>>12309606The main argument is that it's not a proof in itself.
It can be an indication that something is "odd" and should be verified.
We already know that not everything follows this "law".
You might have to do some data manipulation to correctly use it.
Example:
We're investigating collusion among bidders for public contracts.
We expect the cost of the project to be between 1 to 2 millions. So intuitively, you'll get more leadings 1 than 7 for example. As someone would either have to bid 700k which would be a lot lower than expectation or 7 millions which is much higher and if contractors have a sense of what competitors will bid, will most likely not bother bidding 7 millions.
So let's say the bids are:
1 million
1.2 million
1.5 million
2.1 million
2.5 million
3 million
Obviously here I didn't write a bunch of data point but we still get the idea that you get more 1 than 2's then 3's... It's unlikely that someone would bid 5 millions or 500k...
So looking at this, it follows Bendford laws. But it doesn't say either that there wasn't any collusion/fraud and that one of the bidder could have given a price of 900k for the project and that the others decided to slightly bid higher and share the extra 100k.
In such a case, you might want to apply Benford'law on the difference between each bid and the lowest big. It might give you a better idea.
Again, ideally you would want to compare to patterns of bids over other contracts over time.
Another more visual example in my image, the age distribution in the US clearly doesn't follow Benford law.
Personally, I'd be interested to see the curve of the "by how much one candidates won" in each district/states/whatever compared to the Benford law. (Trump had 500 votes in X, Biden had 450 votes in X, the difference is 50, the leading digit is 5). This could remove much of the effect of the size of the population in any district/state/whatever.
