# Claims of US election fraud: a comparison between straight- and split-ticket voters.

When data is manipulated using an algorithm, this can sometimes leave artefacts — tell-tale ‘footprints’ of the processing algorithm. For instance, if we take the modulus of the data (that is, remove the negative signs of the values), we will have a very sharp and distinct boundary at zero. This ‘sharp boundary’ could tell us that something that shouldn’t have been done was done with the data — or alternatively it could be the result of something entirely legit. We would need to dig deeper to find out. Other artefacts are created by linear interpolation, rounding up or correlations.

Recently, the rather colourful Dr Shiva Ayyudurai made the following claim: the more Republican a precinct is, the more votes are ‘taken away’ from Trump!

There are already very comprehensive posts on this topic by Naim Kabir and videos giving the finer detail, so I will only include a brief explanation. Ayyudurai considers the following two quantities in each precinct of a county:

and plots T-R against R. He gets a cloud of points clustered around a line of negative slope and claims this to be a sign of fraud — an ‘algorithm’ that ‘flips’ votes from Trump to Biden. Here is his plot for Oakland County in Michigan:

Ayyudurai’s first claim is that the difference T-R should stay approximately constant as R increases. Another way to put it is that R increases at approximately the same rate as T — the precincts in which Trump is more popular among straight ticket voters, he should also be more popular among split-ticket voters, and the two popularities should increase at the same rate. But why should that be the case? What is a split ticket vote anyway? We can break split ticket voters down into four categories:

(I) Straight Republican down-ticket, non-Trump for President (the so-called ‘never-Trumper’).

(II) Straight Democrat down-ticket, Trump for President.

(III) A mixture down-ticket, non-Trump for President.

(IV) A mixture down-ticket, Trump for president.

Ayyuderai’s quantity T is the percentage that II and IV form of the total of all four categories. But it is not at all clear why that must increase at the same rate as R increases. Suppose R is large. It is entirely conceivable that ‘never-Trumpers’ in Category I dominate split ticket votes, in other words Republicans in the counties Ayyduerai considers are particularly loyal to their local reps and less so to Trump. Because there is a plausible explanation this, on its own accord, is not proof of fraud.

Now, suppose R is small. T being small can be explained by Democrat voters who vote for Biden and go for a few non-Democrats down-ticket — in other words Category III.

Ayyuderai’s second claim relates to a very idiosyncratic choice of line fit to the data. He arbitrarily fits a broken line to a cloud of points and claims that when the horizontal segment of the line fit turns into a sloped one, there is a change in the trend. Supposedly ‘this is where the vote-switching algorithm kicks in’. But there is not enough data to justify fitting the horizontal segment. This is particularly true of his claim for Macomb County.

Ayyduerai’s third claim is regarding how ‘neat’ the point cloud is around the trend. He juxtaposes four counties: Wayne, in which there is a lot variation in the y-axis, against Oakland, Kent and Macomb, with the characteristic ‘downward trending’ cloud. He alleges the use of ‘a vote switching algorithm’ in the latter three instances.

What does this mean? Suppose T splits into two components, Ttrend and Tnoise. Ttrend increases as R increases (but, as we’ve seen, at a slower rate than R), whilst Tnoise is random noise independent of R. The claim amounts to stating that Tnoise has a far smaller variability than it should have.

This is perhaps easier resolved by considering a couple of examples. Ayyduerai claims that since points such as (R=50%, T-R=10%) are outside the point cloud, something is amiss. But for these values of T,R it must be that T=60% — so the share of Trump votes on split ballots has to be higher than the republican share on straight ballots. It is not a shock that this does not happen.

Let’s take another location outside the cloud — (R=60%, T-R=0%) — so that T=60%. Again, it is not very surprising that no precinct fits this profile — it seems to be the case that enough Trump voters vote straight ticket and enough Republican voters do not wish to vote Trump that this case never actually occurs. It is not evidence of fraud.

The Wayne county point cloud is indeed different. It has many more districts with very low Republican straight ticket vote, and very few districts with R greater than 15%. So the only thing that can be fairly compared between Wayne and Oakland/Kent/Macomb is the variation of T for small values of R. And here the difference is, indeed, striking: we observe T-R values of up to 60% for R-values of about 0–10% — meaning that in some precincts, a whopping 50–60% of split ticket voters went for Trump! Whilst in the other plots the T-R values are capped at 20%: showing clearly different split-ticket voter behaviour in heavy Democrat areas of Wayne.

This is to say that split-ticket voters in Democrat areas of the latter backed Trump to a much smaller extent than split-ticket voters in Democrat areas of the the other three. What the explanation for this is, and how the possible different demographics of those Democrat-heavy areas in Wayne might offer an insight is not something I can answer at the moment. However, this is not sufficient data on which to make allegations: it could be that if we considered every country in the US using this method then we would see a nice spread of differently shaped plots exhibiting the heterogeneity of the American electorate.

And what is more important, this is not even the allegation Dr Ayyuderai is making! He alleges the problem is with the algorithm taking away voters in the republican-heavy areas, he does not allege a problem in the democrat-heavy ones.

It furthermore is indicative when people do not pursue certain obvious avenues of enquiry. Dr Ayyuderai did not make any attempt to separate ‘split ticket’ voters into their very different subcategories and to verify which of those were contributing to the effect he was showing. He did not generalise his analysis to other counties and show how Oakland and Macomb were anomalous compared to the ‘typical’ county in the US. When someone contributes analysis as half-baked and incomplete as his to a court submission, one has to wonder whether he did not continue the analysis because it was not giving him the results he was looking for.

Dr Ayyudurai’s wider claims — building on this ‘analysis’ to allege Dominion using a voter’s race to weigh their vote — were part of the ‘Kraken lawsuit’ in Georgia. They were rejected by the intervenors, who noted that Dr Ayyudurai had no expertise to be dealing with the subject. More tellingly, they said:

“In metro areas around Georgia and the United States, white metro-area voters who typically vote for Republican candidates continued to do so in down-ballot races, but a number of them voted for the Democratic candidate in the presidential race. It is quite unclear what this pattern of split-ticket voting could possibly have to do with election fraud.”