OP THE CALCULATION OF CHANCES. 67 



capacity, instead of applying so rude a standard (even if it 

 were capable of being verified) as the ratio between the number 

 of true and the number of erroneous statements which he may 

 be supposed to make in the course of his life. 



Again, on the subject of juries, or other tribunals, some 

 mathematicians have set out from the proposition that the 

 judgment of any one judge, or juryman, is, at least in some 

 small degree, more likely to be right than wrong, and have 

 concluded that the chance of a number of persons concurring 

 in a wrong verdict is diminished, the more the number is 

 increased ; so that if the judges are only made sufficiently 

 numerous, the correctness of the judgment may be reduced 

 almost to certainty. I say nothing of the disregard shown to 

 the effect produced on the moral position of the judges by 

 multiplying their numbers; the virtual destruction of their 

 individual responsibility, and weakening of the application of 

 their minds to the subject. I remark only the fallacy of 

 reasoning from a wide average, to cases necessarily differing 

 greatly from any average. It may be true that taking all 

 causes one with another, the opinion of any one of the judges 

 would be oftener right than wrong ; but the argument forgets 

 that in all but the more simple cases, in all cases in which it 

 is really of much consequence what the tribunal is, the propo- 

 sition might probably be reversed ; besides which, the cause of 

 error, whether arising from the intricacy of the case or from 

 some common prejudice or mental infirmity, if it acted upon 

 one judge, would be extremely likely to affect all the others in 

 the same manner, or at least a majority, and thus render a 

 wrong instead of a right decision more probable, the more the 

 number was increased. 



These are but samples of the errors frequently committed 

 by men who, having made themselves familiar with the diffi- 

 cult formul which algebra affords for the estimation of 

 chances under suppositions of a complex character, like better 

 to employ those formula in computing what are the probabi- 

 lities to a person half informed about a case, than to look out 

 for means of being better informed. Before applying the 

 doctrine of chances to any scientific purpose, the foundation 



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