I’m not one to stay up late watching an election count – let alone stay up even later to watch a US one (and I discourage the habit in my nearest and dearest). I always tell myself (wrongly, as you shall see) that the result will look just the same in the morning whether I follow it overnight or not. So a month ago on Wednesday 4th, by the time we were up, had breakfast and started looking at how it was going across the pond, it was past 8 o’clock in my (Greenwich) time zone (much the same time of day as it was when the household first learnt we’d won the Brexit referendum four years earlier).
At that moment, Trump was the bookies’ clear favourite to win. Browsing the election map for five or ten minutes, I saw why they were giving him such strong odds. The cumulative vote total graphs for each candidate in the swing states were curving over towards flatness and the gaps below Trump’s lines, above Biden’s, were sufficient. I started to get on with the day’s business, still glancing at the electoral map at times.
Then I saw the one of the four anomalous data points analysed in this article*. That is, I looked away from my computer screen momentarily, drank some more tea, looked back – and wondered if my (rather good!) memory for figures had abruptly failed me. What it said simply didn’t fit what I remembered when I’d started sipping my still-very-hot cup of tea.
It was an astonishing thing to see.
That was in Wisconsin. While I was still trying to check my memory, Michigan did the same, as another of the paper’s four anomalies hit. By 9 o’clock UK time, the bookies were rethinking things – and so was I. I did some work, then went out for a walk and got back around half-past eleven, just in time to see the last anomaly take effect in Michigan.
The linked analysis of these four events is very easy to read – or so say I, but for five years my work was researching aspects of statistical anomalies, so here is my summary for anyone who feels differently.
Batches of counted votes can be very unbalanced towards either candidate or they can be large, but there is a strong inverse relationship between the two. The paper analyses a lot of data to show the improbability of both very unbalanced and very large. This is a good test because it tends to get past fraudsters, who are focussed on the raw margin of votes more than the ratio or the batch size.
A secondary tell – and this one is already well-known in fraud detection in third-world countries – is improbable ratios of the losing candidate to minor candidates, e.g. Trump getting little more than twice as many votes as the minor candidates in the second Michigan anomaly when the state’s average (calculated including that data point) was 31 to 1. The paper finds this combination of grossly-violated size-margin ratio and grossly-violated Trump-to-third-party ratio particularly suspicious (as do I). It also computes what happens if you pull these four data points in towards merely the 99th percentile of the size-margin relationship – leaving them still anomalous but not so wildly implausible. (Biden loses his alleged lead in all three states.) It also notes some related statistical oddities.
My guess is that the idea of the US waking up to what I’d woken up to – Trump the heavy odds-on favourite – terrified his enemies. Their pre-election narrative was that Trump would at first ‘appear’ to win, after which ‘days and weeks of counting’ (Zuckerberg) would show he had lost. But while Zuckerberg promised to ‘educate’ America to believe in that, I think someone in the early hours of the 4th panicked that if the US electorate woke up to a bookies-call-it-for-Trump breakfast on Wednesday morning, that would never be erasable from the US mind, no matter how many votes they then ‘found’. So they made sure that didn’t happen. (You never know: it might yet be that what they did to prevent that becomes equally hard to remove from America’s consciousness. You don’t have to be a statistician to think a sudden step function in a smooth graph looks odd.)
So the good news is that my memory for numbers is working fine. The bad news is that I may lose a night’s sleep next election. The very first of the four anomalous points went into the Georgia vote totals soon after 6:30 AM my time – half-an-hour after the normal rising time of Donald Trump and Margaret Thatcher, I am told. (I guess the reason I’m not PM or president is that I’m usually asleep then.) When I first glanced at the results, I thought Georgia was surprisingly close given e.g. the Florida result, but if I’d missed the other three oddities as completely as Georgia’s, I’d have been far less cautious in reviewing the outcome.
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*FYI: the linked paper was easy to access this morning in the UK, but sometime before 9 o’clock eastern US time, it became hard to reach via the link above. (Massive interest overwhelming server, DoS attack, both, …? – Your guess is as good as mine.) You can try here. Another summary of it is here. (I’ll arrange a robust link if the problem does not clear.)
