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Benford's law doesn't apply if values aren't expected to have size-relative even distribution across multiple orders of magnitude, which election data does not.

tialaramex 6y ago
Yup. Here's some data I was looking at earlier (not related to an election in any way) just as an example of what arbitrary real world data can look like https://www.ofgem.gov.uk/data-portal/electricity-prices-day-ahead-baseload-contracts-monthly-average-gb https://www.ofgem.gov.uk/data-portal/electricity-prices-day-... As you can see, doesn't match Benford's law due to sitting boringly in a single order of magnitude range. £10 per MWh is extremely cheap and £100 per MWh is extremely expensive. Neither value is quite impossible hour by hour, but they're not plausible monthly averages for this contract.
- chrisco255 6y ago
  It doesn't work for formulaic data. It has already been used to prove fraud in Iranian elections. It is legally admissible in court of law. It was also only 1/4 of my argument. Dr.Shivas analysis isn't covering Benford's Law. It's a completely different vector of analysis that shows weighted anamolies indicating algorithmic manipulation of the presidential choice as a function of a precinct's straight party Republican vote. Watch his video to see. Source on Benford's: https://www.isaca.org/resources/isaca-journal/past-issues/2011/understanding-and-applying-benfords-law https://www.isaca.org/resources/isaca-journal/past-issues/20... Finally, I'd like to argue that Benford's should be used to trigger an automatic audit of that precinct or district. If there's no fraud then the audit should show that to be the case, and we can dismiss Benford's as an election fraud detection technique if enough false flags are proven. So, let's be scientists about this theory and test it rather than dismiss it.
  - happytoexplain 6y ago
    You would have to elaborate on why Benford's law being applicable to one election makes it applicable in another. If the distribution of Iranian electors doesn't exhibit the stated limitation, then it makes sense why Benford's law would apply in that case but not in the 2020 US case.
    - chrisco255 6y ago
      No, you would have to make your case as to why it wouldn't be applicable. I've heard no such fundamental argument other than handwaving. It's perfectly acceptable to use for election data, just as it's used in population data. And if you really want to prove your case, you should demand an audit be done so we could settle this argument once and for all.
      - tialaramex 6y ago
        You actually were given a very specific fundamental argument way up thread, which you've ignored: Benford's law doesn't apply if values aren't expected to have size-relative even distribution across multiple orders of magnitude.
  - tzs 6y ago
    Precincts in most places are designed to have roughly the same number of voters. Hence, Benford's law does not work for them. Here's a good explanation, using Chicago precinct data [1]. A good rule of thumb is that if Benford's law does not apply to the legal voter population of your precincts/counties/wards/districts/whatever, or when applied to the total number of registered voters in those areas, then it won't apply to the results of a fair election either. (This is why if you ask every adult you know their height in inches and then look at the distribution of first digits, it will look nothing at all like a Benford's law distribution. The heights are going to be the sum of two normal distributions (one for men, one for women)). A good example of that is the county results in Georgia. There is a video going around from a forensic CPA showing the votes by county did not followed Benford's law, but he failed to look at the underlying population. I've written a little web-based simulation using the Georgia data to make it easy to play with the data to get a feel for why Benford's law does not work there [2]. Another way to tell when a deviation from Benford's law is not an indicator of election fraud is to look at what it would take to make the results fit Benford's law. If you can't find any reasonable way to adjust the votes to make it fit, then the lack of fit was not a fraud indicator. (And if you can find such an adjustment, it also needs to stay a Benford fit if you make minor changes to the voter turnout or the split). In the particular case of the 2020 US Presidential election, there is another thing about all of the purported proofs of Biden fraud by Benford: cherry picking. There are plenty of places where the precinct vote for Trump does not fit Benford and the Biden vote does. And there are plenty of places where neither the Biden nor Trump vote fits Benford's law. As you will see if you play with my Georgia simulator, when you have a situation where Benford's law does not apply even a small change in voter turnout or in a candidate's share can cause large changes in the first digit distribution. Because of this, and the large number of cities and counties we have in the US where the underlying population does not follow Benford, there is essentially a large randomness in the first digit distributions. [1] https://www.youtube.com/watch?v=etx0k1nLn78 https://www.youtube.com/watch?v=etx0k1nLn78 [2] https://github.com/tzs/georgia-benford-simulation https://github.com/tzs/georgia-benford-simulation

tialaramex 6y ago

Yup. Here's some data I was looking at earlier (not related to an election in any way) just as an example of what arbitrary real world data can look like https://www.ofgem.gov.uk/data-portal/electricity-prices-day-ahead-baseload-contracts-monthly-average-gb https://www.ofgem.gov.uk/data-portal/electricity-prices-day-... As you can see, doesn't match Benford's law due to sitting boringly in a single order of magnitude range. £10 per MWh is extremely cheap and £100 per MWh is extremely expensive. Neither value is quite impossible hour by hour, but they're not plausible monthly averages for this contract.

chrisco255 6y ago
It doesn't work for formulaic data. It has already been used to prove fraud in Iranian elections. It is legally admissible in court of law. It was also only 1/4 of my argument. Dr.Shivas analysis isn't covering Benford's Law. It's a completely different vector of analysis that shows weighted anamolies indicating algorithmic manipulation of the presidential choice as a function of a precinct's straight party Republican vote. Watch his video to see. Source on Benford's: https://www.isaca.org/resources/isaca-journal/past-issues/2011/understanding-and-applying-benfords-law https://www.isaca.org/resources/isaca-journal/past-issues/20... Finally, I'd like to argue that Benford's should be used to trigger an automatic audit of that precinct or district. If there's no fraud then the audit should show that to be the case, and we can dismiss Benford's as an election fraud detection technique if enough false flags are proven. So, let's be scientists about this theory and test it rather than dismiss it.
- happytoexplain 6y ago
  You would have to elaborate on why Benford's law being applicable to one election makes it applicable in another. If the distribution of Iranian electors doesn't exhibit the stated limitation, then it makes sense why Benford's law would apply in that case but not in the 2020 US case.
  - chrisco255 6y ago
    No, you would have to make your case as to why it wouldn't be applicable. I've heard no such fundamental argument other than handwaving. It's perfectly acceptable to use for election data, just as it's used in population data. And if you really want to prove your case, you should demand an audit be done so we could settle this argument once and for all.
    - tialaramex 6y ago
      You actually were given a very specific fundamental argument way up thread, which you've ignored: Benford's law doesn't apply if values aren't expected to have size-relative even distribution across multiple orders of magnitude.
- tzs 6y ago
  Precincts in most places are designed to have roughly the same number of voters. Hence, Benford's law does not work for them. Here's a good explanation, using Chicago precinct data [1]. A good rule of thumb is that if Benford's law does not apply to the legal voter population of your precincts/counties/wards/districts/whatever, or when applied to the total number of registered voters in those areas, then it won't apply to the results of a fair election either. (This is why if you ask every adult you know their height in inches and then look at the distribution of first digits, it will look nothing at all like a Benford's law distribution. The heights are going to be the sum of two normal distributions (one for men, one for women)). A good example of that is the county results in Georgia. There is a video going around from a forensic CPA showing the votes by county did not followed Benford's law, but he failed to look at the underlying population. I've written a little web-based simulation using the Georgia data to make it easy to play with the data to get a feel for why Benford's law does not work there [2]. Another way to tell when a deviation from Benford's law is not an indicator of election fraud is to look at what it would take to make the results fit Benford's law. If you can't find any reasonable way to adjust the votes to make it fit, then the lack of fit was not a fraud indicator. (And if you can find such an adjustment, it also needs to stay a Benford fit if you make minor changes to the voter turnout or the split). In the particular case of the 2020 US Presidential election, there is another thing about all of the purported proofs of Biden fraud by Benford: cherry picking. There are plenty of places where the precinct vote for Trump does not fit Benford and the Biden vote does. And there are plenty of places where neither the Biden nor Trump vote fits Benford's law. As you will see if you play with my Georgia simulator, when you have a situation where Benford's law does not apply even a small change in voter turnout or in a candidate's share can cause large changes in the first digit distribution. Because of this, and the large number of cities and counties we have in the US where the underlying population does not follow Benford, there is essentially a large randomness in the first digit distributions. [1] https://www.youtube.com/watch?v=etx0k1nLn78 https://www.youtube.com/watch?v=etx0k1nLn78 [2] https://github.com/tzs/georgia-benford-simulation https://github.com/tzs/georgia-benford-simulation