Proportional Representation: A Study in Methods of Election Part 31

Table headings: Col A: Members Col B: Registered Electors Col C: Proportionate Number of Members Col D: Members - Liberal, Labour and Irish Col E: Members - Conservatives Col F: Electorate of Const.i.tuencies held by - Liberal, Labour, and Irish Nationalists Col G: Electorate of Const.i.tuencies held by - Conservative Col H: Voters - Liberal, Labour, and Irish Nationalist Col I: Voters - Conservative Col J: Majority - Actual Col K: Majority - With equal Single Member Const.i.tuencies Col L: Majority - Under Proportional Representation.

A B C DE FG HI J K L Prop Memb Electorate Voters Majority Memb Elect Memb Act Eq PR Metropolis 60 573,141 61 LLI 8 70,056 161,328 Con 52 503,085 242,999 44 47 13 England: South-East 48 472,725 50 LLI 2 24,057 152,213 Con 46 448,668 217,096 44 44 8 S.Midland 38 358,501 38 LLI 3 30,569 116,143 Con 35 327,932 164,052 32 32 6 East 29 294,153 31 LLI 8 70,467 101,736 Con 21 223,686 122,999 13 15 3 South-West 40 330,670 35 LLI 10 76,141 124,852 Con 30 254,529 144,435 20 19 3 W.Midland 58 589,881 63 LLI 9 85,544 195,545 Con 49 504,337 259,382 40 45 9 N.Midland 34 351,792 37 LLI 16 186,167 143,142 1 Con 18 165,625 149,436 2 1 North-West 70 728,292 78 LLI 10 114,035 273,585 Con 60 614,257 332,101 50 54 8 Yorks.h.i.+re 52 565,799 61 LLI 28 317,932 238,032 4 7 1 Con 24 247,867 225,871 North 32 339,289 36 LLI 20 222,202 145,085 8 12 2 Con 12 117,087 124,697

ENGLAND 461 4,604,243 490 LLI 114 1,197,170 1,652,261 Con 347 3,407,073 1,983,068 233 236 48 Wales and Monmouth 34 320,532 34 LLI 25 241,750 148,552 16 18 6 Con 9 78,782 108,036 Scotland 72 636,106 68 LLI 39 335,143 243,425 6 4 2 Con 33 300,963 234,138

Subtotal 567 5,560,881 592 LLI 178 1,774,068 2,044,238 Con 389 3,786,818 2,325,242 211 214 40

Ireland 103 727,562 78 LLI 82 549,467 317,910 61 42 28 Con 21 178,095 154,379

Total 670 6,292,443 670 LLI 260 2,323,530 2,362,148 Con 410 3,964,913 2,479,621 150 172 12 Majority 150 1,641,383 117,473

GENERAL ELECTION, 1900 Table headings: Col A: Members Col B: Registered Electors Col C: Proportionate Number of Members Col D: Members - Liberal, Labour and Irish Col E: Members - Conservatives Col F: Electorate of Const.i.tuencies held by - Liberal, Labour, and Irish Nationalists Col G: Electorate of Const.i.tuencies held by - Conservative Col H: Voters - Liberal, Labour, and Irish Nationalist Col I: Voters - Conservative Col J: Majority - Actual Col K: Majority - With equal Single Member Const.i.tuencies Col L: Majority - Under Proportional Representation.

A B C DE FG HI J K L Prop Memb Electorate Voters Majority Memb Elect Memb Act Eq PR Metropolis 60 601,925 60 LLI 8 73,718 150,047 Con 52 528,207 247,777 44 46 14 England: South-East 48 512,408 51 LLI 3 23,362 140,277 Con 45 489,406 220,829 42 47 11 S. Midland 38 388,361 39 LLI 6 63,375 120,012 Con 32 324,986 164,148 26 27 7 East 29 319,997 32 LLI 9 80,447 101,785 Con 20 239,550 125,375 11 8 4 South-West 40 337,449 33 LLI 14 122,410 127,086 Con 26 215,039 142,269 12 9 1 W. Midland 58 630,931 63 LLI 10 96,089 200,113 Con 48 534,842 261,474 38 43 9 N. Midland 34 378,996 38 LLI 18 211,280 149,794 2 4 0 Con 16 167,716 153,294 North-West 70 794,142 79 LLI 14 176,183 281,634 Con 56 617,957 351,243 42 43 9 Yorks.h.i.+re 52 612,892 61 LLI 26 326,841 239,045 5 1 Con 26 286,051 238,870 North 32 367,007 36 LLI 16 197,102 147,017 2 2 Con 16 169,905 135,459 ENGLAND 461 4,944,108 492 LLI 124 1,370,807 1,657,814 Con 337 3,573,301 2,040,508 213 212 52

Wales and Monmouth 34 342,209 34 LLI 28 286,628 161,190 22 24 8 Con 6 55,581 103,396 Scotland 72 683,840 68 LLI 34 312,781 254,112 Con 34 371,059 258,836 4 6

Britain 567 5,970,187 594 LLI 186 1,970,216 2,073,116 Con 381 3,999,941 2,402,740 195 194 44

Ireland 103 765,258 76 LLI 82 598,469 318,203 61 44 28 Con 21 166,757 145,906

Total 670 6,735,415 670 LLI 268 2,568,685 2,391,319 Con 402 4,166,698 2,548,736 134 150 16 Majority 134 1,598,013 157,417

GENERAL ELECTION, 1906

Table headings: Col A: Members Col B: Registered Electors Col C: Proportionate Number of Members Col D: Members - Liberal, Labour and Irish Col E: Members - Conservatives Col F: Electorate of Const.i.tuencies held by - Liberal, Labour, and Irish Nationalists Col G: Electorate of Const.i.tuencies held by - Conservative Col H: Voters - Liberal, Labour, and Irish Nationalist Col I: Voters - Conservative Col J: Majority - Actual Col K: Majority - With equal Single Member Const.i.tuencies Col L: Majority - Under Proportional Representation.

A B C DE FG HI J K L Prop Memb Electorate Voters Majority Memb Elect Memb Act Eq PR Metropolis 60 626,011 57 LLI 40 385,762 251,937 Con 20 240,249 225,725 20 13 3 England South East 48 583,000 54 LLI 22 273,398 245,046 Con 26 309,602 241,097 4 4 S.Midlands 38 441,803 40 LLI 27 328,386 193,594 16 20 2 Con 11 113,417 172,159 East 29 368,662 34 LLI 25 333,564 170,039 21 28 4 Con 4 35,098 128,991 South-West 40 371,300 34 LLI 34 321,822 176,478 28 24 4 Con 6 49,478 144,342 W.Midland 58 679,903 63 LLI 35 402,148 288,832 12 11 1 Con 23 277,760 286,862 N.Midland 34 420,677 39 LLI 28 358,852 205,066 22 27 5 Con 6 61,825 151,924 North-West 70 869,792 80 LLI 55 680,843 420,969 40 46 12 Con 15 188,949 321,560 Yorks.h.i.+re 52 667,863 62 LLI 41 556,233 340,865 30 42 14 Con 11 111,635 218,778 North 32 409,843 38 LLI 27 345,353 215,748 22 26 10 Con 5 64,490 123,003 England 461 5,438,859 501 LLI 334 3,986,356 2,508,574 207 233 53 Con 127 1,452,503 2,014,441

Wales and Monmouth 34 387,585 35 LLI 34 387,585 217,462 34 35 13 Con 0 -- 100,547 Scotland 72 750,401 70 LLI 60 629,360 367,942 48 48 16 Con 12 121,041 235,098

Britain 567 6,576,845 606 LLI 428 5,003,301 3,093,978 289 316 82 Con 139 1,573,544 2,350,086

Ireland 103 693,417 64 LLI 85 545,748 301,833 67 36 22 Con 18 147,669 144,708

TOTAL 670 7,270,262 670 LLI 513 5,549,049 3,395,811 356 352 104 Con 157 1,721,213 2,494,794 Majority 356 3,827,836 901,017

GENERAL ELECTION, JANUARY 1910

Table headings: Col A: Members Col B: Registered Electors Col C: Proportionate Number of Members Col D: Members - Liberal, Labour and Irish Col E: Members - Conservatives Col F: Electorate of Const.i.tuencies held by - Liberal, Labour, and Irish Nationalists Col G: Electorate of Const.i.tuencies held by - Conservative Col H: Voters - Liberal, Labour, and Irish Nationalist Col I: Voters - Conservative Col J: Majority - Actual Col K: Majority - With equal Single Member Const.i.tuencies Col L: Majority - Under Proportional Representation.

A B C DE FG HI J K L Prop Memb Electorate Voters Majority Memb Elect Memb Act Eq PR Metropolis 60 658,795 57 LLI 26 246,838 254,154 Con 34 411,957 298,821 8 15 5 England: South-East 48 636,108 55 LLI 3 31,221 220,995 Con 45 604,887 334,022 42 49 11 S. Midland 38 490,592 43 LLI 11 146,312 197,717 Con 27 344,280 235,776 16 17 3 East 29 400,062 35 LLI 15 236,234 173,465 1 7 1 Con 14 163,828 170,027 South-West 40 386,514 34 LLI 18 201,726 172,692 2 Con 22 184,788 175,010 4 W. Midland 58 713,761 62 LLI 17 227,430 284,629 Con 41 486,331 334,874 24 22 6 N. Midland 34 446,752 39 LLI 23 334,766 216,469 12 19 3 Con 11 111,986 181,209 North-West 70 928,640 81 LLI 47 636,497 449,324 24 35 7 Con 23 292,143 382,796 Yorks.h.i.+re 52 701,856 61 LLI 89 564,418 365,185 26 37 11 Con 13 137,438 248,507 North 32 430,594 38 LLI 23 354,697 216,760 14 24 6 Con 9 75,897 150,471 ENGLAND 461 5,793,674 505 LLI 222 2,980.139 2,551,390 21 3 Con 239 2,813,535 2,521,513 17 Wales and Monmouth 34 425,714 37 LLI 32 414,613 243,383 30 35 13 Con 2 11,101 116,696 Scotland 72 785,391 68 LLI 61 675,723 394,103 50 50 14 Con 11 109,668 265,770 Sub total 567 7,004,779 610 LLI 315 4,070,475 3,188,876 63 106 30 Con 252 3,188,876 2,903,979

Ireland 103 688,284 60 LLI 82 518,154 356,223 61 30 26 Con 21 170,130 145,437

Total 670 7,693,063 670 LLI 397 4,588,629 3,545,099 124 136 56 Con 270 3,104,434 3,049,416 Majority 124 1,484,195 495,683

GENERAL ELECTION, DECEMBER 1910

Table headings: Col A: Members Col B: Registered Electors Col C: Proportionate Number of Members Col D: Members - Liberal, Labour and Irish Col E: Members - Conservatives Col F: Electorate of Const.i.tuencies held by - Liberal, Labour, and Irish Nationalists Col G: Electorate of Const.i.tuencies held by - Conservative Col H: Voters - Liberal, Labour, and Irish Nationalist Col I: Voters - Conservative Col J: Majority - Actual Col K: Majority - With equal Single Member Const.i.tuencies Col L: Majority - Under Proportional Representation.

A B C DE FG HI J K L Prop Memb Electorate Voters Majority Memb Elect Memb Act Eq PR Metropolis 60 658,795 57 LLI 29 279,492 223,151 Con 31 379,303 264,281 2 9 5 England-- South-East 48 636,108 55 LLI 5 58,248 209,434 Con 43 577,860 311,888 38 45 11 S. Midland 38 490,592 43 LLI 14 170,762 190,120 Con 24 319,830 219,876 10 13 3 East 29 400,062 35 LLI 16 256,750 164,849 3 9 1 Con 13 143,312 154,529 South-West 40 386,514 34 LLI 14 159,494 164,698 Con 26 227,020 168,992 12 6 0 W. Midland 58 713,761 62 LLI 19 246,842 268,125 Con 39 466,919 316,574 20 20 6 N. Midland 34 446,752 39 LLI 21 298,037 202,351 8 13 3 Con 13 148,715 173,545 North-West 70 928,640 81 LLI 39 524,682 400,508 8 11 1 Con 31 403,958 386,045 Yorks.h.i.+re 52 701,856 61 LLI 40 570,544 321,622 28 39 9 Con 12 131,312 239,067 North 32 430,594 38 LLI 25 375,574 200,583 18 28 6 Con 7 55,020 142,388 ENGLAND 461 5,793,674 505 LLI 222 2,940,425 2,345,441 7 Con 239 2,853,249 2,377,185 17 5 Wales and Monmouth 34 425,714 37 LLI 31 388,507 210,525 28 31 9 Con 3 37,207 121,013 Scotland 72 785,391 68 LLI 61 678,395 372,313 50 50 10 Con 11 106,996 277,183

Subtotal 567 7,004,779 610 LLI 314 4,007,327 2,928,279 61 88 14 Con 253 2,997,452 2,775,381

Ireland 103 688,284 60 LLI 84 536,675 350,029 65 34 24 Con 19 151,609 146,982

Total 670 7,693,063 670 LLI 398 4,544,002 3,278,308 126 122 38 Con 272 3,149,061 2,922,363 Majority 126 1,394,941 355,945

APPENDIX VI

PREFERENTIAL VOTING: THE TRANSFER OF SUPERFLUOUS VOTES

(A Memorandum by the Rt. Hon. J. Parker Smith)[1]

(1) _The Element of Chance Involved: Its Magnitude_

An objection, which occurs to every one who considers schemes of Preferential Voting, is that an element of chance is introduced into the result by the methods for the transfer of the superfluous votes of successful candidates. Supposing one part of the supporters of A, a successful candidate, have put down B as their second choice, and the remainder C, and that a certain number of A's votes are superfluous, and have to be transferred, how is it to be determined what number of AB votes, as they may be called, and what number of AC votes shall be transferred? If the question is settled by chance, as, by drawing the necessary number at random from A's heap, by declaring that voting papers shall be used in the order in which they were handed in at the polling booths, or by laying down any other set of arbitrary rules to determine the order in which they shall be counted, an element of uncertainty is introduced by which there seems to be serious danger that B and C will gain or lose unfairly.

Those who are accustomed to dealing with statistics will be prepared to find this danger less than might have been expected; but even they will be surprised to find of how small importance the arbitrary element is discovered, by actual calculation, to be.

The difficulty can be made clear by a numerical instance. Take the case of an election for several seats, where the necessary quota is 6000, and where a favourite candidate, whom we will call A, has received the first votes of 10,000 voters. Though all those voters have agreed in putting the same candidate first, they are divided as to who may wish to be returned next. Six thousand of them put B as their second choice, and the other 4000 C. If the 6000 votes which A requires are drawn wholly from the AB votes, the result of the transfer will be that C is credited with 4000 votes and B with none. This would be clearly unfair, for, in reality, B has received among A's voters much more support than C. To use up the 4000 AC votes and only 2000 AB votes, and to transfer 4000 votes to B and none to C would be equally unfair to C. The course which is exactly fair to both B and C is that the votes which are transferred should be divided between them in the same proportion as that in which the opinions of the whole number of A's supporters is divided. That is to say, strict justice will be done if every 1000 votes which are used or transferred are made up of 600 AB votes and 400 AC votes.

Accordingly, A's quota of 6000 must be made up of 3600 AB votes and 2400 AC votes, and the 4000 papers left to be transferred will consequently consist of 2400 votes for B and 1600 votes for C.

This principle avoids all uncertainty, and is indisputably fair. It remains to consider how to carry it into effect. In most cases there would, in reality, be many more cla.s.ses of votes than in the instance taken above. Even in such cases it is practicable, as will presently be shown, to divide the votes proportionately by an actual process of counting and separation. A certain amount of complication is, of course, introduced, but the extra labour involved does not seem impossible. The question whether this extra labour is necessary must be answered by examining the magnitude of the evil which it is sought to remedy.

If the votes are counted in a random order, it is clear there is a probability that the order in which they are drawn will correspond to the total numbers of each cla.s.s in the ballot-box. It is reasonable to expect that when there are 10,000 ballot papers in an urn the composition of the first thousand drawn out will nearly be the same as that of any other thousand, or of the whole 10,000. The amount of this probability may be determined mathematically, and is very great.

This fact was clearly seen by Mr. Andrae, the statesman by whom the method of preferential voting was introduced into Denmark in 1855, and a mathematician of undisputed eminence. In answer to an objection of the kind now under discussion, he replied: "If this law of mine had already been in operation over the whole of Europe (including Turkey), for a period of 10,000 years, and if the elections in every part of Europe to which the law was applied were to take place, not every one, or three, or seven years, but every week in regular repet.i.tion, these elections throughout Europe, at the rate of a general European election per week, would still have to go on for more than a thousand times the period of years already stated; that is to say, for more than a thousand times ten thousand years, before the chances would be equal that the voting papers should come out of the urn in the order required to form the basis of this problem. Although, therefore, the supposed combination is, mathematically speaking, only an enormous improbability, yet, practically speaking, it is absolutely impossible."[2]

To state the matter more exactly, and as the result of an independent mathematical investigation, it appears that in the case we have stated, if 4000 voting papers were drawn out of A's heap at random, instead of the papers being carefully sorted and proportionately divided, the probability is that neither B nor C would gain or lose more than 11 votes. In other words, it is just even betting that the number of AB votes in the 4000 drawn would lie between 2411 and 2389 (inclusive), and consequently that the number of BC votes will lie between 1589 and 1611.

The odds are more than 3 to 1 neither B nor C would gain or lose more than 20 votes, _i.e._ that the number of AB votes drawn will lie between 2420 and 2380; more than 10 to 1 that neither would gain or lose more than 30 votes; just 50 to 1 that neither would gain or lose more than 40 votes; and about 2000 to 1 that neither would gain or lose more than 60 votes. If the number of cla.s.ses were larger or the number of votes to be drawn smaller, the effect would be much less. It will thus be seen that it is only in the case of very closely contested elections that the element of chance can affect the result. It will also be observed that the _element of chance will not be of importance as between the different parties,_ but only as _between different individual candidates of the same party_, since in almost all cases the electors who are agreed upon the candidate they most desire will also put for their second choice candidates of the same party.

In closely contested elections it must, of course, be admitted that as a result of this method, chance might decide which of two candidates of the same party should be elected. But in closely contested elections in large const.i.tuencies so many elements of chance are always and necessarily involved, that the introduction of a fresh one does not, in reality, make the result more arbitrary. Putting aside all the slight influences which at the last moment decide a score or two of featherweight votes, and a.s.suming that every voter is profoundly convinced of the truth of his opinions, there remains the question of boundaries. A slight change in the line of the boundaries of the const.i.tuency might easily make a difference of fifty votes--a larger difference than what we are concerned with. To carry the dividing lines from North to South instead of from East to West, would, in many localities, completely alter the character of the representation.

These are, in reality, matters of chance, and more arbitrary in their nature than the order in which voting papers are drawn from an urn.

(2) _Method of Eliminating the Chance Element_

If, however, special precautions are still thought necessary, the following method of counting the votes appears to reduce, as far as practicable, the element of chance involved in the transfer of superfluous votes:--

The whole set of voting papers of the const.i.tuency being mixed, the papers, not yet unfolded, are drawn out one by one. Each is stamped, as it is drawn, with a corresponding number, 1, 2, ... in order. It is then unfolded, and sorted according to the names of the candidates marked first and second upon it. Suppose there are six candidates, A, B, C, X, Y, Z; the votes of any candidate, A, will be sorted into six heaps, viz., A votes (_i.e._ votes where A only is voted for), AB, AC, AX, AY, and AZ votes. If A is found to have received more votes than he requires, the order in which the votes will be counted to him will be as follows: Use first the A votes, then use up those heaps where the second name also is that of a candidate who has received more than the necessary minimum. If these heaps give A more than he requires, take the same proportion out of each of such heaps, taking out of each heap the last drawn votes first. If, however, these heaps are used up without giving A as many votes as he requires, take an equal proportion of the votes of each of the remaining heaps--taking out of each heap the last drawn votes first.

_Example_.--Take an election where 6000 is the necessary minimum, and suppose A has 8650 votes, composed as follows:

A 600 AB 2,700 AC 4,500 AX 50 AY 200 AZ 600 ----- 8,650