u/zulufdokulmusyuze

Benford’s law states that the probability that the first digit of a randomly chosen number in a naturally occurring dataset is equal to 1 is 30.1% And there is a solid information theoretic reason for this (the frequencies of digits scale logarithmically, so the probability that the most significant digit is d is log(d+1)-log(d)).

How about the following scenario: If we ask people to choose a positive integer without setting an upper limit, would the first digit of the numbers they choose follow Benford’s law?

I understand this is more of a psychology/human behavior question rather than math question, but it is still interesting from a mathematical perspective.