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Yesterday Shiva Ayyadurai tweeted a video in which he shows a piece of statistical evidence that he claims shows that a computer program was used to switch votes from Trump to Biden in Michigan. The explanation starts at about 18 minutes.

He analysed data from precincts in four counties, plotting the difference between the percentage of votes for Trump and the percentage of straight Republican ballots against the percentage of votes for Trump. In three of the four counties (Oakland, Macomb and Kent), there is a very clear negative correlation between the two values, and in Wayne County there doesn't seem to be much correlation. I haven't been able to find any critical analysis of this approach. He says this is evidence of electoral fraud.

Is there an innocent explanation for this pattern that Shiva Ayyadurai claims to find strange? It could be the case that this trend actually does exist, and this percentage differential decreases as more people vote a straight Republican ticket, but I wouldn't expect the correlation to be as strong as it looks here.

The explanation of analysis method as shown in the video: The explanation of analysis method as shown in the video

An example of what would Shiva Ayyadurai claims should be expected in a normal situation, as shown in the video: An example of what would be expected in a normal situation, as shown in the video

Results for Oakland County early voting:

Results for Oakland County early voting

Results for both early and election day voting in Macomb County: Results for both early and election day voting in Macomb County

Results for Wayne County (early and election day combined): Results for Wayne County (early and election day combined)

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    Wikipedia lists Shiva Ayyadurai as a " promoter of conspiracy theories and unfounded medical claims", so I'm going to bet "no". Seriously, are we going to have to refute every right-wing nutbar's personal theories as to how the "vote was stolen"? – DJClayworth Nov 11 '20 at 23:54
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    @DJClayworth: If they are widely believed, they are in-scope here. – Oddthinking Nov 12 '20 at 3:48
  • Part of the problem with the question is that it accepts Ayyadurai's claim that the pattern is strange. This very assumption is wrong: the pattern is exactly what you would expect. His claim relies on obfuscating–by the use of dodgy math–a pattern which is entirely expected and omitting to mention that the equivalent pattern for Biden votes looks exactly the same, totally undermining the claim. – matt_black Nov 16 '20 at 12:02
  • The link is to someone Twitter title claims to be the inventor of email, which should give some idea of his credibility. – Acccumulation Nov 16 '20 at 22:17
  • Also, I think that expecting people to sit through a more-than-an-hour-long video, that at least for me has trouble loading, to see what the "notable claim" is exactly is a bit much. – Acccumulation Nov 16 '20 at 22:55
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Mathematician Matt Parker did a video on this subject where he points out an error by omission (ie. cherry-picking) and an error in the analysis. When those are corrected, we see the expected strong correlation between voting by candidate and voting by party for both candidates.

Biden votes show the same effect

If this is evidence Trump votes are being switched to Biden, we should see the opposite effect for Biden votes. Biden votes should show an upward trend.

We don't, we see exactly the same effect, just shifted upwards. The shift doesn't matter, it's the slope that does.

enter image description here

Source

It's the slope that matters because what the graph is showing is that there is a strong correlation between candidate votes and party votes just as we'd expect, and just as Dr. Ayyadurai claims should be so, but inverted.

By showing only the Trump data, Dr. Ayyadurai is cherry-picking.

You cannot subtract percentages

They're inverted because of an elementary error in the analysis. You cannot subtract percentages unless you're sure the population sizes are the same. Dr. Ayyadurai subtracts the percentage of Wisconsin voters who voted for Trump by party vs those who vote for Trump by candidate. You can only subtract percentages if they're based on the same size population and this is not true for Wisconsin; percentages of party vs candidate voting there varies between about 45% and 80%.

Itachi0567 provides a good example for how this can go wrong. Consider a district with 1000 votes. 997 were GOP party votes. 2 were for Biden. 1 for Trump. That means voting by party is 100% Trump, but voting by candidate Trump gets 33%. Subtract them and you get -67%. By that logic, Trump got robbed in a district where he won 99.7% of the vote. The conclusion is flawed because it assumes the two populations are the same size.

If we're looking for a direct linear correlation between two variables we expect a line. The equation is Y = MX+B. Here X is GOP Votes / Party Votes, Y is Trump Votes / Candidate Votes, and M is how strongly they're correlated. Dr. Ayyadurai used (Trump Votes / Candidate Votes) - (GOP Votes / Party Votes) for his Y-axis which is effectively Y-X. This has the effect of inverting the slope.

y = mx + b
y - x = mx + b - x
y - x = (m - 1)x + b

y - x = (m - 1)x + b is what Dr. Ayyadurai graphed. m - 1 will cause a positive slope to go negative.

What should have been plotted is Trump Votes / Candidate Votes vs GOP Votes / Party Votes per district. When we do that, we see the expected strong correlation for both parties.

enter image description here

Source


Let's acknowledge the problem with these voter fraud analyses: they are fishing expeditions and subject to confirmation bias.

These fishing expeditions are fueled by Trump's unsupported claims of voter fraud. Trump claims there is evidence, but he has repeatedly shown none. And for most people that's the end.

Some people go hunting for evidence to support the conclusion ex post facto. These people may be well meaning, but are liable to be less critical of their analysis when it yields a positive result. This is yet another example.

An honest analysis of the integrity of US election would not presume an outcome, would not be hunting to prove a claim ex post facto, and would critically review their analysis. Such analyses have been conducted again and again and find no evidence for widespread voter fraud.

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    "You cannot subtract percentages unless you're sure the population sizes are the same." That's not really true. If 60% of the population support Biden, and 50% of the voters support Biden, it's perfectly valid to say that there's a 10% differential between voter and general population support for Biden. – Acccumulation Nov 16 '20 at 22:00
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    @Acccumulation The problem comes when you draw conclusions. If 95% of the population votes its evidence something odd has happened. If 10% of the population votes, maybe voters have a different preference than the general population. – Schwern Nov 16 '20 at 23:23
  • @Acccumulation I'll take a clear example from this comment on the video. Consider a district with 1000 votes. 997 were GOP party votes. 2 were for Biden. 1 for Trump. That means voting by party is 100% Trump, but voting by candidate Trump gets 33%. Subtract them and you get -67%. By that logic, Trump got robbed in a district where he won 99.7% of the vote. The flaw is assuming the two populations are the same size. – Schwern Nov 16 '20 at 23:24
  • I'm not objecting to the claim that the difference is, in this case, of limited meaning, but that the difference is in general not meaningful. – Acccumulation Nov 16 '20 at 23:26
  • @Acccumulation I'm not sure I understand what that means. Do keep in mind the maths lesson is in the context of rebutting the claim. Would you suggest a better way to express the problem with subtracting percentages? – Schwern Nov 16 '20 at 23:31
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So, I found this analysis. I will quote from it.

TL;DR: Shiva Ayyadurai makes an hypothesis (Democrats and Republicans are equally likely to vote down-ballot Republican and Republican President) and finds out that his hypothesis is wrong.


The main quantity Ayyadurai is concerned with is the difference between the % of votes for down-ballot Republican candidates vs. % of votes for the incumbent president, Donald J. Trump.

He shows that, the higher the percentage of Republican voters in a precinct, the more negative this difference is— i.e, there is a higher percentage of votes for Republican down-ballot candidates than there are for President Trump, the more Republican a precinct is.

According to the good doctor, the pattern you’d expect is this flat line:

[insert here the same image present in the question. not included to prevent an overly scroll-intensive answer]

To Dr. Shiva, this discrepancy is evidence of algorithmic foul play. To him, the negatively sloped line is evidence that the state of Michigan used the weighted voting feature of Dominion vote-tallying machines to steal votes from Trump and grant them to President-Elect Biden.

The thing is, the lad is just straight-up wrong. You wouldn’t expect a flat line at all: you’d expect the negatively sloping line, exactly as we see. The guy’s just making a wrong assumption in his analysis, leading to this wild conclusion. Let’s dig into why the above flat line would not be expected.

The author then goes on making a few assumptions to replicate the results:

Some assumptions that everyone can probably agree with:

  • Democrats are less likely to vote for Republican down-ballot candidates.
  • Democrats are (slightly) more likely to vote for Trump than they are for Republican down-ballot candidates [...]
  • Republicans are highly likely to vote for Republican down-ballot candidates.
  • Republicans are likely to vote for Trump, but less so than for down-ballot candidates [...]

Simple process: let's say you have two populations, D and R, each with a preference For down-ballot R candidates or Against, and also a preference For or Against the R president.

Let's model these as probabilities for downballot R candidates and for the R president like so:

[some code presented]

Using these probabilities, we can now simulate the voting outcomes of several precincts, with the fraction of Republican vs. Democrat voters randomly generated to get a good spread.

And now we plot the difference between down-ballot Republican votes and Trump votes, just as Dr. Ayyadurai does:

enter image description here

What’s going on?

To be honest, I didn’t have to simulate a damn thing to expect the above result. We can prove that we’d see a pattern like this given first principles.

The percentage mix of Republican vs. Democrat in each precinct just linearly combines their voting preferences. The higher the percentage of Republicans, the more influence over the vote counts you’d expect from them. The same goes for the converse case — the lower the percentage of Republicans, the higher the influence of Democratic vote preferences in vote tallies.

The act of dialing the percentage of Republicans up and down in a precinct is just blending these two extremes.

Let’s take a look at the extreme with 100% Democratic precincts:

enter image description here

Okay, and how about 100% Republican precincts?

enter image description here

Oh weird, and what do you get when we just smear from one set of points to another, as if you were blending relative influences of each group of voters?

enter image description here

What a surprise!

You’d expect this pattern any time Democrats are slightly more likely to vote Trump than they are to vote down-ballot Republicans, and if Republicans are more likely to vote down-ballot Republicans than they are to vote for Trump. No foul play involved, just two populations with voting preferences that get blended in each precinct based on relative size.

There would only be a flat line if the difference between likelihoods to vote down-ballot Republican and Republican President are exactly the same for Democrat and Republican voters. I’d never expect that, would you?

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    It would have been better to have had the y-axis not as a difference but as the individual Trump support. You might then have expected before seeing the data that the slope might be slightly upwards but not at 45 degrees. If you then take the difference you get the downward slope as shown, again not at 45 degrees – Henry Nov 12 '20 at 11:07
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    Good answer. Another way to think about it is that if a district has 100% of straight party ballots voting R, Trump can only perform worse among individual candidate voters. Conversely, if 0% of straight party ballots vote R, Trump can only perform better among individual candidate voters. In between is just an interpolation of the extremes, so the negative slope is wholly unsurprising. – Nuclear Hoagie Nov 12 '20 at 21:04
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Your original question said:

Is there an innocent explanation for this strange-looking pattern? It could be the case that this trend actually does exist, and that Republicans in predominantly Republican precincts are less enthusiastic about Trump than Republicans in predominantly Democratic precincts, but I wouldn't expect the correlation to be as strong as it looks here.

I understand that usually, discussion of clarifications of the question should be done as comments, but the massive amount of obfuscation involved in the original claim, as evidenced by you apparently not even understanding what the claim is, is an integral part of addressing the claims.

Suppose there are 1000 people in a precinct. 700 of them are planning on voting for Biden, and 300 are planning on voting for Trump. They get to the polling place, and the poll worker asks "Do you want to vote by candidate or by party?"

What this video is doing is taking the number of Trump voters who vote by candidate and dividing it by the total number of people who vote by candidate, then doing the same for those who vote by party. Then they're creating a graph whose x-axis is the second percentage, and the y-axis is the first percentage minus the second paragraph.

For example, suppose 400 Biden voters and 200 Trump voters vote by candidate. Then 300 Biden voters and 100 Trump voters vote by party. We take 100/(100+300) = 25%, and that's our x coordinate. We also take 200/(200+400) = 67% and subtract 25% to get 42%. That's our y coordinate.

Now suppose the numbers stay the same, except 100 Trump voters by candidate. Then we have 200/(200+300) = 40% for the x coordinate, and 40%-100/(100+400) = 20% for the y coordinate.

So by having more Trump supporters vote by party, the x coordinate increased, and the y coordinate decreased. In other words, we have a negative slope. So these graphs show exactly what we should expect. As more Trump voters choose to vote by party, this convoluted formula that is used to generate the y coordinate yields a smaller number.

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    Is this just repeating Matt Parker's analysis? – Schwern Nov 17 '20 at 4:36
  • @Schwern No. It's explaining in detail what the original claim is. And it's working through an example. – Acccumulation Nov 17 '20 at 6:29

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