Quote:Rule 19In an effort to keep the focus of the forum on gambling, Vegas, and math, comments of a political, racial, religious, sexual, or otherwise controversial nature are not allowed. We recommend taking such discussion elsewhere (Added 8/13/19).

However, since there is such significant betting on the election, that we do allow discussion of that. As a general rule, we allow mathematical and scientific discussion of anything, to include the election and the coronavirus. Such discussion must be of an academic nature. A good rule of thumb if a post about a sensitive topic is allowable if it does not betray the personal opinion of the poster.

With that out of the way, there is an accusation out there that the Michigan election results were faked as evidenced by allegedly not being in compliance with Benford's Law. Briefly, that suggests that the digits of numbers of a random nature tend to follow certain distributions. A good way to catch falsified numbers, for example on an income tax return, is if the digits do not follow expected distributions. Human beings are notoriously bad at randomizing without the aid of computers.

What got me interested in the topic was this post by Evenbob at DT, alleging the vote counts by county in Michigan were he says in part, "Applied to the election in MI, Biden’s vote numbers in do not match Benford’s law at a 99.999% level." I have surfed around a bit and the best argument I have found about this is There is Undeniable Mathematical Evidence the Election is Being Stolen at The Red Elephants. This articles makes a number of points, just one of them about Benford's Law. I will not endeavor to argue the other points here.

First, here is a list of the county by county election results in Michigan, which allegedly has the fake vote totals. At this time (10:47 AM Nov 9, 2020) 99% of the vote is in, so these totals can be expected to change slightly.

County | Biden | Trump | Total |
---|---|---|---|

Alcona County | 2,142 | 4,848 | 6,990 |

Alger County | 2,053 | 3,014 | 5,067 |

Allegan County | 24,447 | 41,381 | 65,828 |

Alpena County | 6,000 | 10,686 | 16,686 |

Antrim County | 7,289 | 9,783 | 17,072 |

Arenac County | 2,773 | 5,928 | 8,701 |

Baraga County | 1,475 | 2,512 | 3,987 |

Barry County | 11,804 | 23,473 | 35,277 |

Bay County | 21,718 | 30,919 | 52,637 |

Benzie County | 5,480 | 6,600 | 12,080 |

Berrien County | 37,438 | 43,518 | 80,956 |

Branch County | 6,161 | 14,066 | 20,227 |

Calhoun County | 28,417 | 35,900 | 64,317 |

Cass County | 9,122 | 16,686 | 25,808 |

Charlevoix County | 6,939 | 9,841 | 16,780 |

Cheboygan County | 5,435 | 10,171 | 15,606 |

Chippewa County | 6,651 | 10,682 | 17,333 |

Clare County | 5,199 | 10,861 | 16,060 |

Clinton County | 21,963 | 25,095 | 47,058 |

Crawford County | 2,612 | 4,955 | 7,567 |

Delta County | 7,605 | 13,206 | 20,811 |

Dickinson County | 4,569 | 8,469 | 13,038 |

Eaton County | 31,297 | 31,797 | 63,094 |

Emmet County | 9,662 | 12,135 | 21,797 |

Genesee County | 120,082 | 99,199 | 219,281 |

Gladwin County | 4,524 | 9,893 | 14,417 |

Gogebic County | 3,573 | 4,600 | 8,173 |

Grand Traverse County | 28,682 | 30,502 | 59,184 |

Gratiot County | 6,693 | 12,104 | 18,797 |

Hillsdale County | 5,883 | 17,037 | 22,920 |

Houghton County | 7,755 | 10,380 | 18,135 |

Huron County | 5,349 | 11,949 | 17,298 |

Ingham County | 94,221 | 47,640 | 141,861 |

Ionia County | 10,899 | 20,655 | 31,554 |

Iosco County | 5,371 | 9,760 | 15,131 |

Iron County | 2,493 | 4,216 | 6,709 |

Isabella County | 14,072 | 14,815 | 28,887 |

Jackson County | 32,004 | 47,381 | 79,385 |

Kalamazoo County | 83,674 | 56,823 | 140,497 |

Kalkaska County | 3,003 | 7,436 | 10,439 |

Kent County | 186,753 | 165,318 | 352,071 |

Keweenaw County | 672 | 862 | 1,534 |

Lake County | 2,288 | 3,946 | 6,234 |

Lapeer County | 16,368 | 35,480 | 51,848 |

Leelanau County | 8,793 | 7,915 | 16,708 |

Lenawee County | 20,916 | 31,539 | 52,455 |

Livingston County | 48,218 | 76,980 | 125,198 |

Luce County | 842 | 2,109 | 2,951 |

Mackinac County | 2,589 | 4,258 | 6,847 |

Macomb County | 225,561 | 264,535 | 490,096 |

Manistee County | 6,107 | 8,321 | 14,428 |

Marquette County | 20,465 | 16,287 | 36,752 |

Mason County | 6,802 | 10,207 | 17,009 |

Mecosta County | 7,373 | 13,265 | 20,638 |

Menominee County | 4,315 | 8,117 | 12,432 |

Midland County | 20,493 | 27,675 | 48,168 |

Missaukee County | 1,967 | 6,648 | 8,615 |

Monroe County | 32,975 | 52,710 | 85,685 |

Montcalm County | 9,703 | 21,815 | 31,518 |

Montmorency County | 1,628 | 4,171 | 5,799 |

Muskegon County | 45,508 | 44,544 | 90,052 |

Newaygo County | 7,874 | 18,864 | 26,738 |

Oakland County | 433,982 | 325,916 | 759,898 |

Oceana County | 4,944 | 8,892 | 13,836 |

Ogemaw County | 3,475 | 8,253 | 11,728 |

Ontonagon County | 1,391 | 2,358 | 3,749 |

Osceola County | 3,214 | 8,928 | 12,142 |

Oscoda County | 1,342 | 3,466 | 4,808 |

Otsego County | 4,743 | 9,779 | 14,522 |

Ottawa County | 64,566 | 100,511 | 165,077 |

Presque Isle County | 2,912 | 5,343 | 8,255 |

Roscommon County | 5,166 | 9,670 | 14,836 |

Saginaw County | 51,068 | 50,784 | 101,852 |

St. Clair County | 31,363 | 59,184 | 90,547 |

St. Joseph County | 9,262 | 18,128 | 27,390 |

Sanilac County | 5,966 | 16,194 | 22,160 |

Schoolcraft County | 1,589 | 3,090 | 4,679 |

Shiawassee County | 15,371 | 23,154 | 38,525 |

Tuscola County | 8,713 | 20,310 | 29,023 |

Van Buren County | 16,800 | 21,591 | 38,391 |

Washtenaw County | 157,130 | 56,241 | 213,371 |

Wayne County | 587,074 | 264,149 | 851,223 |

Wexford County | 5,838 | 12,102 | 17,940 |

Source: Michigan presidential results at politico.com.

Next, here are frequency figures of the first and second digits of, shall we say, random large numbers.

Digit | First digit expectations | Second digit expectations |
---|---|---|

0 | 0.00% | 11.97% |

1 | 30.10% | 11.39% |

2 | 17.61% | 10.88% |

3 | 12.49% | 10.43% |

4 | 9.69% | 10.03% |

5 | 7.92% | 9.67% |

6 | 6.69% | 9.34% |

7 | 5.80% | 9.04% |

8 | 5.12% | 8.76% |

9 | 4.58% | 8.50% |

Total | 100.00% | 100.00% |

The next three tables shall show the first digit frequency for total votes, Biden votes, and Trump votes, as well as the expected total by digit according to Benford's Law. I shall also state the chi square statistic and p value. The p value is the probability that random results would be less skewed that those observed.

Before I continue, an argument could be made that a total of 83 counties is not enough to apply the chi-squared test. This argument has some merit. The rule of thumb is there should be an expected total of each digit of at least 5. In this case, the expected total of nines is only 3.80. For the limited data, I can't think of a better test, but am all ears to ideas.

That said, here is the table for the first digit of total votes.

Digit | Count | Expectations |
---|---|---|

1 | 30 | 24.99 |

2 | 14 | 14.62 |

3 | 9 | 10.37 |

4 | 5 | 8.04 |

5 | 6 | 6.57 |

6 | 7 | 5.56 |

7 | 3 | 4.81 |

8 | 7 | 4.25 |

9 | 2 | 3.80 |

Total | 83 | 83.00 |

chi-squred statitistic = 6.110748

p value = 0.634828

Here is the table for the first digit of Biden votes.

Digit | Count | Expectations |
---|---|---|

1 | 15 | 24.99 |

2 | 17 | 14.62 |

3 | 9 | 10.37 |

4 | 8 | 8.04 |

5 | 11 | 6.57 |

6 | 9 | 5.56 |

7 | 5 | 4.81 |

8 | 4 | 4.25 |

9 | 5 | 3.80 |

Total | 83 | 83.00 |

chi-squred statitistic = 10.080136

p value = 0.259446

Here is the table for the first digit of Trump votes.

Digit | Count | Expectations |
---|---|---|

1 | 22 | 24.99 |

2 | 13 | 14.62 |

3 | 11 | 10.37 |

4 | 11 | 8.04 |

5 | 7 | 6.57 |

6 | 2 | 5.56 |

7 | 3 | 4.81 |

8 | 7 | 4.25 |

9 | 7 | 3.80 |

Total | 83 | 83.00 |

chi-squred statitistic = 9.134425

p value = 0.331083

All three p values look very normal. So, how about the second digits.

Here is the table for the second digit of total votes.

Digit | Count | Expectations |
---|---|---|

0 | 9 | 9.93 |

1 | 8 | 9.45 |

2 | 10 | 9.03 |

3 | 3 | 8.66 |

4 | 7 | 8.33 |

5 | 11 | 8.02 |

6 | 9 | 7.75 |

7 | 11 | 7.50 |

8 | 8 | 7.27 |

9 | 7 | 7.05 |

Total | 83 | 83.00 |

chi-squred statitistic = 7.33793

p value = 0.60198

Here is the table for the second digit of Biden votes.

Digit | Count | Expectations |
---|---|---|

0 | 7 | 9.93 |

1 | 12 | 9.45 |

2 | 8 | 9.03 |

3 | 8 | 8.66 |

4 | 10 | 8.33 |

5 | 8 | 8.02 |

6 | 8 | 7.75 |

7 | 8 | 7.50 |

8 | 9 | 7.27 |

9 | 5 | 7.05 |

Total | 83 | 83.00 |

chi-squred statitistic = 3.11012

p value = 0.95977

Here is the table for the second digit of Trump votes.

chi-squred statitistic = 3.11012

p value = 0.95977

Digit | Count | Expectations |
---|---|---|

0 | 14 | 9.93 |

1 | 9 | 9.45 |

2 | 8 | 9.03 |

3 | 8 | 8.66 |

4 | 6 | 8.33 |

5 | 4 | 8.02 |

6 | 14 | 7.75 |

7 | 7 | 7.50 |

8 | 6 | 7.27 |

9 | 7 | 7.05 |

Total | 83 | 83.00 |

chi-squred statitistic = 9.81754

p value = 0.36546

Bottom line is these election results look perfectly compliant with Benford's Law to me.

Of course, I welcome all comments and arguments to the contrary, so long as they are mathematical in nature and don't betray personal political opinions.

significant deviations from Benfords

Law in the election results for Biden.

If I remember correctly Mondale versus Reagan 84 resulted in defeat 49:1 statewide. How does Benfords law apply there.

I'm not of the mathematicians club so forgive me if that question is a stupid one

Quote:darkozTo apply Benfords law to this election would it not make sense to first examine results in other elections?

If I remember correctly Mondale versus Reagan 84 resulted in defeat 49:1 statewide. How does Benfords law apply there.

I'm not of the mathematicians club so forgive me if that question is a stupid one

I think it's a mathematical formula to determine if numbers were randomly generated as they would in counting vote totals in a county

Or

A human input a vote total for all the counties trying to use random numbers

Quote:EvenBobThis guy seems legit and he found

significant deviations from Benfords

Law in the election results for Biden.

Go to the 20 minute mark. Look at the rows for 4 and 5. The results are skewed because Biden has too many 4s and too few 5s. Now recall that this is a first digit test. Ask yourself: is it GOOD to replace 5s with 4s at the start of numbers when you're cheating and trying to win?

Quote:rdw4potus

Go to the 20 minute mark. Look at the rows for 4 and 5. The results are skewed because Biden has too many 4s and too few 5s. Now recall that this is a first digit test. Ask yourself: is it GOOD to replace 5s with 4s at the start of numbers when you're cheating and trying to win?

Is this in a foreign language? I have

zero math training.

Quote:EvenBobIs this in a foreign language? I have

zero math training.

If you don't

realize that 4<5

then how can

you say that

someone

seems legit?

Quote:sabreIf you don't

realize that 4<5

then how can

you say that

someone

seems legit?

From the comments section of the video:

Mathematician here. I'm afraid you've made a big mistake in this analysis by not first plotting a histogram of the magnitudes of the dataset. Looking at it, it seems this is very restricted. Almost all numbers come in at 4 or 5 digits. As a result, Benford's law would not be expected to fit well.

This problem then worsens as you look at specific areas, and renders your chi squared tests invalid.

In order to properly test against an expectation of Benford you need data which ranges nicely over several orders of magnitude.

Answer by the video author:

NEDL

12 hours ago

Hi, and many thanks for a thought-provoking comment. I am aware of these applicability limitations of the Benford's law. However, there are two redeeming counterarguments one can make here. First, all of the tests have at least 30 (and generally much more) observations for all digits, basically a textbook case for Chi-squared applicability. Some alternative tests like Kolmogorov-Smirnov or Kuiper would be most relevant in case of smaller datasets (Chi-squared has higher power in larger samples). Second, as for orders of magnitude, the data does span seven, with most coming in 3 to 5 digits (3 is actually more frequent than 5). The more important question is whether you would have expected such data to abide by Benford's law under the null. This can be evidenced by Monte Carlo simulations and past elections. I plan to do a second video on the topic later in the week, addressing most notable suggestions and comments, including yours (will certainly do histograms, Monte Carlo, past elections, second-digit tests, and, if time allows, alternative goodness-of-fit tests).

Aren't there ways of cheating to avoid being caught by Benfords law

Such as raising each county of Bidens total by the same exact amount.

It still generates a random number because you are adding the exact same number of votes to an already random numbers keeping them looking random.

Quote:EvenBobThis guy seems legit and he found

significant deviations from Benfords

Law in the election results for Biden.

That is a reasonable argument he makes and the guy does know how to perform statistical tests.

His smoking gun at the end of the video is Biden votes in 755 voting jurisdictions in what he calls Swing States. Here is his table.

Number | Actual | Expected |
---|---|---|

1 | 205.00 | 227.28 |

2 | 138.00 | 132.95 |

3 | 94.00 | 94.33 |

4 | 102.00 | 73.17 |

5 | 44.00 | 59.78 |

6 | 54.00 | 50.54 |

7 | 43.00 | 43.78 |

8 | 40.00 | 38.62 |

9 | 35.00 | 34.55 |

Total | 755.00 | 755.00 |

I did the math and he is right, the p value is 1.97%. There is a shortage of Biden vote totals that begin with 1 or 5 and a surplus that begin with a 4. However, the results of results this skewed or more is close to 2%. My response is 2% is not that low. You can slice and dice the data all kinds of ways and it won't be hard to find some test that has a value under 2%.

To make any accusations of voter fraud there should be evidence beyond a reasonable doubt and 2% is definitely more than enough to have reasonable doubt. At least to me.

Second, I don't necessarily buy that voting district voting populations make for a good Benford test. For example 21 out of Michigan's 83 counties have a voting total in the range of 12,080 to 18,135. That is 25.3% in that tight range. I suspect that given typical rural county sizes and population densities that there are a lot of counties that frankly look similar to each other, violating the assumption of independence in Benford's test.

To be more convinced, I'd like to see the same test applied to the same states but different years.

In conclusion, decent video and I don't dispute the math. However, I just don't agree that the results he presents look very fishy.

Quote:rdw4potusIf total ballots and total trump look normal, that's a pretty strong indication that the Biden count is real but odd. Manipulating the Biden vote requires manipulating the total ballots and/or the trump vote.

Can you give some numbers to back this up, please.

It is admissible at least in cases of showing fraud in a company’s financial statements.Quote:ssho88Can statistical findings based on Benford's Law be used as court evidence ? I mean any court case not specifically to US Election 2020 case.

To explore that further, I downloaded the entire USA spreadsheet and applied Benford's Law to the first and second digits of the populations of all 3,142 counties. The following table shows the number of counties by the leading digit in the population for 2019. The expected column shows the expected total per Benford's Law.

First Digit | Total | Expected |
---|---|---|

1 | 954 | 945.84 |

2 | 590 | 553.28 |

3 | 371 | 392.56 |

4 | 307 | 304.49 |

5 | 230 | 248.79 |

6 | 205 | 210.35 |

7 | 163 | 182.21 |

8 | 175 | 160.72 |

9 | 147 | 143.77 |

Total | 3142 | 3142.00 |

The result of a chi-squared test has a p value of 37.42%. So that looks very normal.

The next table does the same thing, but with the second digit in the population figures.

Second Digit | Total | Expected |
---|---|---|

0 | 377 | 376.03 |

1 | 328 | 357.84 |

2 | 355 | 341.92 |

3 | 322 | 327.80 |

4 | 307 | 315.17 |

5 | 302 | 303.76 |

6 | 324 | 293.38 |

7 | 284 | 283.89 |

8 | 274 | 275.15 |

9 | 269 | 267.06 |

Total | 3142 | 3142.00 |

A chi-squared test of this table has a p value of 68.59%. So again, it conforms with Benford very nicely.

https://www.cambridge.org/core/journals/political-analysis/article/benfords-law-and-the-detection-of-election-fraud/3B1D64E822371C461AF3C61CE91AAF6D

Quote:unJonI found this paper on Benford’s law as applied to elections. I haven’t had a chance to read more than the abstract so far. But wanted to link it here in case others are interested. It’s from 2017 so shouldn’t have a politically motivated conclusion as applied to current election.

Here is a more direct link. I skimmed the paper. It basically uses Benford to analyze some elections in the Ukraine that were suspected of being fixed. I suspect similar academic papers will be written about this election.

So far, I have yet to see anything in 2020 that fails a Benford test beyond a reasonable doubt.

a living and he found 'massive fraud' in

GA. You can skip the first half where he

mostly explains how this works.

Quote:EvenBobHere's a guy who does Benford's Law for

a living and he found 'massive fraud' in

GA. You can skip the first half where he

mostly explains how this works.

This guy just does an eyeball test of the results with statements like, "You can just tell there are a lot of anomalies in here." So I had to do a chi-squared test myself on his table of the first digit for Georgia. Here are the same tables he has at the 9:30 point.

This first table is the first digit of the Biden vote total in Georgia's 159 counties.

Digit | Count | Expectations |
---|---|---|

1 | 47 | 47.86 |

2 | 40 | 28.00 |

3 | 16 | 19.87 |

4 | 21 | 15.41 |

5 | 7 | 12.59 |

6 | 9 | 10.64 |

7 | 9 | 9.22 |

8 | 5 | 8.13 |

9 | 5 | 7.28 |

Total | 159 | 159.00 |

Here are the results of a chi-squared test:

chi-squred statitistic = 12.600898

p value = 0.126339

That p value is 1.14 standard deviations south of an 0.5 average.

Next, here is the same table for Trump votes.

Digit | Count | Expectations |
---|---|---|

1 | 43 | 47.86 |

2 | 36 | 28.00 |

3 | 12 | 19.87 |

4 | 15 | 15.41 |

5 | 9 | 12.59 |

6 | 17 | 10.64 |

7 | 9 | 9.22 |

8 | 9 | 8.13 |

9 | 9 | 7.28 |

Total | 159 | 159.00 |

chi-squred statitistic = 11.230501

p value = 0.188978

That p value is 0.88 standard deviations south of an 0.5 average.

With p values of 12.6% and 18.9% for the two tables, this is a little more skewed than expectations, but nothing that screams fraud. Show me something that is more than three standard deviations from expectations and I'll start to take fraud accusations seriously.

Quote:Wizardand I'll start to take fraud accusations seriously.

This is why statistical math is such a

joke. I have a friend in his 80's who

was a math teacher for 55 years and

still makes money tutoring on the

net. He wants nothing to do with

stat or probability math because

he says you can manipulate it to

say anything you want it to say.

Four people will come up with

four different conclusions using

the same input data. To him this

isn't real math, it's voodoo. I

understand now what he's talking

about. It's joke math.. Like the math

people who tell me you can't beat

roulette. I just smile and answer

'whatever you say' and go out and

beat it every time.

Quote:EvenBobThis is why statistical math is such a

joke.

I, too, throw tantrums when the stats don’t reaffirm my prior beliefs.

Quote:mcallister3200People interpret statistics however they want, not manipulate. The nation would be a lot less dumb if our educational system put students on a statistics and probability path rather than calculus path by default.

Mark Twain said 'There are three kinds of lies:

lies, damned lies, and statistics.' He was

mainly talking about political stats. I can

guarantee that if I post 10 different sources

for voter fraud using Benford, all the math

people here will say nope, their math is

wrong, nothing to see here. So there is

no point in even discussing it.

Wayne Allen Root, famous Vegas oddsmaker,

says the fix was in and a few insiders made

millions by betting Biden at the right minute.

Just before Fox called AZ for Biden, Trump's

odds of winning with bookmakers went all

the way to 8 to 1, and right then millions

worldwide was bet on Biden. After Fox

called AZ the odds went back to even

money immediately. Root says a few very

rich insiders knew the election was fixed

and took full advantage of it.

Quote:EvenBobMark Twain said 'There are three kinds of lies:

lies, damned lies, and statistics.' He was

mainly talking about political stats. I can

guarantee that if I post 10 different sources

for voter fraud using Benford, all the math

people here will say nope, their math is

wrong, nothing to see here. So there is

no point in even discussing it.

Wayne Allen Root, famous Vegas oddsmaker,

says the fix was in and a few insiders made

millions by betting Biden at the right minute.

Just before Fox called AZ for Biden, Trump's

odds of winning with bookmakers went all

the way to 8 to 1, and right then millions

worldwide was bet on Biden. After Fox

called AZ the odds went back to even

money immediately. Root says a few very

rich insiders knew the election was fixed

and took full advantage of it.

So now you're saying Fox is in on the fix? They were the only news organization to call AZ early, so I guess that's really the only way your story could possibly work. Wow, that's a very odd co-conspirator.

Quote:EvenBobMark Twain said 'There are three kinds of lies:

lies, damned lies, and statistics.' He was

mainly talking about political stats. I can

guarantee that if I post 10 different sources

for voter fraud using Benford, all the math

people here will say nope, their math is

wrong, nothing to see here. So there is

no point in even discussing it.

Wayne Allen Root, famous Vegas oddsmaker,

says the fix was in and a few insiders made

millions by betting Biden at the right minute.

Just before Fox called AZ for Biden, Trump's

odds of winning with bookmakers went all

the way to 8 to 1, and right then millions

worldwide was bet on Biden. After Fox

called AZ the odds went back to even

money immediately. Root says a few very

rich insiders knew the election was fixed

and took full advantage of it.

I had Biden at -130 bet the day before election. Election night when Florida was going Trump I tried to double down on Biden at +400. Couldn’t get it down though. There was a crazy swing in the market that I thought was an overreaction. It was.

Quote:EvenBobThis is why statistical math is such a

joke. I have a friend in his 80's who

was a math teacher for 55 years and

still makes money tutoring on the

net. He wants nothing to do with

stat or probability math because

he says you can manipulate it to

say anything you want it to say.

.

One of my favorite books is How To Lie With Statistics. It is on one of my bookshelves.

https://en.wikipedia.org/wiki/How_to_Lie_with_Statistics#:~:text=How%20to%20Lie%20with%20Statistics%20is%20a%20book%20written%20by,to%22%20articles%20as%20a%20freelancer.

Direct: https://www.youtube.com/watch?v=etx0k1nLn78.

people who are experts in the

field and they all say Benford's

Law used in elections is useless

because the "spread of orders of

magnitude" of the numbers

involved are not large enough.

It has to do with precinct size.

Precincts don’t have that much

size variation in them.

So that's that. Never mind.

Quote:WizardI just ran across a new video on Benford's Law and the 2020 Election by one of my favorite YouTubers, Matt Parker. He mainly looks at applying Benford's Law to the Chicago election results.

I just watched this as was going to post a link. Matt makes math fun and entertaining.

Quote:EvenBobI've read about 5 articles from

people who are experts in the

field and they all say Benford's

Law used in elections is useless

because the "spread of orders of

magnitude" of the numbers

involved are not large enough.

It has to do with precinct size.

Precincts don’t have that much

size variation in them.

So that's that. Never mind.

That is Matt's point in the video I just posted.

In my opinion a good place to start is to do a Benford test on the total population in each jurisdiction or the total voting population. Doing that in the various counties in Michigan or the combined United States seems to pass a Benford test. These are the only two regions I've done the test on. If that seems to indicate a natural spread in population numbers, it's fair to consider a Benford test on vote totals.

This is historic, I think it's the first time you've changed your position on something.

Quote:Wizard

This is historic, I think it's the first time you've changed your position on something.

I never had a position to change.

I had never heard of this stupid

'law' before I posted about it. I

just assumed it was true because

it had the word 'law' attached to

it. I should have realized that in

math 'law' is just a meaningless

word.

Quote:EvenBobI never had a position to change.

I had never heard of this stupid

'law' before I posted about it. I

just assumed it was true because

it had the word 'law' attached to

it. I should have realized that in

math 'law' is just a meaningless

word.

The word "law" in mathematics seems to mean something that is always true and self-evident. For example, the Commutative Law says that a+b=b+a. It's just obvious and fundamental. Not something that I think can be formally proven as it is part of the foundation on which math is built.

To be honest, I am now sure why Bedford's Law is a "law." It is a true statement, but it can be proven with logarithms. It seems more like a theorem to me. Perhaps one of the other math-heads on the forum can take this further.

Also what’s the deal with some people calling it math, and some people calling it maths, is that just like the thing where some people insist on inserting unnecessary “u’s” in inappropriate places after an o like color/colour, behavior/behaviour etc?

Quote:WizardIt seems more like a theorem to me.

It's a theory that says if the

numbers are just the right

kind of groupings, this

thing might work. Or not.

It's just more pretend

probability math that real

math people don't go near.

Quote:DRichOne of my favorite books is How To Lie With Statistics. It is on one of my bookshelves.

Fascinating book. Was required reading in a stats class I took in 1989. I really should re-read. Thanks!

Quote:WizardI just ran across a new video on Benford's Law and the 2020 Election by one of my favorite YouTubers, Matt Parker.

Thank you for sharing. I had not heard of Matt, but that was a great video. I'll certainly start diving through more.

So, at least as a check for the honesty of data coming from Wayne County, I thought I might take a look at the 2016 election ... and the results were "interesting" to say the least. First, they don't make it easy. Transparency laws require the data be published (eventually) but the data for Detroit was scanned as image data into a PDF which required OCR software to turn back into "real" data. And then a check to be sure the OCR didn't mess with too many data points. Finally I got this:

For President Trump the table looks like this (Wish I could show the graph, it's more informative)

Digit | Count | Expectations |
---|---|---|

0 | 22 | 0 |

1 | 252 | 350.7 |

2 | 137 | 205.2 |

3 | 164 | 166.5 |

4 | 153 | 112.9 |

5 | 145 | 92.3 |

6 | 89 | 77.9 |

7 | 94 | 67.6 |

8 | 59 | 59.6 |

9 | 50 | 53.4 |

As we can see the data looks a little wonky ... the first thing to notice is 22 precincts reported zero votes for President Trump ... virtually a statistical impossibility, even in Detroit ... but it appears the numbers my have been manipulated .... So we begin to wonder, since President Trump won Michigan in 2016, might his campaign have been manipulating the data?

Then we have a look at the data for Secretary Clinton ... and we find the data is totally wacked .... (again, the Excel chart shows it better)

Digit | Count | Expectations |
---|---|---|

0 | 0 | 0 |

1 | 92 | 350.7 |

2 | 179 | 205.2 |

3 | 279 | 166.5 |

4 | 232 | 112.9 |

5 | 163 | 92.3 |

6 | 107 | 77.9 |

7 | 64 | 67.6 |

8 | 33 | 59.6 |

9 | 16 | 53.4 |

Benford analysis shows that the data was clearly manipulated for Secretary Clinton, and probably for President Trump ... but it really doesn't indicate how the data was changed or who was supposed to be the beneficiary .... Thoughts?

You mean English English, as opposed to 'simplified English' for American's $:o)Quote:mcallister3200Are a “property” and “law” interchangeable terms in mathematics?

Also what’s the deal with some people calling it math, and some people calling it maths, is that just like the thing where some people insist on inserting unnecessary “u’s” in inappropriate places after an o like color/colour, behavior/behaviour etc?

Quote:pjt36

For President Trump the table looks like this (Wish I could show the graph, it's more informative)

Digit Count Expectations 0 22 0 1 252 350.7 2 137 205.2 3 164 166.5 4 153 112.9 5 145 92.3 6 89 77.9 7 94 67.6 8 59 59.6 9 50 53.4

As we can see the data looks a little wonky ... the first thing to notice is 22 precincts reported zero votes for President Trump ... virtually a statistical impossibility, even in Detroit ... but it appears the numbers my have been manipulated .... So we begin to wonder, since President Trump won Michigan in 2016, might his campaign have been manipulating the data?

Then we have a look at the data for Secretary Clinton ... and we find the data is totally wacked .... (again, the Excel chart shows it better)

Digit Count Expectations 0 0 0 1 92 350.7 2 179 205.2 3 279 166.5 4 232 112.9 5 163 92.3 6 107 77.9 7 64 67.6 8 33 59.6 9 16 53.4

May I see the raw data? I'd like to to a Bedford test on the total combined votes. I suspect this is a situation like Matt Parker described in Chicago where the precincts are so small and consistent in population that you expect first digit clumping.

Quote:EvenBobIt's a theory that says if the

numbers are just the right

kind of groupings, this

thing might work. Or not.

It's just more pretend

probability math that real

math people don't go near.

Well not really. It works anytime there is some exponential growth or power law that generates the numbers. It’s just a question of asking whether that assumption is applicable to a given situation. The neat thing is it pops up in unexpected places like a normal distribution does.

1st digit | 2nd digit | |||
---|---|---|---|---|

0 | 0 | 7 530 | 0.000% | 11.983% |

1 | 18 095 | 6 702 | 28.795% | 10.665% |

2 | 11 124 | 6 596 | 17.702% | 10.496% |

3 | 8 475 | 6 485 | 13.487% | 10.320% |

4 | 6 119 | 6 379 | 9.737% | 10.151% |

5 | 5 358 | 6 246 | 8.526% | 9.940% |

6 | 4 227 | 5 978 | 6.727% | 9.513% |

7 | 3 381 | 5 764 | 5.380% | 9.173% |

8 | 3 137 | 5 553 | 4.992% | 8.837% |

9 | 2 924 | 5 607 | 4.653% | 8.923% |

1st digit | 2nd digit | |||
---|---|---|---|---|

0 | 0 | 7 555 | 0.000% | 12.023% |

1 | 18 099 | 6 884 | 28.802% | 10.955% |

2 | 11 177 | 6 608 | 17.786% | 10.516% |

3 | 8 408 | 6 543 | 13.380% | 10.412% |

4 | 6 157 | 6 426 | 9.798% | 10.226% |

5 | 5 343 | 6 046 | 8.503% | 9.621% |

6 | 4 268 | 5 859 | 6.792% | 9.324% |

7 | 3 387 | 5 751 | 5.390% | 9.152% |

8 | 3 115 | 5 718 | 4.957% | 9.099% |

9 | 2 886 | 5 450 | 4.593% | 8.673% |

Quote:mipletHere are the 2016 Wayne county results. https://www.waynecounty.com/elected/clerk/november-8-2016-general.aspx

Just eyeballing this table of Wayne County election results in 2016, each precinct has total votes in the three digits. It is not going to be appropriate to apply Bedford's Law to such data.

Exactly the same issue as Matt Parker discussed about Chicago.

Charlie, if you have the vote totals in a spreadsheet, can you share them please.

miplet linked to the Wayne County data, but those are the scanned images (pita to work with)

You're almost certainly right that this data suffers the same shortcomings as Parker's analysis of Chicago

The Benford analysis for the Total vote in Wayne County shows a more reasonable Benford distribution, but you can see the spike at 2-3 from Secretary Clinton's returns easily overlayed, even on that curve.

Digit | Count | Expectations |
---|---|---|

0 | 0 | 0 |

1 | 296 | 350.7 |

2 | 151 | 205.2 |

3 | 192 | 166.5 |

4 | 153 | 112.9 |

5 | 101 | 92.3 |

6 | 92 | 77.9 |

7 | 64 | 67.6 |

8 | 58 | 59.6 |

9 | 58 | 53.4 |

I also had a look at 2016 precinct data from Los Angeles County (4500+ datapoints) and saw similar results .... though Secretary Clinton's graphed peaked at 5 there rather than 2.... But I suspect, again, that this data is similar to the Chicago and Detroit data. This will probably be true for any large metropolitan area as their precincts are more uniform in size. Statewide analysis at the precinct level may work, but this data's more likely to be "honest" as it includes large areas not controlled by any one political faction.

Finally, took a look at the "last two" digits for Secretary Clinton's returns which showed a similar "random" distribution as Parker's Chicago data.

---

edit: Let me just add here that the expected "random" distribution for the two digit trailing test should be 11.65 for any single instance but this does show spikes above 20 for 93 and 98 .... probably nothing :)

---

.....

So since we've apparently put the "Human Generated" manipulation issue to bed (or at least failed to demonstrate it via Benford), anyone want to have a look at the Edison Research data to see if the machines themselves have been compromised ;-P

---

2nd Edit: ... an interesting presentation by Dr. Shiva Ayyadurai addresses the "Machine" issue here;

MIT PhD Analysis of Michigan Votes Reveals Unfortunate Truth of US Voting Systems

.... One significant conclusion is that whatever the math, the systemic issues raised are real ... and if those aren't fixed, bookmakers are going to stop taking bets on elections.