Benford's law doesn't give much of a guarantee except in highly specific scenarios. You can however show it's pretty accurate if you've got a 'smooth' probabili

Benford's law doesn't give much of a guarantee except in highly specific scenarios. You can however show it's pretty accurate if you've got a 'smooth' probability distribution spanning multiple orders of magnitude (how much of a guarantee you can give depends on how specific you define what it means to be 'smooth'). The rigged elections example you gave was, I believe, mostly explained by the fact that the number of votes they were looking at were all roughly the same order of magnitude [1]. [1]: https://www.youtube.com/watch?v=etx0k1nLn78 https://www.youtube.com/watch?v=etx0k1nLn78