Methods of Election. 201 



There is, however, another objection which is of great 

 importance. Borda's method holds out great inducements 

 to the electors to vote otherwise than according to their real 

 views. For if an elector strongly desires the return of a 

 particular candidate, he not only gives his two votes to that 

 candidate, but he also takes care to give his remaining vote 

 to the least formidable of the other candidates. The effect 

 of this is to give a great advantage to second-rate candi- 

 dates. Thus not only does Borda's method fail to interpret 

 the true wishes of the electors, supposing that they vote 

 honestly, but it holds out great inducements to them to vote 

 otherwise than according to their real views. 



Laplace discussed the question of the best mode of electing 

 one out of several candidates, and by an analytical investiga- 

 tion was led to Borda's method.* He states distinctly that 

 this method is the one indicated. by the theory of probabili- 

 ties. He then proceeds to point out the objection just 

 stated, and expresses the opinion that the method would, 

 without doubt, be the best if each elector would write the 

 names of the candidates in what he thinks the order of 

 merit. We have seen, however, that this is far from being 

 the case. 



Methods of the Second Class. 



The simplest method of the second class is the French 

 method of double elections. In this method each elector has 

 one vote, as in the single vote method, already described. If, 

 however, no candidate obtain an absolute majority of the 

 votes polled, a second election is held. For this second 

 election only the two candidates who obtained the largest 

 number of votes at the first election can be candidates. The 

 result is that the successful candidate is returned by an 

 absolute majority of those who vote at the second election, 

 so that it would appear, at first sight, that the successful 

 candidate represents the views of a majority of the 

 electors. We must not lose sight, however, of two facts, 

 first, that all the electors who vote at the first election may 

 not vote at the second election ; second, that those who do 

 so vote merely have to choose between the two remaining 

 candidates, and that, consequently, they may not be repre- 



* Journal de VEcole Poly technique, cahiers vii. and viii., pp. 169, 170 ; 

 Theorie Analytique des Probabilites, pp. 101, 299; Todhunter's History 

 of Probability, pp. 547, 548. 



