Methods of Election. 215 



we arrive at the three inconsistent propositions (1), (2), (3) we 

 are to abandon the one which is affirmed by the smallest 

 majority, it follows that the proposed method will give the 

 correct result in all cases. 



We have, then, arrived at two results. First, that if the 

 electors affirm any two of the propositions (1), (2), (3) and 

 affirm the contrary of the remaining one, and so affirm three 

 consistent propositions, then the result of the method of 

 election which is here proposed, will be that which is the 

 logical consequence of these propositions, whilst the methods 

 in ordinary use may easily give a different result. Second, 

 that if the electors affirm the three propositions (1), (2), (3) 

 which are inconsistent, then the result of the method pro- 

 posed is that which is the logical consequence of abandoning 

 that one of the three propositions which is affirmed by the 

 smallest majority. 



Another way of Applying Proposed Method. 



The method may be stated in another form, which may 

 sometimes be more convenient. For each first place count 

 one vote ; then, if any candidate has an absolute majority, 

 elect him. But if not, count in addition one vote for each 

 second place ; then, if the lowest candidate has not got half 

 as many votes as there are electors, reject him, and proceed 

 to a final scrutiny between the remaining two. But, if not, 

 take the aggregate for each candidate of the results of the 

 two counts; then reject all who have less than one-third of 

 the votes now counted, and, if necessary, proceed to a final 

 scrutiny. 



This process will give the same final result as the method 

 already described. This is readily seen as follows : — 1st. If 

 any one has an absolute majority on the first places, the elec- 

 tion is settled at the first scrutiny, and the result is mani- 

 festly correct, and therefore the same as that of the proposed 

 method. 2nd. If no one has an absolute majority on the 

 first places, but some one has on first and second places less 

 than half as many votes as there are electors, it is manifest 

 that more than half the electors consider that candidate 

 worse than each of the others, so tliat he ought to be 

 rejected, and hence the result of the final scrutiny will be 

 correct, and therefore in accordance with that of the proposed 

 method. 3rd. If neither of the above events happen, we 

 take the aggregate. Now (as has already been remarked) 

 the result of taking the aggregate is to give us exactly the 



