308 Transactions. 



It will not be necessary in many cases to fill up the whole of Table VI 

 or Table VIII, which would require \m (m — 1) entries in the trial table, 

 where tn is the number of candidates. (These counts in any case, become 

 simpler as the ballot-papers become sorted out in the process of counting.) 



From the first preferences shown in Table I the first count would show 

 —A, 110 votes : B, 90 ; C, 40 ; D, 100 ; E, 60. We could count first the 

 papers on which A, the highest candidate in this count, beats C, and the 

 number of papers on which C beats A. We find that C is preferred to A 

 on 210 papers out of 400 ; A is therefore rejected (provisionally, at least), 

 and his papers are distributed according to the second preferences shown 

 on them. C is then matched against D, whom he beats by 240 to 160 ; 

 against B, beating him by 210 to 190 ; and, finally, against E, obtaining 

 240 as against E's 160. C is therefore elected. Only m — 1 counts have 

 been necessary (in this case. 4), and each count is simpler than the one 

 before. 



If in the above counting it had been found that B beat C, then it would 

 have been necessary to try B against A to ascertain whether the incon- 

 sistent case had occurred ; but even then the process of counting might be 

 considerably shortened ; and, in general, any candidate whose trial total 

 has been completed may be rejected if that trial total is not greater than 

 \n (m - 1). 



I have purposely chosen an example in which the lowest candidate on 

 the first count is the candidate who should be declared elected, as it shows 

 in a most striking manner the unsoundness of Ware's method, in which the 

 lowest candidate of the first and each succeeding count is rejected. This 

 is the method under the Electoral Act of 1907 in Western Australia. Still 

 more fallacious is the Queensland method under the Act of 1905, where all 

 the candidates except the two highest are rejected at the first count. The 

 second ballot stands in the same category, and, moreover, is open to other 

 objections, especially in that it requires two polls, and gives opportunity 

 for intrigue of various kinds. 



The method I have explained gives, I claim, the real choice of the 

 electors, as far as that can be expressed by any system of voting, and it is 

 not too complicated in operation. I venture to claim also that every 

 elector could easily understand the principle involved in the counting : 

 we simply cut out in turn each candidate that is shown to have no chance 

 of election until we have one successful candidate left. 



If proportional representation were to be finally adopted, an interim 

 adoption of my method in single-member constituencies would train the 

 electors in the habit of indicating their preferences. 



