quota. The total number of votes for each party is then divided by the quota. The quotient so obtained is the share of representation of the party. If the sum of the quotients (**•) See not." (*"«), § 73. BY E. L. PIESSE, B.SC, LL.B. 23 1913. is not equal to the number of members to be elected, the remaining seats can go to the parties with the largest remainders, or otherwise as may be thought fit ; it matters little how the remaining seats are dealt with if the House is at all large. The proportion of seats to voters in each party can thus be made as exact as the number of members will allow. Next, the number of votes for each party in each district is divided by the quota, and members equal in number to the quotient so obtained are selected from the candi- dates of the party in that district. The total number of seats allotted to a party in the various districts will be less than the total number of seats to which it is entitled, for in some or all of the districts there will be remainders. The unallotted seats are then given to the districts v/ith the largest remainders. Each party's share of representation in each district has now been ascertained. It only remains to choose the members for the party in eacli district from the candidates of the party in the district; the candi- dates to be chosen will be those of the party who are highest on the poll.f^ob) 64. As an example, let us apply the system of the uni- form quota to the Tasmanian General Election of 23rd January, 1913. The first choices (with the single trans- ferable vote) obtained by the parties were as follow -. — General Elecii Tasmania, 2Srd J an van/, for the Parties. 1913.— Fo^e* District. Liberal. Labor. Independent, Grand Total. ill 6839 6174 7717 8566 6861 6932 6441 7132 6677 4451 977 13,771 12,615 14 849 Franklin ... 15 243 VVilmot 12,289 All 36,157 31,633 977 68,767 (90b) On the system of If nomire unique, see — Le Systevw du Xombre 7'niquc, a pamphlet of 8 pages publislied by the Comite Republicain de la R.P., 23 Rue Pasqnier, Paiis. Lachapelle (see § 61), pp. 89-102, 230-5, 258-9. Groussier (see § 61), pp. 103-4, 191-3. :24 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. I assume that these numbers represent the relative strengths of the parties. With a party-list system, as each elector would have several votes, the numbers would be multiples of these (subject to a slight disarrangement of the votes in Wilmot) ; but these numbers will serve foi 4:he illustration. We first divide the total number of votes polled, 68,767, by the number of members to be elected, 30; the result is the quota, 2292. The total of the votes for each party is then divided by 2292; the results are, Liberal, 15-78; Labour, 13-79; Independent, 0'43. The members to be allotted to the parties are therefore Liberal, 16; Labour, 14; Independ- •ent, 0 (which, it may be noticed, was the result given by the single transferable vote). Next divide the totals of the votes for the parties in the various districts by the quota. The results are: — 'General, Election^ Tasmania, 23rd January, 1913. — Share of Representation in each District according to the Method of the Uniform Quota. District. Liberal Labor, Independent. Grand Total. i Bass 2-98 2-70 3-37 3-74 2-99 3-02 2-81 311 2-91 1-94 — 6-00 Darwin — 5-51 Denisoii — 6-48 Franklin Wilmot — 6-65 0-43 5 36 All 15-78 13-79 0-43 '• 30 1 ■ Allotting seats first to whole quotas, the Liberals would get two seats in Bass, Darwdn and Wilmot, and three in Denison and Franklin, total 12 ; and the remaining four seats would go to the districts in which there are the great- est remainders, namely Bass, Darwin, Franklin, and Wil- mot. Similarly the Labour Party would get, from whole quotas, three seats in Bass and Denison, two in Darwin and Franklin, and one in Wilmot, total 11 ; and the remaining three seats would go to Darwin, Franklin, and Wilmot. The result of the election would therefore be : - - BY E. L. PIESSE, B.SC, LL.B. 25 1913. General Election, Tasmania, 2?>rd January, 1913. — Result according to the Method of the Uniform Quota. District. Liberal Labor. Independent. Grand Total. Bass Darwin 3 3 3 3 3 3 3 2 0 6 ' 6 Denison Franklin 6 7 NVilmot 5 All 16 14 0 30 As between the parties the result would be the same as with the single transferable vote; but in Franklin (in which 15,243 vot-es were polled) there would have been seven members instead of six, of whom the Liberals would have had four, and in Wilmot (in which only 12,289 votes were polled) there would have been only five mem- bers instead of six, and there would thus have been a greater approach to electoral equality between electors in these two districts than with the same number of members for each district. It w^ould remain only to choose the members from the candidates of each party in each district. For each party the candidates highest on the poll wovild be chosen ; these, of course, would not necessarily be the same if each elector had several votes as when he had only one vote. 65. From this illustration two of the principal advan- tages of the method of the uniform quota can be seen : first, districts in which political interest is more active may get more members than districts in which, although the number of electors enrolled is the same, fewer voters go to the poll; second, it is no longer necessary to alter boundaries as the distribution of popu- lation changes, for the method (so far as the size of the House allows) will give proportional representation to the districts in spite of differences in their electoral populations. The method, then, gives proportional representation as between parties throughout the country; proportional representation as between parties in each district; and proportional representation as between districts of varying sizes. 26 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. Multiple Transferable Vote Systems. 66. In these systems a voter gives equal votes to a num- ber of candidates less than the number of members to be elected, and marks other candidates in an order of pref- erence. The name " multiple transferable vote " describes such systems ; but they might also be called "limited vote systems with preferential voting." 67. To appreciate the relation of the multiple transfer- able vote to other systems used in many-membered con- stituencies, the following arrangement of these systems in order of development will be useful : — (a) The single non-transferable vote. This is used in Japan. (^^). (b) The single transferable vote. (c) The limited vote, in which an elector gives equal votes to a number of candidates less than the number of members to be returned. The limited vote was used in England from 1867 to 1885 in thirteen three- member constituencies and one four-member constituency. (^^) (d) The limited vote with preferential voting, or the multiple transferable vote. (e) The block vote, or scrutin de Jiste, in which an elector votes for as many candi- dates as are to be elected. This is the sys- tem used for the Federal Senate. The block vote (with the modification that the elector might vote for fewer than the number to be elected) was used in Tasmania for the House of Assembly from 1856 to 1870 in one five- member constituency and one three-member constituency, and from 1885 to 1896 in eight two-member constituencies. Of these, the single transferable vote gives approxi- mately proportional representation (§§ 6-21); the single untransferable vote and the limited vote give representa- tion to minorities, but not in proportion to their strengths ; while the multiple transferable vote, with suitable rules, gives, as is shown below, the same approximation to pro- portional representation as the single transferable vote. (") See .1. JI. llaui])hre}S, Pniixirt'ntittil Hcprcfcnt atio/i {}^o\u\ox\. 1!)11) pp. 28:3-y. (") Benoist (s«'e§Gl) collectis otliei- instances of the use of tlie limited vote ([). 13). BY E. L. PIESSE, B.SC. LL.B. 27 1913. 68. As an example of the multiple transferable vote^ let us take a contest in a six-member district between two parties each nominating six candidates, in which each voter has three first choices, and second, third and fourth choices; and let us suppose that there is neither cross- voting between the parties nor short-voting within a party . The first stage of the scrutiny will be to count the first choices obtained by each candidate. The total of these for all candidates will be three times the number of voters. The quota will be one-sixth (if the Hare quota is used) or one-seventh (if the Droop quota is used) of the total number of first choices; i.e., three-sixths (Hare) or three-sevenths (Droop) of the number of voters. Some candidates will have sur- pluses above the quota, and there must be rules for trans- ferring these: when all surpluses have been transferred, there may be one or more seats unfilled, and there must be rules for excluding the candidates lowest on the poll and distributing their votes. Various sets of rules have been proposed. To illustrate the importance of the differences between the rules, let us take an extreme case based UDon the following ballot- papers (A, B, C, D, E, F being supposed to be the candi- dates of one party) — 1 A D 1 B Fl i" ^ h F [C ti^ QUOTA II?. PROPORTIONAL REPRESENTATION, II., R.S. TAS. Let us suppose that A, B, C are the candidates of one section, and D, E, F the candidates of another section, of the same party ; the supporters of the lirst section give a first choice to each of A, B, C, and their subsequent choices to the candidates of the second section (as in the first ballot-paper) ; the supporters of the second section give their first choices to D, E , F , and their subsequent choices to A, B, C (as in the second ballot-paper). Let us further suppose that this party has two-thirds of all the voters, and is therefore entitled to four out of the six members; and that on making up the totals of the first choices, A, B, C are found to have each just a quota (either Hare or Droop) ; that all but three of the candi- dates of the other party have been excluded ; and that Z>, E, F each have fewer votes than the three remaining candidates of the other party. There will, then, be just a quota of papers marked like the first ballot-paper ; and the other ballot-papers for the party will be marked like the second ballot-paper. A, B, C having just a quota each, there are no votes to be transferred from them, and D, E , F get no benefit from the second, third, and fourth choices given to them on the quota of papers on which A, B, C have first choices. D, E, F being lowest on the poll, one of them has to be excluded ; let it be D. Suppose that the rules provide {~^) that the vot€S of an excluded candidate are to be divided among the candidates having second or next available choices on the papers on which the excluded candidate has a first choice. On /9's papers, the second, third, and fourth choices have been given only to candidates who are already returned. Consequently there is no candi- date available to receive /)'s votes; and all of his votes are lost. One of E, F, say E, is now lowest on the poll; his votes cannot be transferred and are also lost ; finally the votes of the third candidate F are lost. We are left, then, with three elected candidates of the party we have been considering and three candidates of the other party. The other party, numbering only one-third of the voters, and so entitled only to two members, thus gets three. The failure to obtain proportional representation has arisen in this case because there were no candidates to (^) The rules of the " Launceston Voting System " for pre-electioM contained in The Tajfrna/tif/n Workers' Political League Election Manv%l (Tasmanian ;-Jews Pi-intinji Works, Hol)arr, 1912) have this ju'cvision. BY E. L. PIESSE, B.SC, LL.B. 29" 1913. whom (with the rules supposed) the votes of the excluded candidate could be transferred. With the single transfer- able vote (and no cross-voting or short-voting), an excluded candidate's votes can always be transferred if there is another candidate of the same party unelected, but in the cases just considered, although E, F are still unelected, the rules do not permit of />'s votes going to them. 69. The following table shows the representation which the Launceston Voting System may give to a party having 60 per cent, of the voters in a two-party contest in a six- member district. In the cases in which disproportional representation is shown to be possible, it should be remem- bered that the assumptions necessarv for these cases are not likely to be realised very frequently. Multiple Transferable Vote according to the Launceston Voting System in a Six-Member District— Possible Representation of a Party having 60?^^ of the Voters, and so entitled, to Four Members. Nuuibn- of First Choices allowed Members Returned. to each Elector. 4 The party must get four members. If three members are returned each with just a quota, the partv may fail to return a fourth (see §68); totars. 3 If two members are returned each with just a quota, the party may return only one more; total 3. If one member is returned with just a quota, the party will get three others; total 4. The party must get four members. 70. Disproportional representation through a division of a party into two sections (as in the cases just considered) can be avoided if the rules provide that on the distribu- tion of a surplus or of the votes of an excluded candidate the votes skall go to the other candidates having first 30 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. choices on the same papers if there are no candidates avail- able with second or subsequent choices. (^*) In the case supposed in § 68, neither A, B, or G are available, and JJs> votes would be divided between K and F. If E and F were still lowest on the poll, one of them would be excluded, and his votes (including those he had obtained from D) would go to F , who would have all the first choices given to D, E , and himself. Thus no votes would be lost, and the party, if the total of the first choices polled for D, E, F entitled it to another seat, would get the seat. Let us suppose, then, that we have rules which pro- vide for the transfer of a vote so long as there is an vinex- cluded candidate, whether with a first choice or a subse- quent choice, marked on the same paper. (^^) With such rules no votes are lost by a party, and it will be found that the argument in regard to the single transferable vote contained in §§ 6-21 is applicable. Either the Hare quota or the Droop quota will give representation approxi- mately proportional, and the Droop quota will be prefer- able to the Hare quota. (*•) There is an objpcti'Mi to such a rule, liowever, at all events in pre- elections. One of the reasons for preferring the multiple transferable vote to the single transferable vote in an election such as the pre-election of the candidates of a party is that with the single vote a section as small as the quota (one-seventh), and possibly out of sympathy with the rest of the party, may return a candidate who will stand for the party as a whole ; whereas with the multiple vote, the quota (if there are three first choices) is three-sevenths, and the rules are intended to prevent the return of any candidate with less than a quota of supporters. If D, E, F are the candi- dates of a small section, and if i>'s votes go to E, and ^'s to F, F has as many votes as if each voter of the section had given him three first choices, and so a section as small as one-seventh is enabled to return a candidate. C^) A set of rules providing for all possible cases would be rather complicated. The scrutiny, too, would be difficult. Mr. J. H. Humphreys (Minutes of Evidence taken hefore the Boyal Commission, on Systems of Election, Stationery Office, Lcmdon, 1910, Cd. 5352, at p. 40) has pointed out that counting of votes is more laborious when there are several votes on a paper than \«hen there is only one. " Whenever the ballot-paper (as in the Belgian syst«m and with the single transferable vote) represents but one vote only, the process of counting consists of snorting papers according to the votes given, and then in counting the heaps of papers so formed. Whenever there is more than one vote recorded upon a ballot-paper it be- comes necessary to extract the particulars of each vote upon recording sheets." With the multii)le transferable vote and fractional transfers, fractional values add a further complication. These difficulties are avoided in the I-aunceston Voting System of the Labour Party in Tasmania, in which no choice can have a fractional value. BY E. L. PIESSE, B.SC, LL.B. 31 1913. Single Transferable Vote Systems. 71. The argument in §§ 6-21 has been restated more fully and clearly by Mr. F. W. Barford, of Melbourne, in a paper A Study in Proportional Rejyrcsentation read at the meeting of the Australasian Association for the Advancement of Science held in Melbourne in January, 1913. Close Contests. 72. In a note to § 4, I collected some information as to the frequency of close contests. Students interested in this aspect of representation will find further information in the following papers in the Journal of the Royal Statis- tical Society : — John Biddulph Martin: Electoral Statistics: A Review of the Working of our Representative System from 1832 to 1881, in view of Prospective Changes therein. Journal of the Royal Statistical Society, March, 1884 (XLVII., 75-115). J. A. Baines : Parliamentary Representation in Eng- land, illustrated by the Elections of 1892 and, 1895. Journal of the Royal Statistical Society, March, 1896 (LIX., 38-118). Table D shows the distribution of seats according to the majority per cent, in 1892 and 1895 ; Table G the percentage of the majority in each constituency at these elections. F. Y. Edgeworth : Miscellaneous Applications of the Calculus of I^rohahilities. Journal of the Royal Statistical Society, September, 1898 (LXI., 534-544). Sir Richard Biddulph Martin: The Electoral " Sudng of the Pendulum." Journal of the Royal Statistical Society, December, 1906 (LXIX., 655-707). Single-Member Constituencies. 73. It is well known that single-member constituencies usually fail to give proportional representation to parties, and sometimes put a minority in power. (-^). But it is commonly said that this defect will be remedied if the (*») The case against the single-membei- system is stated by .J. H. Humphreys {Propnrtionnl Reprene/itation {London, VJll), Ch. v.); and by Professor J. R. Commons, in his Prirport tonal lleprestutation (2nd edition. New York, 1907) at pp. .36-85, his illustrations being taken mainlj fi-om elections in the United States. 32 QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. constituencies are approximately equal in electoral popula- tion and if members are elected by a system of preferential voting ensuring that the candidate returned has received votes from a majority of the electors (as in the elections for the Legislative Council in Tasmania). The following paragraphs will show that equality of constituencies and an absolute majority system are insufficient to secure even that the majority in the country shall have a majority in the House, to say nothing of a majority proportional to its strength. (-'''^) (**) Mr. L. F. Giblin, M.H.A., has pointed out to me that it is possible even with proportional representation for the minority in the country to win a majority of seats. With proportional representation the total rep- resentation of each party depends to some extent (though to a much less extent than with single-member districts) on the distribution of the strengths of the parties among the disuicts. If members are allotted to parties district by district, the representation, although proportional as nearly as possible in each district, may become disproportional for the country as a whole. The only sure way to secure exactly pioportional representation is to allot seats in proportion to votes throughout the country, as in the method of the uniform quota. Mr. Giblin writes : — " It should be noted that proportional voting with (he single transferable vote may result in putting a minority in povvec, and, when the number of constituences is small, the chance is not a remote one. In Tasmania under the present system, in which the Droop quota is used, assume that the quotas are the same in each division. Let party A return 16 members and party B 14 members. There being 35 quotas in the five districts, the 14 members for party B will represent a majority in the country if B's votes are more than 17 i quotas, i.e., if the sum of its remainders is more than 3^ quotas. If B's votes are more than 17^ quotas, A's are less than 17^, and the sum of its remainders is less than 1^. That is party A (the minority in the country) will get a majority in Parliament if the votes not absorbed as quotas are divided between the parties A and B in less than the ratio 3:7. In practice, the parties are fairly equally divided and no party is likely to be lepresented in any division by less than two members out of six. Within the range thus indicated, it may be assumed approxi- mately that any remainder from 0 to one quota is equally likely to occur. On these conditions, the chance of a majority of 16 members being returned by a minority of voters may be stated roughly as 1 in 14. That is to say, in every 14 elections in which the result was 16 to 14, there would be on an average one in which the minority of the voters returned the majority in Parliament. This, however, is but a small matter compared to the case in which 16 members are returned on each side, when the odds are more than 2 to 1 that one party is entitled to an additional member. If the number of members was altered to 7 in each district, making 35 members in all, this high probability of disproportional representation would be removed, but tlie chance of a majority of 18 to 17 being returned by a minority of voters would, under the same assumptions as above, be nearly 1 in 4, It should be noted that this possibility of disproportional representaticm, though not uf^gligible, is small c<>mj)ared to the possibilities with singkvmember districts, and that it is equally present in the different List systems, excepting 2a, we can see from (4) that x > 50, i.e., the smaller party gets a majority of the seats. Thus, if the average strength of S in the districts in which it has a majority is 51 %, and the average strength of L in the districts in which it has a majority is just over 57 %, S, the smaller party, will get more seats than L, the larger party, and so the smaller party will have a majority over the larger in the House, although the larger has a majority of over 6 % above the smaller in the country. 75. J. R. Commons ("^) gives the following illustration of a distribution of votes which would give the smaller party the majority of seats. A country is divided into 40 districts, and in each of these 5500 electors vote. In 25 districts the smaller party obtains 2800 votes, and the larger 2700 votes ; in 15 districts, the smaller party obtains 2000 votes and the larger 3000 votes. The votes polled are, then : Smaller Party. 2800 in 25 districts 70,000 2000 in 15 districts 30,000 100,000 Larger Party. 2700 in 25 districts 67,500 3500 in 15 districts 52,500 120,000 (Vi^ Proporfioual Rrvi'cxi'ufatlon, 2n(l edition (New Yoi-k. 1011), pp. 48-49. BY E. L. PIESSE, B.SC, LL.B. 35- 1913. The smaller party thus obtains 25 seats with only 100,000 votes, while the larger party with 120,000 votes obtains only 15 seats. 76. Professor Edgeworth {^^) has shown that in the general elections of 1886, 1892, and 1895 in Great Britain the ratios, fn umber of Unionist supporters) 4- (number of Unionists and number of Gladstonians) in the various constituencies, were distributed about an average in accord- ance with the normal law of error. Such a distribution will give a majority to the larger party in the House which will be a greater percentage of the House than the strength of the larger party in the country is of the total number of electors, as appears from a comparison of the actual result of these elections with the percentages of representation calculated from the curve of error repre- senting the distribution. The Right Hon. J. Parker Smith, in his evidence before the British Royal Commission on Systems of Election f^^), gives reasons why the majority is usvially exaggerated if single-member constituencies are used. He mentions a calculation by Major Macmahon, who has shown that if in a two-party contest the voters are in the ratio of A to B, then the members elected may be expected to be at least in the ratio of .4^ to B^. Thus if the strengths of the parties are 55 % to 45 % (A : B = 11 : 9), the members may be expected to be in the ratio of IP to 9'', or nearly 2 to 1; i.e., a party with 5 % more than half the electors may be expected to get nearly two- thirds of the members. 77. Statistics of elections in' single-member constitu- encies in which the conditions of § 74 — approxi- mate equality between the constituencies in num- ber of votes, and either only two candidates or else preferential voting — are fulfilled, are scarce. It is one of the disadvantages of single-member constituencies, especi- ally in new countries, that redistribution is required much more frequently than with grouped districts, and the sizes of the constituencies are usually by no means equal when a few years have elapsed since the last redistribution. Also, the proportion of electors who vote varies largely from one constituency to another. In Australia at the {^) Misri'llaneouii Applic itions of the Calculus of Prohahilities, Journal of the Royal Statistical Society, September, 1898 (LXL, 534 544). ('^) Muiutm of Evidence tahfn 'hefov the Boy at Cominiaxion on Siii^tcms of Election (Stationery Office. London, 1910, Cd. 5352), Question 1253, p. 81. 3G QUOTA IN PROPORTIONAL REPRESENTATION, II., R.S. TAS. House of Representatives election in 1910 (^") the num- bers of electors enrolled in the constituencies in each State varied up to about 15 % from the mean for the State. The number of voters varied even more : leaving out a few very large and a few very small constituencies, the num- bers of voters varied up to about 20 % or 25 % from the mean for the State. These numbers, however, were much more nearly equal than is usually the case with single- member districts, and this election is consequently more suitable as an illustration of the arguments in §§ 73-76 than any other of which I have statistics. In New South Wales, at this election, there were con- tests between one Liberal candidate and one Labour can- didate (or betw^een two such candidates and a third who obtained so few votes that he need not be taken into account) in 24 constituencies. In these the Labour candi- dates polled 245,000 votes and the Liberal candidates 203,000 ; and consequently the Labour party, in proportion to its strength, was entitled to 13 seats and the Liberal party to 11. The seats won by the parties were Labour 17, Liberal 7. In Queensland, there were contests between one Labour candidate and one Liberal candidate in each of the nine constituencies. The Labour ctxndidates polled 89,000 votes and the Liberal candidates 76,000; the members to which the parties were entitled were consequently 5 to 4. The seats won by the parties were Labour 7, Liberal 2. In Victoria, there were contests between one Labour candidate and one Liberal candidate in 19 constituencies. The Labour candidates polled 216,000, and the Liberal candidates 192,000; the members to which the parties were entitled were consequently 10 and 9 ; and these were the numbers of seats actually won by the parties. The results in New South Wales and Queensland, then, confirm the predictions referred to in § 76, that single- member constituencies will usually exaggerate the majority obtained by the larger party In Victoria \he election gave exactly proportional representation in the 19 con- stituencies considered. But it is to be noted on the one hand that a loss by Liberal candidates in Victoria of only 800 votes, spread over four constituencies in which their majorities were very small, would have given the Labour party 14 members and reduced the Liberal mem- (^°) 8eo Klfcthns. 1010. Statistics relating to the Senate Election ; the Gen ral Election for the Home of Representatives (&c."). (Papers of the Parliament of the Commonwealth of Australia. Xo. 1 of 1910). BY E. L. PIESSE, B.SC, LL.B. :^7 1913. bers to 5 ; and on tlio other hand that a gain of only 700 votes in a constituency in which the Labour majority was small would have given the Liberal party 10 seats and the Labour party only 9 — that is, a party having only 47 per cent, of the voters would have had a majority of the seats. Remark as to the Conclusions of this Paper. 78. In discussing the various methods of proportional representation noticed in this paper, with the exception of the method of the uniform quota, I have considered the result that may be expected to occur in a single district. But in estimating the probability that an election through- out the country will give proportional or disproportional representation, it must be remembered that under- or over- representation in some districts is likely to be balanced by over- or under-representation in others, unless the sys- tem used has been deliberately constructed (as was the D'Hondt) with the object of favouring one party (the larger party in that case) ; and consequently that the result of an election in many districts is more likely to be in proportion to the strengths of the parties than an election in one district. (^^^) This qualification, however, does not apply to the argument against the single-member sys- tem, in which the country has been considered as a whole. (=») But see '§73, note (■«•), by Mr. L. F. Gibliii. NOTES ON HYMENOPHYLLUM PELTATUM (POTE) DESV By L. EoDWAY (Read 19tli May, 1913.) Prof. Ewart has recently pointed out (Proc. B, S. Vict. Oct,, 1911) tliat the fern which has been familia^r to us as H. Wilsoni, Hook, or H. unilaterale, Willd, will be more correctly named if we call it H. peltatum, Desv, This little fern is very widely dispersed in Tasmania. It ^nd H. tunhriclgeme, L., are the only two members of the genus with serrated leaves which are natives of Tasmania. The two used to be confounded, but the great difference of the indusia permits of immediate recognition. In H. iun- hridgense the indusia are semicircular with a straight serrate terminal margin. In if. peltatum the indusium is oblong, with an entire margin. H. peltatutn varies in size. In the commonest condition in whicli it is found the leaf does not exceed 5 cm. in length, the pinnae about 1 cm., giving the plant much the appearance of H". tunhridgense, except that the pinnules almost all grow on the upper margin of the pinnse. When the plant grows under more favourable conditions it acquires a much taller habit. The leaf may be as long as 17 cm., though the breadth does not increase. The pinnules .are erect, i)ut when at all wilted they recurve, giving the leaf -a characteristic appearance. BIBLIOGRAPHY OF PROPORTIONAL REPRE- SENTATION IN TASMANIA. By E. L. PiESSE, B.Sc, LL.B. (Read 12th May, 1913.) Introduction 39 Bibliography 45 Index of Authors o7 General Bibliographies 57 Appendices — The various rules proposed or used in Tas- mania for the transferable vote 1. The Electoral Bill, 1896 58 2. The Electoral Act, 1896 60 3. The Electoral Bill, 1899 63 4. The Electoral Act, 1907 67 5. The Launceston Voting System 72 INTRODUCTION. Proportional representation was introduced in Tasmania by the Electoral Act of 1896, in which a form of the Hare system was used for two of the electorates of the House of Assembly. The causes which led to the adoption of the Hare system were thus stated by the late Mr. Justice Andrew Inglis Clark in the following paragraphs, contributed by him to the report by Messrs. J. G. Davies and R. M. Johnston on the elections for the Senate and House of Representatives in Tasmania in 1901 (^) : — The Clark-Hare system of voting was introduced into the electoral law of Tasmania in consequence of the frequent fail- (1) See Bibliography No. 16. 40 BIBLIOGRAPHY OF PROPORTIONAL REPRESENTATION, R.S. TAS. ure of the ordinary system of voting to secure a proportionato representation of the preponderating opinions of the electors on political questions either in single or plural electorates. Under the first Electoral Act, which provided for the election of the members of a bicameral Legislature, the city of Hobart, by the " block vote," elected five representatives to the House of Assembly as- one electorate, and the city of Launceston elected three representatives to the same branch of the Legis- lature in the same manner. Under that system it was discovered that a majority of the electors, in each of the two electorates, could elect all the representatives, and leave a very large minority totally unrepresented in the Legislature. To remedy this evil those two electorates were divided into eight single electorates. But under this system it was discovered that when three or more candidates presented themselves for election, it very frequently happened that the successful candidate was elected by a minority of the total number of votes recorded. The same thing sometimes occurred in the rural electorates, which were all single electorates, but the number of candidates in the rural electorates did not often exceed two. It was also dis- covered that the division of the cities of Hobart and Launces- ton into eight single electorates reduced the area of each electorate, and the number of voters to such small dimensions that the agents and canvassers of the several candidates could easily interview every resident elector and ascertain very closely the number of purchasable or otherwise controllable votes. After the representation of the cities of Hobart and Laun- ceston was increased to six and four members, those electorates were divided into five electorates, each of which returned two members. At the same time, two rural electorates, each returning two members, were created. Under this plan it was discovered that the majority of electors in the total number of the electorates which returned two members frequently secured a much larger representation in Parliament than that to which it was proportionately entitled, and thereby gave a preponderance of voting power in the Legislature to a political party which had secured only a minority of the total number of votes recorded at a general election. In several instances neither of the successful candidates in a dou))le electorate was elected by a majority of votes. The lastmentioned result was frequently produced by a large number of the electors voting for onlv one candidate out of the five or six who were in the field. With a view of avoiding these serious defects, the cities of Hobart and Launceston were converted into two electorates under the Clark-Hare system, which enables every section of political opinion which can command the requisite quota of votes to secure a number of representatives proportion n to to its numerical strength. It also utilises every vote recorded if the elector chooses to exercise the whole of his power to indi- cate his preferences. If any vote is not used to help in the election of a representative, it is because the voter has chosen BY E. L. PIESSE, B.SC, LL.B. 41 1913. to indicate his preferences for a less number of candidates than the number of representatives to be elected in the electorate in which he rotes. (") (•) Tho followiug table show.s the constitution of the House of Assembly from I80H : — The Tlou.sc of Axacmhlij from 1856. 1 VIS .2 £ to III Total Number of Members. Reference. Remarkg. 1866-1870 22 Ho hart, 5 30 Electoral Act, 1856 The mode of voting in the member.-; (19 Vict. No. 24), multi-member districts was Launces- Section 4 by striking out names so as ton, 3 Electoral Act, 1857 to leave a number less than members (21 Vict. Xo. 32), Schedule or equal to the number to be elected 1870-1885 32 32 Electoral Act, No. 4, 1870 (34 Vict. No. 12), Sections 2, 4, 7, 8 Hobart and Launceston were divided into single-member districts, and two more members given to the North- west Coast 1885-181)3 '20 8 two- 30 Electoral Act, No. 7, One more member was given membpr 1885 (49 Vicf. No. to Hobart and one to Laun- districts 12), Schedule 1 Electoral Act, 1890 (54 Vict. No. 13), Schedule 2 ceston, and Hobart was divided into three districts and Launceston into two, each j-eturning two members. The country districts were redistributed, and East Devon, Kingborough, and Wellington were made two- member districts. In the two-member districts the voting was by striking out names so as to leave one name or two 1893-1896 21 8 two- 37 Electoral Act Amend- A member was given to the member ment Act, 1893 (57 West Coast districts Vict. No. 8), Section 3 Electoial Act, 1896 1896-1898 27 Hobart 6 37 Hobart and Launceston were members (60 Vict. No. 49), each made one district. Launces- Schedule 2 The two-member districts in ton, 4 the country were divided members into single-member districts 1898-19 1 1 28 Hobart. 6 38 Electoral Act Amend- A second member was given membeis ment Act, 1898 (62 to the West Coast Launces- Vict. No. 68), Sec j ton. 4 tion 3 members 1901-19U7 lio 35 Electoral Act, 1901 (1 Ed. VII. No. 57), Section 6 1907 5 six- member districts 30 Electoral Act, 1907 (7 Ed VII.No. ()),l^ec- tion 13 4*2 BIBLIOGRAPHY OF PROPORTIONAL REPRESENTATION, R.S. TAS. The Electoral Bill of 1896 was brought in by Mr. Clark, then Attorney-General in Sir Edward Braddon's Ministry. The Bill applied Hare's method to two electorates — Hobart (6 members) and Launceston (4 members), leaving the rest of the country in single-member electorates. The rules for transferring surpluses originally proposed (Appendix 1 below) were those of Hare, but in answer to critics who thought that these rules left too much to chance, Mr. Clark proposed the modifications from which the rules of the Act have come to be known as the Hare- Clark system, and by which the most important part of the element of chance was removed. (Appendix 2.) The element of chance in the transfer of surpluses had been noticed by Miss Fawcett in 1872 (Henry Fawcett and Millicent Garrett Fawcett, Essays and Lectures, Lon- don, 1872, pp. 336-368), by H. R. Droop in 1881 {On Methods of Electing Eepresentatives, Journal of the Sta- tistical Society, XLIV., June 1881, pp. 141-196, it p. 182), by Sir John Lubbock in L890 {Representation, London, 1890) and others; and had been discussed by Mr. Clark himself as long ago as 1874, in a paper in The Quadrilateral. {^) Sir John Lubbock pointed out that the element of chance might be reduced if rules such as those afterwards employed by Mr. Clark were used; but he did not think it necessary to use such rules. Mr. Clark's contribution to the rules, although anticipated by Sir John Lubbock, was original, so far as I can learn, and these rules are still commonly known as the Hare-Clark rules. Mr. Clark's principal claim to be remembered in connection with the Hare system is not, however, derived from these arithmetical details, but from his having been the means of using the Hare system for the first time in a Parliamentary election in a British country. The Electoral Act of 1896 contained a provision that it should remain in force only until 31st December, 1897, but it was afterwards extended, and it remained the elec- toral law of Tasmania until repealed by the Electoral Act of 1901. The elections held under it were: for the State House of Assembly: Hobart (6 members) and Launceston (4 members), 20th January, 1897 (see Bibliography, Nos. 3, 4, 6, and Hobart Mercury, 21st January, 1897; Hobart (6 members) and Launceston (4 members), 9th March, 1900 (see Mercury, 10th and 12th March, 1900) ; for the Commonwealth House of Representatives (5 members) and Senate (6 members), the whole of Tasmania being one con- O See liiblu.gruphy No. 1. BY E. L. PIESSE, B.SC, LL.B. 43 1913. stituency for each House, 29tli March, 1901 (see Biblio- graphy Nos. 16, 17, and Mercury, 30th March, 1st April, 5th April, 1901). The quota used in the Act of 1896 was the quota orig- inally used by Hare, although the quota now usually admitted to be the correct quota — the Droop quota — had been proposed as early as 1872, and had been used in Xew Zealand in the Representation Bill of 1889 and by Sir John Lubbock in 1890. The Hare system came under discussion again in 1899, when the Electoral Bill of that year (Bibliography No. 7) was before the House of Assembly. Mr. Clark meanwhile had become a justice of the Supreme Court of Tasmania, and the Bill was brought in by Mr, D, C. Urquhart. It was proposed to apply the Hare system to the whole of Tasmania, which was to be divided into seven districts returning from four to seven members each, and new and more elaborate rules for dealing with surpluses (see Appendix 3) were to be used. There was little dis- cussion now of arithmetical details, and the debates were mainly of the political effects and difficulties of the system. The supporters of the system urged that it provided repre- sentation for minorities. It is noticeable to one familiar with present-day discussions that there was little mention of the proportional representation of parties ; but this was scarcely to be expected, for there were then no definit-e parties as we have now. The opponents of the system argued that it was not understood; that electors did not want it ; and, in particular, that the country districts (other than the West Coast) were against it ; that there were no principles or parties to be represented ; and that large districts were difficult to canvass. The bill was withdrawn by tiie Government, and the Electoral Act of 1896 (in which, as previously mentioned, the Hare sys- tem was uscid only in Hobart and Launceston) was con- :'tinued until 1901." In 1901 Sir Elliott Lewis introduced an Electoral Bill ('^) in which the Hare system (with the rules of the Act of 1896) was to be used for the whole of Tasmania. The Hare system was opposed on much the same grounds as in 1899, and the Government gave way, and reverted to the single-member system throughout Tasmania. The electoral law was again under consideration in 1906. It was desired that Commonwealth and State should use joint electoral rolls, and the most convenient (■*) t^ee liibii igrapliy ■ o. 15. 44 BIBLIOGRAPHY OF PROPORTIONAL REPRESENTATION, R.S. TAS. way to arrange for this was to adopt the five divisions for the House of Representatives as districts for the House of Assembly. The House of Assembly had hitherto had 35 members, but it was thought that 30 would now be sufficient. Mr. J. W. Evans, for these and other reasons, brought in an Electoral Bill, in which Tasmania was divided into five districts, each returning six members, to be elected under the rules of the Electoral Act of 1896. This Bill was withdrawn, and another was introduced, which became law next year as the Electoral Act of 1907. In this Act, new rules for transferring surplus votes and the votes of excluded candidates were used, and the Droop quota was introduced in place of the Hare quota used in the Act of 1896. These rules embody what is called the fractional method of transfer; they are based on a device published by Mr. J. B. Gregory, of Melbourne, in 1890 (^), and used independently by Miss A.M. Martin, of Adelaide (*^). The rules are the same as those proposed in the Proportional Representation Bills, 1902, 1905, and 1906 of South Australia, and are similar to the rules in the Parliamentary Elections Bill, 1900, of Victoria, and to the rules in the Commonwealth Electoral Bill introduced in the Senate on 24th January, 1902.(6«») Their form is understood to be due to Professor E. J. Nanson and Mr. John Mackey, of Melbourne. The name '' Hare-Clark " is sometimes used of these rules, but this is a misnomer. The frame of the rules is entirely different from Mr. Clark's; his provisions for dealing with surpluses are merged in a neater method, in which all chance disappears; the Hare quota of the Act of 1896 is abandoned, and, moreover, the rules are based on pro- posals made by Mr. Gregory some years before Mr. Clark's Bill was under discussion. Under the Act of 1907 the following General Elections for the House of Assembly have been held: — 30th April, 1909 (see Bibliography No. 26); 30th April, 1912 (see Bibliography No. 30; and 23rd January, 1913 (an official report on which is now in preparation ; see also Biblio- graphy Nos. 35, 36, 37). In 1912 the Tasmanian Workers' Political League adopted in the " Launceston Voting System" for pre-elec- (*) See Bibliography No. 4, p. in. (*) See Bibliography No. 5, p 19, aii'l also Effective Voting the Basis of Good Munieijxd Gorernnient : An E.rj>osition of the Principles and Practice of Proportional Pepresentalion. Issued by the Proportional Representation Committee ofOntario, Toronto, 1898, pp. '23-24. (^*) A clear explanation of the rules is contained in a memorandum circulHted with the draft Bill. BY E. L. PIESSE, B.SC, LL.B. 45 1913 tions (^), a further modification of the original Hare sys- tem. Instead of a single transferable Yote, the Launces- ton Voting System gives several votes (but a less number than the number of members to be elected), and there is provision for transferring surplus votes and the votes of lowest candidates. The idea of using several votes is bor- rowed from the Brandt system, due to Mr. ?. J. Brandt, of Melbourne, used by the Labour Party in Victoria for its pre-elections : but in the Brandt system there is no quota or surplus, and the votes of lowest candidates are transferred until only the number required to be elected remain. The object of having several votes in place of only one is to make the quota larger, and so ensure that the elected candidate shall have received support from a considerable body of the voters; also, the provision for several votes prevents the struggle for the first chcic-e which has been found to be an undesirable feature of the single transferable vote. The rules of the Launceston Voting System are nrinted in Appendix 5. BIBLIOGRAPHY. 1874. 1. [Andrew Inglis Clark.] Hare's System of Repre- sentation. (In The Quadrilat^al, Vol. L, No. 11, Nov. [1S74], pp. 249-251). This is an unsigned article, but I am informed by Mr. William Burn, of Hobart, the only survivor of the four members of '' The Quadrilateral," that the author was Andrew Inglis Clark. The leading features of the system ; the probable effects of adopting it. Reference to the objection to Hare's method of dealing with a surplus, and suggestion that of the candidates not yet elected the one who has the greatest number of first choices shall be entitled to as many votes from papers on which he is marked second as he requires for election. 1896. 2. Tasmania: ''The Electoral Act, 1896" (60 Vict. No. 49). For an account of this Act, see the Tntroduczion. The speech of Mr. Attorney-General Clark in moving (') See Bibliography ' o, 34. 46 BIBLIOGRAPHY OF PROPORTIONAL REPRESENTATION, R.S. TAS. the second reading of the Bill (1896, No. 3) is reported in the Hobart '' Mercury " of 13th August. The debate on the amendment to Clause 115, substituting the Clark method of dealing with surpluses for Hare's method propo^^ed in the Bill when introduced is reported in the "Mercury" of 20th August. The rules originally proposed and Mr. Clark's rules in the form finally adopted in the Act are printed in Appendices 1 and 2. 3. R. M. Johnston (Government Statistician, Tasmania). Observations on the Working Results of the Hare System of Election in Tasmania. {In Papers and Proceedings of the Royal Society of Tasmania, 1897, pp. 69-96 and two diagrams. Also issued as a pamphlet by Government Printer, Hobart, 1897, pp. 1-32 (iiichiding title and analysis) and two diagrams, 8vo.) 1. The chief merit of the Hare system is the large electoral division, permitting the units of any body of opinion as large as a quota to luiite and obtain a mem- ber. 2. The merits of the preference and transferable vote. 3. Popular exaggerated estimates of the influence upon results of the distribution of surpluses, illustrated by the experience of the election of 1897 in Hobart and Launceston. 4. General questions arising out of this election : — modification of the Hare system introduced by A. I. Clark; proportion between surpluses and all votes in the 1897 elections-; the value of the element of chance remaining with the Clark-Hare method ; the relative values of the preferences at the 1897 elections ; what is the best index of general favour (the aggregate of all preferences better than the first choices) ; the effect of marking only three preferences ; the propor- tion of invalid ballot-papers (365 per cent, in Hobart), and the nature of the defects (53 per cent, not due to the peculiarities of the Hare system) ; improved form of ballot-paper ; suggestions for the conduct of the scrutiny. 5. How to simplify the ballot for those who cannot read or write. 6. Reply to critics of the method of distribution of surpluses used by the returning offi- cers at the 1897 election. Table: Analysis of the voting at the 1897 election in Hobart, showing the various counts and the final result. Table showing the values of the effective preferences for each candidate at this election, with diagram. Tal)le showing the first, second, and third preferences recorded for each candidate at the same election, with diagram. Illustration of the method of marking ballot-papers, and explanation of the various counts of a scrutiny. Reprinted in 19a. BY E. L. PIESSE, B.SC, LL.B. 47' 1913. 1897. 4. W. Jethro Brown . The Application of the Hare System in Tasmania. {In Papers and Proceedings of the Koyal Society of Tasmania, 1897, pp. 79-92 (supplementary pages). Also as a ]xi>?rphlet, The Hare System of Election in Tasmania, rejjrinted from the " Tasmania?! News," May 13th, Uth, 15th, and lUh, 1897, " Tasmanian News " Office, Hohart, Svo., pp. 1-13. Also in Law Quarterly Review, Jan., 1899, XV., 51-70 [see 9]. Also in The New Democracy, A Political Study [see 10]). Discussion of the modifications of Hare's proposals adopted in the Electoral Act of 189G— the country not one constituency but divided into districts, the elector to give preferences to at least three candidates, the pro- visions for transfer of surpluses. Account of the elec- tion in Hobart in 1897, and copy of R. M. Johnston's analysis of the voting (see 3). Reprinted in 19<(. 1898. 5. Catherine Helen Spence. Effective Voting: Aus- tralia's Opportunity. An Explanation of the Hare Sys- tem of Representation. f Adelaide: Shawyer and Co., 1898, pp. 1-28, ^vo.) The time occupied in the scrutiny at the elec- tion in Hobart in 1897 (p. 13). Analysis of the voting (as in 3), and remarks (pp. 19-22). 1899. 6. R. M. Johnston (Government Statistician, Tasmania). Further Observations on the Plare System. (Government Printer ,. Tasmania, n.d. (? 1899), 12 2?i?., 8?'o.) A comparison of the Hare system with the single- member system, exemplified by elections in Tasmania. An example showing that the Hare system gives pro- portional representation. 7. Tasmania: House of Assembh/. The Electoral Bill, 1899 (Bill 4). See Introduction. The debates on the second read- ing, in which the continuance of the Hare system was discussed, are reported in the "Mercury" of 14th, 15th, and 16th June, 1899. The debates in Committee, on -48 BIBLIOGRAPHY OF PROPORTIONAL REPRESENTATION, R.S. TAS. the clauses of the Bill involving the Hare system are reported in the " Mercury " of 23rd June, 30th June, 19th August, and 24th August. On 3rd August, 1424 electors of Hobart in a petition asked that the Hare system " introduced without the consent of the electors, and limited to one Parliament, be not continued without their consent." The Bill was reported with the pro- visions as to the Hare system intact, but was after- wards withdrawn by the Government (" Mercury," Sept. 20), and the Electoral Act of 1896 was extended. The rules proposed in this Bill are printed in Appendix 3. 8. Herbert Nicholls. An Election under the Clark- Hare System. ("Mercury" Office, Hobart, 1899, 12 pp., 8vo.) The various stages of the counting explained ; the rules used for transferring surpluses are those pro- posed in the Electoral Bill, 1899 (see 7 and Appendix 3). 9. W. Jethro Brown. The Hare System, with Special Reference to its Application in Tasmania. (In Law Quarterly Review, Jan., 1899, XV., 51-70). See 4. 10. W. Jethro Brown. The New Democracy. A Political Study. (London: Macmillan s has been reduced to the num- ber of members to be elected. 6. If at any time after the first counting of the ballot- papers it becomes necessary to exclude the lowest candidate from the poll as hereinbefore directed, and it shall be found that two or more candidates have the same number of votes and occupy_ together the lowest nosition on the poll, then and in every such case whichever one of such candidates was found to have received the least number of votes upon the first counting of the ballot-papers shall be deemed to be the lowest on the poll; and if at any time it becomes necessary to exclude from the poll one or more of any number of candidates who have received the same number of votes upon the first coun^-'ntained a sur- plus ; or (b) A o-ididate oxchuU^d on account of his being Ic) vest on the poll, nnd which is therefore transferred to the candidate next in the order of the voter's preference. The transfer value of all votes is either 1 or some fraction of 1. BY E. L. PIESSE, B.SC, LL.B. 73 1913. Section G, — Method of Counting Votes. 1. The ballot-papers shall first be examined and all i^iforraal papers rejected. 2. Wherever during the process of the count the i-ules pro- vide for a transfer of surplus votes from one candidate to other candidates, all the voting-papers concerned in the said transfer shall be shuffled before the transfer is commenced. 3. The number of first choices for each candidate shall be counted, and on each paper a mark shall be made opposite the name of each candidate who receives one of such choices. Each candidate shall be credited with one vote for each such choice given to him. 4. The aggregate number of such first choices shall be divided by one more than the number of candidates required to be elected, and th^ quotient increased by one, disregarding any remainder, shall be the quota, and (except as hereinafter pro- vided in Rule 9) no candidate shall be elected until he obtains a numl)er of votes equal to or greater than the quota. 5. Any candidate who has, upon the first choices being counted, a number of such votes equal to or greater than the quota shall be declared elected. 6. Where the number of such votes obtained by any candi- date is in excess of the quota, the surplus shall be transferred to the next available candidate in the following manner: — (i) All the voting-papers on which a first choice is recorded for the elected candidate shall he re-examined and the number of second, or next ^-onsecutive, choices, recorded therein for each unelected candidate shall be counted, (ii) The surplus of the elected candidate shall be divided by the total number of votes obtained by him on the counting of the first choices, and the resulting fraction shall be the transfer value.