Has Dr. Shiva Proven Michigan Voter Fraud?

A recent youtube video by Dr. Shiva Ayyadurai claims that precinct-level data in Michigan reveals voter fraud.  Dr. Shiva has a Ph.D. in biological engineering from MIT.  He has twice run for senate in Massachusetts as an independent, once after losing the Republican primary.  He also has some "interesting" views on other topics, as detailed on his Wikipedia page.

   

My favorite part of the video is when Dr. Shiva says that Michigan has "around 86 counties".  Why not just say 83, the actual number?

Dr. Shiva analyzed data from the four largest counties in Michigan (Wayne, Oakland, Macomb, and Kent).  He made scatterplots of the precinct data for each county, comparing the straight ticket percentage for Republicans to the difference between Trump percentage and R straight ticket percentage.

On the Oakland County plot, he drew a horizontal line segment, followed by a downward sloping line.  While this seems to fit the Oakland data, it doesn't fit the Kent or Macomb data any better than just a regression line.  The plotted lines slope downward.  He claimed that this is proof of votes being taken away from Trump.

Note that the three counties Dr. Shiva accuses of fraud use three different voting vendors.  His video isn't focused on Dominion Voting Systems--his theory would implicate all three vendors.

Matt Parker, a math popularizer, responded to Dr. Shiva.

He points out a serious mathematical error.  Dr. Shiva subtracts two percentages that don't come from the same population!  This results in nonsensical data.  As Parker points out, this subtraction isn't really necessary to make the point Dr. Shiva wants to make.  You can just find a correlation between R   straight party percentage and Trump percentage.  I did this for Kalamazoo County.

The correlation is quite strong, as we would expect.  Dr. Shiva is asserting that the proportions of Republican straight ticket voters and Trump voters among non-straight ticket voters should be about the same.  That is, the slope of the regression line should be (approximately) 1.  However, we find that the slope is actually less than 1.  Dr. Shiva claims that this is evidence of voter fraud--that an algorithm in the vote counting machine has flipped votes from Trump to Biden (while presumably not flipping straight ticket votes).  But is this assumption correct?

Parker points out that this assumption can be checked by plotting straight ticket D votes against Biden votes.  If Trump votes were flipped to Biden, those votes should show up in this plot, right?  But the slope of the regression line for this plot is also less than 1.

This disproves the vote-flipping theory.  But what is causing the slopes of both these plots to be less than 1?  Parker didn't try to answer this, but there is a reasonable explanation.  When a precinct leans heavily to one party, there will be more people who defect to the minority party than the reverse because there are more people in the majority party to defect.

Consider an example.  Say a precinct has 100 voters, 80 typically vote R and 20 typically vote D.  Say half of the voters of each party vote straight ticket, 40 R and 10 D.  Then the R percentage of straight ticket votes is 40/(40+10) = 80%.  Now say 10% of each party's non-straight ticket voters defect to the other party's candidate.  That would be 8 R and 2 D voters.  Then the non-straight ticket voters break down 40-8+2 = 34 R and 10-2+8 = 16 D.  The R percentage of non-straight ticket voters is 34/50 = 68% R, less than the 80% R straight ticket voters.

Feel free to construct your own example.  As long as the proportion defecting from each party is the same, you will find the same effect.  Thus there is a reasonable explanation for the fact that non-straight ticket votes are less partisan than straight ticket votes.  Dr. Shiva is mistaken.