THE ALTERNATE VOTE. 363 



selected at once on his absolute majority, the other two being 

 thrown out at the first count. However large the committee or 

 the constituency, one vote more than half the votes given secures 

 the election of the best man : this is on the count of the first 

 votes. The counting or addition of preferences cannot alter the 

 fact, that one more than half the committee think him the best 

 man. There is no need to go any further, the selection has been 

 made on the original votes alone ; the majority is so decisive, that 

 alternate votes could not alter it. No applicant, whether there 

 are two or three, can get more votes than the man who has one 

 more than half the votes or an absohite majority. This is the 

 first case — the absolute majority case. 



9. If, in counting the number of all the original votes and 

 the expressed second preferences or alternate votes for each one 

 of the three applicants, we find that one man has fewer votes than 

 half the number of voters ; that is, fewer than a quarter of all 

 these combined original and alternate votes (which, as each com- 

 mittee man gives one of each, comes to twice the number of the 

 committee), we are certain that man is not the best man. 



To ask a committee man to vote for two out of three appli- 

 cants, is the same thing as to ask him to vote against one appli- 

 cant. If 211 is the number of committee men, and one candidate 

 gets less than n votes, out of all the votes, original and alternajte, 

 it is clear there are more than n voters against him : it is evident 

 that more than half the committee think him worse than one at 

 any rate of the others. It is absolutely certain that he, with less 

 than a fourth of the combined original and preference votes, is 

 not the best man, and so he may be thrown out ; having abso- 

 lutely no chance of beating the best man, under any circumstances 

 whatever. 



If in a committee of twelve giving twelve votes and twelve 

 preferences, one of the applicants has less than six votes, say 

 five, that shows that more than six, say seven, do not think him 

 the best man ; he must be thrown out and his alternate votes 

 distributed between the other two will settle which of them should 

 be elected. This is the second case — that of the absolute minorUy 

 of the electors ascertained by counting the combined votes. 



10. If we take anv three different numbers, and add them up, 

 and then divide the sum by three, we get the average or mean ; 

 and of these three numbers one of necessity must be less than 

 the mean, one must be greater, and the third may be the mean 

 itself, or either greater or less than the mean ; and in every case 

 the one or the two that are greater exceed the mean by just as 

 much as the mean exceeds the two or the one that are less than 

 it. This of course is very evident where the middle number hap- 

 pens to be the mean : — thus 2, 3, 4, — 3 is one-third of (2 + 3 + 4) 

 or 9, 2 is one less than 3, as 4 is one more than 3. So too in the 

 more ordinarv case, where the middle number is not the mean, 

 say 2, 3, 5, which added give 10, and a mean of 3^ ; 2 and 3 are 

 below the mean, 5 is above it. 2 is if below the mean, 3 is |^ 

 below the mean, together i§, and 5 is just as much above the 

 mean as these two are below it. So too i, 4, 5, gives the same 

 facts. I must apologise for this elementary arithmetic. You will 



