128 Measurement of Belief. [CHAP. vi. 



events happen in the long run ? There is a lottery with 100 

 tickets and ten prizes; is a man s belief that he will get a 

 prize fairly represented by one-tenth of certainty ? The mere 

 reference to a lottery should be sufficient to disprove this. 

 Lotteries have flourished at all times, and have never failed 

 to be abundantly supported, in spite of the most perfect con 

 viction, on the part of many, if not of most, of those who put 

 into them, that in the long run all will lose. Deductions 

 should undoubtedly be made for those who act from super 

 stitious motives, from belief in omens, dreams, and so on. 

 But apart from these, and supposing any one to come forti 

 fied by all that mathematics can do for him, it is difficult to 

 believe that his natural impressions about single events would 

 be always what they should be according to theory. Are 

 there many who can honestly declare that they would have 

 no desire to buy a single -ticket ? They would probably say 

 to themselves that the sum they paid away was nothing 

 worth mentioning to lose, and that there was a chance of 

 gaining a great deal; in other words, they are not appor 

 tioning their belief in the way that theory assigns. 



What bears out this view is, that the same persons who 

 would act in this way in single instances would often not 

 think of doing so in any but single instances. In other 

 words, the natural tendency here is to attribute too great an 

 amount of belief where it is or should be small ; i.e. to de 

 preciate the risk in proportion to the contingent advantage. 

 They would very likely, when argued with, attach disparag 

 ing epithets to this state of feeling, by calling it an un 

 accountable fascination, or something of that kind, but of 

 its existence there can be little doubt. We are speaking 

 now of what is the natural tendency of our minds, not of 

 that into which they may at length be disciplined by educa 

 tion and thought. If, however, educated persons have sue- 



