CONDOKCET. 353 



For in general when we have no mathematical symbols to guide 

 us in discovering Condorcet's meaning, the attempt is nearly 

 hopeless. 



We proceed then to analyse the Essay. 



662. Condorcet's first part is divided into eleven sections, 

 devoted to the examination of as many Hypotheses ; this part 

 occupies pages 1 — 136. 



We will consider Condorcet's first Hypothesis. 



Let there be 2^ + 1 voters who are supposed exactly alike as to 

 judgment ; let v be the probability that a voter decides correctly, 

 e the probability that he decides incorrectly, so that v-\-e — l ; 

 required the probability that there will be a majority in favour 

 of the correct decision of a question submitted to tiie voters. We 

 may observe, that the letters v and e are chosen from commencing 

 the words lerite and eiTeur. 



The required probability is found by expanding (v + e)^^"^^ by 

 the Binomial Theorem, and taking the terms from v^^'^^ to that 

 which involves v^'^^ e^, both inclusive. Two peculiarities in Con- 

 dorcet's notation may here be noticed. He denotes the required 

 probability by V^; this is very inconvenient because this symbol 

 has universally another meaning, namely it denotes V raised to 



the power q. He uses — to denote the coefficient of ^;""^'e'" in 



m 



the expansion of (v + e)"; this also is very inconvenient because 



the symbol — has universally another meaning, namely it denotes 



a fraction in which the numerator is w and the denominator is m. 

 It is not desirable to follow Condorcet in these two innovations. " 

 We will denote the probability required by </> (q) ; thus 



^ (q) = v^^^ + (2q + 1) v'^ e + ^^^^^^^"1 v''-' e^ + . .. 



I 2^ + 1 



663. The expression for (/> {q) is transformed by Condorcet 

 into a shape more convenient for his purpose ; and this trans- 

 formation we will now give. Let </> (2' + 1) denote what ^ {q) 



23 



