Methods of Election. 229 



that Borda's method may lead to the rejection of a candidate 

 who has an absolute majority of the electors in his favour as 

 against all comers. It has also been shown above by the 

 help of this theoretical method that Condorcet's practical 

 method is erroneous. Thus it will be seen that the 

 theoretical method is of use in testing the accuracy of other 

 methods. From the description which has been given above, 

 however, it is not clear what the result of the theoretical 

 method is, even in the simplest cases, when discordant 

 propositions are affirmed, for if there be three candidates 

 only, and with the notation already used, we have a = 1, 

 b = 2, e = 3, each candidate is superior to one other 

 candidate, and A is superior by most, whilst C is inferior by 

 least. Thus, according to the above description, it is not 

 certain which of the two, A or C, wins. In another passage, 

 however,* Condorcet explains how he deals with any case of 

 three candidates, and the process he adopts in the case of 

 inconsistent propositions is to reject the one affirmed by the 

 smallest majority. This is exactly the process which has 

 been described above, and which was shown to be in 

 accordance with the method proposed. Thus it is clear that 

 in the case of three candidates the result of the proposed 

 method will always be the same as that of Condorcet's 

 theoretical method. 



The general rules for the case of any number of candi- 

 dates as given by Condorcet*}" are stated so briefly as to be 

 hardly intelligible. Moreover, it is not easy to reconcile 

 these rules with the statements made in the passage quoted 

 above, and as no examples are given it is quite hopeless to 

 find out what Condorcet meant. 



Comparison of Proposed Method with Condorcet's 

 Theoretical Method. 



Comparing the method proposed in this paper with 

 Condorcet's theoretical method, we see that, so far as any 

 conclusion can be drawn from the votes of the electors the 

 two methods always agree. In those cases in which no 

 conclusion can be drawn from the votes the results of the 

 two methods will not always be the same. It is equally 

 impossible to prove either of these results wrong. Con- 



* (JEuvres, vol. xiii., p. 259. 



j-Essai snr V application de V analyse a la prooaUUte des decisions vendues 

 a la pluralite des voix, pp. 125, 126. 



