On a Facebook page, different groups are competing for a prize that the group with the largest number of votes will receive.
Now, it is possible to purchase votes from "fake" accounts on Facebook for these surveys.
I know that Benford's law is used to check the plausibility of numbers across many different contexts, by suggesting that there should be an almost-universal constant ratio between leading digits. Looking at the below distribution of votes, I wonder if there is a similar concept that describes the ratio between the number of votes of subsequent participants (i.e., votes that the winner received divided by votes that the second place received, 2nd place votes / 3rd place votes, etc.).
For example, it seems to me like the vote ratio between top 1 and top 2, 2 and 3, and 3 and 4 are quite close to 2, and this ratio gets closer to 1.
Should one expect there to be an exponential distribution, or perhaps a logistic distribution, with places 1 and 2 very close at a high level, and bigger relative differences in the middle, and the losers very close at a low level?
If so, would this be Benford's Law, or does it follow from another formalized rule?
In the given context, there are 26 voting options, and the number of votes depends, I guess, on the network and outreach of each of the option's participants.
The top 3 options currently have 466, 239, 117 more votes (in addition to the 4 faces displayed).
Benford's Law is nothing about the ratio between top 1 and top 2. For Benford's Law we use firstly numbers starting with the digit 1, that is
So part of your answer is: No, this is not Benford's Law. I do not answer the part about "Should one expect there to be..." Perhaps that will find better answers at https://stats.stackexchange.com