Methods of Election. * 213 



been demonstrated that if the opinions of the electors are 

 such that there is a majority in favour of A as against B, and 

 likewise a majority in favour of A as against 0, the method 

 of election which is proposed will certainly bring about the 

 correct result ; whereas it has been shown by the considera- 

 tion of particular examples that the methods in ordinary use 

 may easily bring about an erroneous result under these cir- 

 cumstances. Thus the proposed method cannot bring about 

 a result which is contrary to the wishes of the majority, so 

 that the proposed method satisfies the fundamental condi- 

 tion. 



The method which is proposed has, I think, strong claims. 

 It is not at all difficult to carry out. The result will, as 

 often as not, be decided on the first scrutiny. Wq* simply 

 require each elector to put down the names of two of the 

 three candidates in order of preference. Then for each first 

 name two votes are counted, and for each second name one 

 vote is counted. The number of votes for each candidate is 

 then found. The third part of the sum total may be called 

 the average; then all candidates who are not above the 

 average are at once rejected. The lowest candidate must, 

 of course, be below the average. The second is just as likely 

 to be below as above the average. If he is below, the 

 election is settled; but if he is above the average, a second 

 scrutiny is necessary to decide between him and the highest 

 candidate. 



Cases of Inconsistency. 



We have now to consider what is the result of the pro- 

 posed method in those cases in which there is not a majority 

 for one candidate against each of the others. The methods 

 which have been described have been shown to be erroneous 

 by examining cases in which either one candidate has an 

 absolute majority of the electors in his favour, or a candidate 

 A is inferior to B and also to C, or a candidate A is superior 

 to B and also to C. Now it is not necessary that any of 

 these cases should occur. If a single person has to place 

 three candidates in order of preference he can do so, and it 

 would be quite impossible for anj^ rational person to arrive 

 at the conclusions 



B is superior to C ... ,.. ... (1) 



C is superior to A ... ... ... (2) 



A is superior to B ... ... ... (3) 



