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According to Wikipedia:

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.
...
It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature).

Beford's Law is not some universal phenomenon, and it failing to hold is not "proof" of fraud. For instance, we can play this game with the vote percentages that Donald Trump received in 2016: 11 first digit of 3, 19 first digit of 4, 16 first digit of 5, 9 first digit of , and 1 first digit of 7 (yes, this adds up to 56; some states don't assign electors based on state-wide totals, and there's also DC). Clearly, Trump's vote percentages were fraudulent! In the reddit thread, u/Three-Twelve says

In the case of the Milwaukee data and Detroit cited in the pictures above, the number of votes per voting area does not span over several orders of magnitude, so Benford's Law is not applicable.

The size of a precinct is likely a stronger predictor of the number of votes for Biden, than Biden's support is. If these people want to claim that this is evidence that the number of voters per precinct is not random, that would be more supported by the evidence, but also much more vacuous (it's hardly earth shattering news that some precinct sizes are preferred over others).

The amount by which a candidate's level of support predicts their vote count, compared to how well precinct size does, will increase the more that level of support varies (as a percentage of that support). Thus, if Biden's support varies between 90% and 95%, and Trump's varies from 5% to 10%, Biden's support is varying by a bit more than 5% (the math is a bit confusing, as this is a percentage of a percentage; 5% is a bit more than 5% of 90%), and Trump's support is varying by 100% (5% is 100% of 5%). So Trump's vote totals will vary more than Biden's, and thus Trump's totals will have more variance across orders of magnitude, and Beford's Law will be more applicable (note that Jo Jorgensen, who has even less support than Trump, has a distribution that is also closer to Benford). For an apples to apples comparison, we'd want to compare to places where Trump was the favored candidate, but those are rural areas, and I would expect precinct sizes to vary more in rural areas than in cities.

The Wikipedia article further says:

Based on the plausible assumption that people who fabricate figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results.

Biden's distribution is consistent neither with Benford, nor with a uniform distribution. It is, however, a very good fit for a Poisson or lognormal distribution.

Whenever you have a statistical analysis, it's important to remember that the what it can tell you is that the observed data is unlikely given your null hypothesis. Going from that to that the null definitely is false requires further justification, and assuming that because the null is false that means that your favored alternative is true is a false dichotomy. If someone has a model in which this voting data is unlikely, all that is an argument for is that their model is false. Democrats engaging is fraud is just one possible way the model could be false.

According to Wikipedia:

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.
...
It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature).

Beford's Law is not some universal phenomenon, and it failing to hold is not "proof" of fraud. For instance, we can play this game with the vote percentages that Donald Trump received in 2016: 11 first digit of 3, 19 first digit of 4, 16 first digit of 5, 9 first digit of , and 1 first digit of 7 (yes, this adds up to 56; some states don't assign electors based on state-wide totals, and there's also DC). Clearly, Trump's vote percentages were fraudulent! In the reddit thread, u/Three-Twelve says

In the case of the Milwaukee data and Detroit cited in the pictures above, the number of votes per voting area does not span over several orders of magnitude, so Benford's Law is not applicable.

The size of a precinct is likely a stronger predictor of the number of votes for Biden, than Biden's support is. If these people want to claim that this is evidence that the number of voters per precinct is not random, that would be more supported by the evidence, but also much more vacuous (it's hardly earth shattering news that some precinct sizes are preferred over others).

The amount by which a candidate's level of support predicts their vote count, compared to how well precinct size does, will increase the more that level of support varies (as a percentage of that support). Thus, if Biden's support varies between 90% and 95%, and Trump's varies from 5% to 10%, Biden's support is varying by a bit more than 5% (the math is a bit confusing, as this is a percentage of a percentage; 5% is a bit more than 5% of 90%), and Trump's support is varying by 100% (5% is 100% of 5%). So Trump's vote totals will vary more than Biden's, and thus Trump's totals will have more variance across orders of magnitude, and Beford's Law will be more applicable (note that Jo Jorgensen, who has even less support than Trump, has a distribution that is also closer to Benford). For an apples to apples comparison, we'd want to compare to places where Trump was the favored candidate, but those are rural areas, and I would expect precinct sizes to vary more in rural areas than in cities.

The Wikipedia article further says:

Based on the plausible assumption that people who fabricate figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results.

Biden's distribution is consistent neither with Benford, nor with a uniform distribution. It is, however, a very good fit for a Poisson or lognormal distribution.

According to Wikipedia:

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.
...
It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature).

Beford's Law is not some universal phenomenon, and it failing to hold is not "proof" of fraud. For instance, we can play this game with the vote percentages that Donald Trump received in 2016: 11 first digit of 3, 19 first digit of 4, 16 first digit of 5, 9 first digit of , and 1 first digit of 7 (yes, this adds up to 56; some states don't assign electors based on state-wide totals, and there's also DC). Clearly, Trump's vote percentages were fraudulent! In the reddit thread, u/Three-Twelve says

In the case of the Milwaukee data and Detroit cited in the pictures above, the number of votes per voting area does not span over several orders of magnitude, so Benford's Law is not applicable.

The size of a precinct is likely a stronger predictor of the number of votes for Biden, than Biden's support is. If these people want to claim that this is evidence that the number of voters per precinct is not random, that would be more supported by the evidence, but also much more vacuous (it's hardly earth shattering news that some precinct sizes are preferred over others).

The amount by which a candidate's level of support predicts their vote count, compared to how well precinct size does, will increase the more that level of support varies (as a percentage of that support). Thus, if Biden's support varies between 90% and 95%, and Trump's varies from 5% to 10%, Biden's support is varying by a bit more than 5% (the math is a bit confusing, as this is a percentage of a percentage; 5% is a bit more than 5% of 90%), and Trump's support is varying by 100% (5% is 100% of 5%). So Trump's vote totals will vary more than Biden's, and thus Trump's totals will have more variance across orders of magnitude, and Beford's Law will be more applicable (note that Jo Jorgensen, who has even less support than Trump, has a distribution that is also closer to Benford). For an apples to apples comparison, we'd want to compare to places where Trump was the favored candidate, but those are rural areas, and I would expect precinct sizes to vary more in rural areas than in cities.

The Wikipedia article further says:

Based on the plausible assumption that people who fabricate figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results.

Biden's distribution is consistent neither with Benford, nor with a uniform distribution. It is, however, a very good fit for a Poisson or lognormal distribution.

Whenever you have a statistical analysis, it's important to remember that the what it can tell you is that the observed data is unlikely given your null hypothesis. Going from that to that the null definitely is false requires further justification, and assuming that because the null is false that means that your favored alternative is true is a false dichotomy. If someone has a model in which this voting data is unlikely, all that is an argument for is that their model is false. Democrats engaging is fraud is just one possible way the model could be false.

Source Link
Acccumulation
  • 2.7k
  • 1
  • 13
  • 18

According to Wikipedia:

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.
...
It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which is common in nature).

Beford's Law is not some universal phenomenon, and it failing to hold is not "proof" of fraud. For instance, we can play this game with the vote percentages that Donald Trump received in 2016: 11 first digit of 3, 19 first digit of 4, 16 first digit of 5, 9 first digit of , and 1 first digit of 7 (yes, this adds up to 56; some states don't assign electors based on state-wide totals, and there's also DC). Clearly, Trump's vote percentages were fraudulent! In the reddit thread, u/Three-Twelve says

In the case of the Milwaukee data and Detroit cited in the pictures above, the number of votes per voting area does not span over several orders of magnitude, so Benford's Law is not applicable.

The size of a precinct is likely a stronger predictor of the number of votes for Biden, than Biden's support is. If these people want to claim that this is evidence that the number of voters per precinct is not random, that would be more supported by the evidence, but also much more vacuous (it's hardly earth shattering news that some precinct sizes are preferred over others).

The amount by which a candidate's level of support predicts their vote count, compared to how well precinct size does, will increase the more that level of support varies (as a percentage of that support). Thus, if Biden's support varies between 90% and 95%, and Trump's varies from 5% to 10%, Biden's support is varying by a bit more than 5% (the math is a bit confusing, as this is a percentage of a percentage; 5% is a bit more than 5% of 90%), and Trump's support is varying by 100% (5% is 100% of 5%). So Trump's vote totals will vary more than Biden's, and thus Trump's totals will have more variance across orders of magnitude, and Beford's Law will be more applicable (note that Jo Jorgensen, who has even less support than Trump, has a distribution that is also closer to Benford). For an apples to apples comparison, we'd want to compare to places where Trump was the favored candidate, but those are rural areas, and I would expect precinct sizes to vary more in rural areas than in cities.

The Wikipedia article further says:

Based on the plausible assumption that people who fabricate figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results.

Biden's distribution is consistent neither with Benford, nor with a uniform distribution. It is, however, a very good fit for a Poisson or lognormal distribution.