382 PROBABILITY OF JUDGMENTS. [CHAP. XXI. 



this apparently supernumerary system of data, determine the 

 values of x and k ? If the hypothesis, adopted by Poisson and 

 all other writers on the subject, of the absolute independence of 

 the events whose probabilities are denoted by x and k be retained, 

 we should be led to form a system of five equations of the type (3), 

 and either select from these that particular pair of equations which 

 might appear to be most advantageous, or combine together the 

 equations of the system by the method of least squares. There 

 might exist a doubt as to whether the latter method would be 

 strictly applicable in such cases, especially if the values of x and k 

 afforded by different selected pairs of the given equations were very 

 different from each other. M. Cournot has considered a somewhat 

 similar problem, in which, from the records of individual votes in 

 a court consisting of four judges, it is proposed to investigate the 

 separate probabilities of a correct verdict from each judge. For 

 the determination of the elements x, x', af', x'" 9 he obtains eight 

 equations, which he divides into two sets of four equations, and 

 he remarks, that should any considerable discrepancy exist be- 

 tween the values of x 9 x', a/', x" 9 determined from those sets, it 

 might be regarded as an indication that the hypothesis of the in- 

 dependence of the opinions of the judges was, in the particular 

 case, untenable. The principle of this mode of investigation has 

 been adverted to in (XVIII. 4). 



6. I proceed to apply to the class of problems above indicated, 

 the method of this treatise, and shall inquire, first, whether the 

 records of courts and deliberative assemblies, alone, can furnish 

 any information respecting the probabilities of correct judgment 

 for their individual members, and, it appearing that they cannot, 

 secondly, what kind and amount of necessary hypothesis will best 

 comport with the actual data. 



PROPOSITION I. 



From the mere records of the decisions of a court or deliberative 

 assembly, it is not possible to deduce any definite conclusion re- 

 specting the correctness of the individual judgments of its members. 



Though this Proposition may appear to express but the con- 

 viction of unassisted good sense, it will not be without interest to 

 show that it admits of rigorous demonstration. 



