Mark Siddall
November 4, 2020
Suppose there was something really important going on. This could be whether the fact that Trump is ahead in Pennsylvania and Georgia means we are doomed to another 4 years of his antics. Or, less partisan, what your chances of dying are if you happen to catch SARS CoV 2 in this now stronger second wave of infection. (We’ll leave aside for now whether the two items are related).
There is a ton of data out there you could parse to make a sensible estimate on both or either of those questions. With respect to Biden and Trump in Georgia, the New York Times has lots of information in the home-stretch on vote counts. Each of the CDC, Johns Hopkins and your local health department have data on COVID-19 outcomes.
At the time of my writing, Trump has 49.7% over Biden’s 49% of the vote in Georgia. You’d be forgiven for being despondent knowing that only 5% of the vote remains uncounted. But what really matters in terms of the outcome is just how many of those quarter-million or so yet-to-be counted votes should be expected to break for Biden.
Down the page, The Times dutifully reports under “Absentee votes for presidential candidates” that Biden is getting 52% of the absentee vote. A little back-of-the-napkin math shows convincingly that giving Biden 52% of the 250,000 remaining votes is not enough for him to prevail on those electoral college votes. So… time to focus on Pennsylvania? Maybe not!
Similarly, you might be at least a bit reassured that the US no longer has a 6% case-fatality rate for COVID-19. It’s reported as 2.5% at time of writing by the go-to national tracking site at Johns Hopkins. But a 2.5% case fatality is right about where Spanish flu was a century ago, so maybe it’s worth hiding inside a bit longer.
You will be relieved to hear that things are much better than they appear to be in both cases. And you would know this if you hadn’t developed a mental block in pre-calc.
Both of the quoted numbers are average rates of change, or cumulative numbers. That is to say, that over the course of the entire vote count so far, Biden has received 52% of the mail-in ballots in Georgia. That’s an average. Over the course of the entire pandemic 2.5% of cases in the US have died. That’s an average.
But neither of those reflect what is actually happening now.
In June, the case fatality rate was 6%. Now the average is 2.5%. But that includes the people from April through June! The current, or instantaneous rate at this moment, is really a lot closer to less than 1%, and that’s the number you really need to know. What your chance of dying has been if you got sick is interesting to your health insurance company. What you want to know is what your chances of dying are now if you got sick now. And the answer is waaaaay lower than the 2.5% being reported as a cumulative average.
You’re welcome!
So what about Biden in Georgia? The cumulative, or average, rate of absentee ballots breaking for Biden is too low for him to prevail. But the current instantaneous rate (over the last 100,000 votes counted) is actually closer to 68%. And if that holds or goes up, Biden will take Georgia with 49.8% of the vote leaving Trump with 48.9% and no grounds for a recount (has to be less than a 0.5% difference).
You’re welcome!
The reason both of these are true is because overall averages that you are being handed are only meaningful now if what is happening now is the same as what was happening before now. In truth, in both cases, things have changed. It’s not just you, I have gone blue in the face trying to get my fellow evolutionary colleagues to comprehend historical contingency. Karl Popper described the subjective interpretation of probabilities as “a strangely unsatisfactory theory of learning… It is a theory of diminishing returns” one that, as new information is acquired, “attributes an immense authority to our past” and “makes a revision practically impossible.”
Healthcare workers have gotten much better at keeping people alive. The average rate of survival over the pandemic is an underestimate of the current rate of survival and fails to capture the monumental strides made by talented and courageous people. The average number of mail-in votes going to Biden over the course of the last two days is an underestimate of the current rate because the rural votes have all been counted by now. What’s being counted now are the highly populous urban areas that break for Biden not at 52% but at 70%.
It’s a heterogenous world. And that’s why we had pre-calc and calculus.
Do the math, or the math does you.
UPDATE:
9 am November 5
As predicted, the percentages in GA continue to move in Biden’s direction. Fewer than 19,000 votes separate Biden and Trump. The GA Secretary of State Brad Raffensperger said that fewer than 25,000 votes remained to be counted. If true, and if Biden gets 68% of them as he has been, we’ll be in for a peach of a recount. However, if the reported 96% number of counted is correct, then there’s really more like 200,000 votes left to count. If Biden keeps getting 68% of those he’ll best Trump by something very close to what I described above.
There are many more blue urban votes left to count than there are red rural ones left to count. Taking all 24 Georgia counties that have not yet counted 95% of their votes, and allocating the outstanding votes according to the percentages (50% plus the margin) in the table gives Biden 20,000 more votes and Trump only about 8,500 more votes. That’s a net gain of 11,000 for Biden, not overcoming the 18,000 vote deficit he currently has. It’s gonna be close.
UPDATE:
9 am November 6
Biden has taken Georgia by a few hundred votes. Not the 250,000 needed to avoid a recount if Trump wants it. Meanwhile applying the same principles above to the Pennsylvania race suggests that Biden will easily overcome the current 5,500 vote deficit. Not by a lot.
UPDATE:
9 am November 7
Biden’s excess votes in PA currently only create a 0.43% margin. Not enough to avoid a recount. However, his current rate of accumulating votes suggests the final difference will be more like 0.67%. And we will be done.