CONDORCET. 369 



of tribunals until a certain number of opinions in succession on 

 the same side has been obtained, the opinions of those tribunals 

 being disregarded in which a sj^ecified plurality did not concur. 

 Let V be the probability of an opinion for one alternative of the 

 question, "svhich we will call the affirmative; let e be the proba- 

 bility of an opinion for the negative ; and let z be the j)robability 

 that the opinion will have to be disregarded for want of the re- 

 quisite plurality. Thus v + e + z = 1. Let r be the number of 

 ojDinions on the same side required, q the number of tribunals. 

 Suppose (v-}-zy to be expanded, and let all the terms be taken 

 between v^ and v*" both inclusive ; denote the aggTegate by (v). 

 Let (f> (e) be formed from (f> (v) by putting e for v. Then (/> {v) is 

 the i^i'obability that there will be a decision in the affirmative, 

 and (f> {e) is the jDrobability that there will be a decision in the 

 negative. But, as we have said, Condorcet does not discuss the 

 case. 



685. Hitherto Condorcet has always supposed that each voter 

 had only two alternatives presented to him, that is the voter had 

 a proposition and its contradictory to choose between ; Condorcet 

 now proposes to consider cases in which more than two proj)o- 

 sitions are submitted to the voters. He saj^s on his page 86 that 

 there will be three Hy23otheses to examine ; but he really arranges 

 the rest of this j^art of his Essay under tiuo H}qDotheses, namely the 

 tenth on pages 86 — 94?, and the eleventh on pages 95 — 136. 



686. Condorcet's tenth Hypothesis is thus given on his 

 page XLII : 



...celle oil Ton suppose que les Yotans peuvent non-seulement voter 

 pour ou centre une proposition, mais aussi declarer qu'ils ne se croient 

 pas assez instruits pour prononcer. 



The pages 89 — 94? seem even more than commonly obscure. 



687. On his page 94< Condorcet begins his eleventh H}-]30- 

 thesis. Suppose that there are 6^ + 1 voters and that there are 

 three propositions, one or other of which each voter affirms. Let 

 V, e, i denote the probabilities that each voter will affirm these 

 three propositions respectively, so that ?; + e + /=l. Condorcet 

 indicates various problems for consideration. We may for example 

 suppose that three persons A, B, C are candidates for an office, 



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