200 Methods of Election. 



Borda's Method. 



This method was proposed by Borda in 1770, but the 

 first published description of it is in the volume for 1781 of 

 the Memoirs of the Royal Academy of Sciences. For some 

 remarks on the method see Todhunter's History of 

 Probability, p. 433, where the method is described. In the 

 case of three candidates, it is as follows. Each elector has 

 three votes, two of which must be given to one candidate, 

 and the third vote to another candidate. The candidate 

 who obtains the greatest number of votes is elected. 



In order to show that this method may lead to an 

 erroneous result, suppose that there are twelve electors, of 

 whom five prefer A to B and B to C, whilst two prefer A to 

 C and C to B, and five prefer B to C and C to A. Then the 

 votes polled will be, for A, fourteen ; for B, fifteen ; for 

 C, seven. Thus B is elected. It is clear, however, that this 

 result is wrong, because seven out of the whole twelve 

 electors prefer A to B and C, so that, in fact, A has an 

 absolute majority of the electors in his favour. Hence, then, 

 Borda's method does not satisfy the fundamental condition, 

 for it may lead to the rejection of a candidate who has an 

 absolute majority of the electors in his favour. 



It may be observed that the result of the poll on Borda's 

 method may be obtained, in the case of three candidates, 

 by adding together the corresponding results in the polls on 

 the methods already described. 



If there be n candidates, each elector is required to 

 arrange them in order of merit ; then for each highest place 

 n — 1 votes are counted ; for each second place, n — 2 votes, 

 and so on ; n — r votes being counted for each r th place, 

 and no votes for the last place. The candidate who obtains 

 the greatest number of votes is elected. 



Borda does not give any satisfactory reason for adopting 

 the method. Nevertheless he had great faith in it, and 

 made use of it to test the accuracy of the ordinary or single 

 vote method, and arrived at the extraordinary conclusion 

 that in any case in which the number of candidates is equal 

 to or exceeds the number of electors, the result cannot be 

 depended upon unless the electors are perfectly unanimous. 

 This in itself is sufficient to show that Borda's method must 

 be capable of bringing about a result which is contrary to 

 the wishes of the majority. 



