Talk:US presidential elections 2020/Fraud allegations

"Benford law"
What follows does not resolve the controversy either way, it basically says that "Benford law" appears by itself insufficient.

Benford law is presumably to do with dependence of presumed probability distribution on scaling, like counting number of people, or of dozens of people, or hundreds of people. But in case at hand, it may give artifacts. I looked at Allegheny, PA data. Those come as election day votes, absentee ballots, totals for each candidate, and also numbers of registered voters and total numbers of those voted, per voting district. Plots of leading digit histograms of Biden and Trump totals are accurately presented in the article However, leading digits of both Biden on-the day votes and absentee votes (not the totals) look "as expected", falling down. While doing it with numbers of registered voters and total votes received give "wrong" shapes. This may be spurious, however. The thing is, that if we place numbers of total votes per district in boxes (corresponding to ranges of per-district votes), with ranges selected in hundreds of votes,

[0,99], [100, 199], [200,299],...,

then Trump numbers in those range boxes will look like

417, 334, 287, 139, 67, 42, 15, 10, 4, 4, 3, 0, 1

(so, in 417 districts Trump totals were in the 0 to 99 votes range, etc)

while Biden's

57, 246, 428, 325, 169, 53, 29, 7, 5, 3, 1, 0, 0

So, most Trump district are below hundred votes, followed by 100 to 200 votes; this produces lots of leading ones (in just under-100 boxes, leading digits are roughly equally distributed in Trump case, with 50 having leading 1). While for Biden, his districts mostly produced 200 to 400 votes with considerably less of under-100 districts (and there are just two leading ones in under-100 range). Number of over-1000 districts is small for both and can be ignored. So the apparent meaning is that Biden votes come from larger districts

As a test, I run counting with different number bases (I tried bases 5, 7, 11, 12,14, 16, 18), and leading numbers distributions tend to become "correct" -shaped for all, with a larger base. I am not sure what it is supposed to be "according to science" in different number bases, but effect of this on the leading digit is also kind of "scaling", so I suppose by the same logic, or its absence, it is supposed to have the same, 1/x kind of shape using any number base before taking leading digit? (Please correct me if I am wrong here...) --Resup (talk) 20:03, 8 November 2020 (UTC)


 * Benford's law makes two assumptions:
 * The values are randomly distributed over a range of multiple orders of magnitude.
 * Fraudsters are more likely to change the first digit in a number than other digits, i.e. adding or subtracting even figures like 100 or 200 votes / dollars.
 * I looks to me that 100 or 200 votes have been added to most Biden totals.
 * Correction: Actually the changes do not have to be even numbers. They can be random numbers in a certain range, as long the distribution is not normalized to match Benford's law.
 * This is what we need to do:
 * Put Trump and Biden numbers in a spreadsheet in increasing order, both in separate columns. (Ignore which district the came from.)
 * Compare the nth Trump count to the nth Biden count and calculate the %.
 * Plot % and log(n) for both counts.
 * We should see some discontinuity in the % plot.
 * Another test to do is to calculate the logarithm of each count and plot the distribution.
 * P.S. - Can you post a link to the Allegheny, PA data.
 * Update: I found the data here. Unfortunately I am unable to open the .xls file in LibreOffice. -- Petri Krohn (talk) 01:05, 9 November 2020 (UTC)
 * Progress: I converted the .xls file online to .numbers file for macOS. Unfortunately the Apple App Store did not allow me to download the latest version or any version of Numbers as I am still running Mojave. I tried following these instructions. Actually I may have "purchased" Numbers already in 2019 for some other Mac. Let's see how it works. Or I could use MATLAB, but I would still need to get the numbers out in .csv format. ... ....
 * Did not work. The .xlm file is in some Microsoft XML format that none of my applications or converters are able to parse or understand. Where did you get your raw data? -- Petri Krohn (talk) 02:47, 9 November 2020 (UTC)

Allegheny, PA, First digit tally, Base 16
This is base 16, not base 10 ! (Write all numbers in base 16, and investigate distribution of the leading digit, which now can be from 0 to 15, when that digit is written in the usual base-10 way).

What are we supposed to see here ? ---Resup (talk) 20:35, 8 November 2020 (UTC)

Column=2 Registered Voters

{1,288},{2,553},{3,261},{4,102},{5,40},{6,13},{7,12},{8,9},{9,10},{10,3},{11,6},{12,4},{13,7},{14,9},{15,6}

Column=3 DEM Joseph R. Biden/Kamala D. Harris Election Day

{0,7},{1,21},{2,44},{3,76},{4,158},{5,211},{6,201},{7,206},{8,143},{9,101},{10,58},{11,42},{12,28},{13,16},{14,4},{15,7}

Column=4 Absentee

{0,1},{1,297},{2,46},{3,50},{4,81},{5,59},{6,58},{7,96},{8,102},{9,92},{10,83},{11,84},{12,66},{13,80},{14,66},{15,62}

Column=5 Total Votes

{1,668},{2,86},{3,21},{4,14},{5,16},{6,23},{7,25},{8,33},{9,47},{10,50},{11,44},{12,62},{13,89},{14,75},{15,70}

Column=6 REP Donald J. Trump/Mike R. Pence Election Day

{0,15},{1,284},{2,115},{3,99},{4,85},{5,78},{6,86},{7,73},{8,67},{9,53},{10,75},{11,69},{12,64},{13,54},{14,56},{15,50}

Column=7 Absentee

{0,11},{1,356},{2,282},{3,213},{4,105},{5,68},{6,50},{7,41},{8,38},{9,25},{10,23},{11,27},{12,22},{13,16},{14,20},{15,26}

Column=8 Total Votes

{0,1},{1,386},{2,120},{3,65},{4,96},{5,71},{6,66},{7,68},{8,64},{9,63},{10,49},{11,54},{12,50},{13,60},{14,54},{15,56}

Column=9 LIB Jo Jorgensen/Jeremy Spike Cohen Election Day

{0,122},{1,204},{2,212},{3,175},{4,163},{5,135},{6,100},{7,73},{8,47},{9,32},{10,19},{11,13},{12,8},{13,9},{14,8},{15,3}

Best Biden places
{election day, absentee, total} for both. Note that Biden roughly doubles his election day result on the absentee count, while Trump does 1/2. --Resup (talk) 23:37, 8 November 2020 (UTC)

PITTSBURGH WARD 2 DIST 1 Biden {292,745,1037}; Trump {286,119,405}

OHIO DIST 3 Biden {309,610,919}; Trump {531,176,707}

MOON DIST 5 Biden {251,665,916}; Trump {787,265,1052}

N FAYETTE DIST 5 Biden {305,602,907}; Trump {940,267,1207}

ROBINSON DIST 9 Biden {222,657,879}; Trump {661,252,913}

N FAYETTE DIST 3 Biden {255,601,856}; Trump {703,208,911}

N FAYETTE DIST 2 Biden {298,552,850}; Trump {700,190,890}

MCCANDLESS WARD 6 DIST 3 Biden {178,641,819}; Trump {395,220,615}

MOON DIST 6 Biden {290,518,808}; Trump {803,233,1036}

PITTSBURGH WARD 4 DIST 7 Biden {441,343,784}; Trump {98,27,125}

OHIO DIST 2 Biden {150,600,750}; Trump {543,224,767}

PITTSBURGH WARD 2 DIST 2 Biden {176,557,733}; Trump {168,89,257}

S FAYETTE DIST 3 Biden {353,376,729}; Trump {578,113,691}

PINE DIST 5 Biden {205,512,717}; Trump {549,180,729}

PITTSBURGH WARD 14 DIST 31 Biden {152,551,703}; Trump {111,58,169}

MOON DIST 2 Biden {209,494,703}; Trump {537,182,719}

HAMPTON DIST 11 Biden {245,452,697}; Trump {609,131,740}

PITTSBURGH WARD 14 DIST 7 Biden {291,399,690}; Trump {47,12,59}

PITTSBURGH WARD 1 DIST 1 Biden {222,465,687}; Trump {121,59,180}

EDGEWOOD DIST 1 Biden {221,462,683}; Trump {82,24,106}