BORDA. 433 



Borda observes that the ordinary mode of election is liable to 

 error. Suppose, for example, that there are 21 voters, out of 

 whom 8 vote for A, 7 for B, and 6 for (7; then A is elected. But 

 it is possible that the 7 who voted for B and the 6 who voted 

 for C may agree in considering A as the worst of the three can- 

 didates, although they differ about the merits of B and G. In such 

 a case there are 8 voters for A and 13 against him out of the 

 21 voters ; and so Borda considers that A ought not to be elected. 

 In fact in this case if there were only A and B as candidates, or 

 only A and C as candidates, A would lose ; he gains because he 

 is opposed by two men who are both better than himself. 



Borda suggests that each voter should arrange the candidates 

 in what he thinks the order of merit. Then in collecting the 

 results w^e may assign to a candidate a marks for each lowest 

 place, a + h marks for each next ^Dlace, a + 2b marks for each next 

 place, and so on if there are more than three candidates. Suppose 

 for example that there are three candidates, and that one of them 

 is first in the lists of 6 voters, second in the lists of 10 voters, and 

 third in the lists of 5 voters ; then his aggregate merit is ex- 

 pressed by 6 {a + 2h) + 10 {a + h) + oa, that is by 21a + 225. It 

 is indifferent what proportion w^e establish between a and h, be- 

 cause in the aggregate merit of each candidate the coefficient of a 

 will be the whole number of voters. 



Condorcet objects to Borda's method, and he gives the follow- 

 ing example. Let there be three candidates. A, B, and C\ and 

 suppose 81 voters. Suppose that the order ABC is adopted by 

 30 voters, the order A CB by 1, the order CAB by 10, the order 

 BAG hy 29, the order BGA by 10, and the order GBA by 1. In 

 this case B is to be elected on Borda's method, for his aggTegate 

 merit is ex^Dressed by 81a + 1095, while that of ^ is expressed 

 by 81a + 1015, and that of G by 81a + 335. Condorcet decides 

 that A ought to be elected ; for the proposition A is better than B 

 is affirmed by 30 + 1 + 10 voters, w^hile the proposition B is better 

 than A is affirmed by 29 + 10 + 1 voters, so that A has the ad- 

 vantage over B in the ratio of 41 to 40. 



Thus suppose a voter to adopt the order ABG; then Condorcet 

 considers him to affirm with equal emphasis the three propositions 

 A is better than B, B is better than C, A is better than 0; but 



28 



