The Path to the Winner’s Fallacy
How a successful SARS-CoV-2 Virus response lead to the greatest misconceptions and conflicting international restrictions.
From the onset we have seen countries from the old continent take a stance aimed at protecting their most vulnerable citizens. Are the statistics we read a series of biased interpretations or just fallible measures?
Ironically the Grand Duchy of Luxembourg is now penalized by those exact same sovereigns for perusing measures taken before the first reported case. Might have to cherish the bad and can we defeat the Winner’s Fallacy or are we burdened to succumb?
Take the path from the curse to the cure, and discover the common missteps that would else lead you astray through the trails of disinformation.
Trump is right
Admittedly it can be cognitively unsettling to grant much credit to the author of The Art of the Deal when his economic-policy rational seems bounded by a Twitter word count. Despite the tariffs inefficacy and undue friction, credit when credit is due.
Initially mocked for non-sarcastically saying the U.S. would “have very few cases” (VOA) if it were simply to “stop testing”— it was then again equally astounding to see the Belgian authorities classify Luxembourg in the Orange Zone (RTBF) just weeks later.
Bitterly, for those returning from the Grand Duchy, it is recommended to self-quarantine and get tested when entering its neighbouring Kingdom. The 45th President of United States’ assessment was right when warning that testing is a double edged sword.
Without testing, or weak testing, we would be showing almost no cases. Testing is a double edged sword — Makes us look bad, but good to have!!!
Donald J. Trump (@realDonaldTrump)
Keep it simply surreal
Most political decisions in Belgium are famously confronted with the country’s complicated institutional interplay — with just 5 governments and 7 health ministers, the Federal Government is in the process of breaking the Guinness World Record for the longest time a government is in current affairs (in peacetime and measured post-election).
For just 11.5 million Belgians, they infamously beat Iraq and Cambodia with 541 days on record (in 2010) and are currently 122 days short of such performance. Drawing parallels with the acclaimed EU presidency role Belgium assumed at the time, the current lull in the bickering should leave sufficient time to focus on reigning in the health pandemic.
At least one would think so, until the Belgian Foreign Affairs Ministry establishes that quarantine and tests are called for upon returning from Luxembourg. Despite the ability to rely on medical doctors and epidemiologists, a quick statistics refresher may be overdue.
Lies, Damned Lies and Statistics
As we come to the winner’s fallacy, we start to tread carefully as we move from the descriptive statistics to interpretation. All taunting commentary aside, you will find some common missteps (enumerated below) do warrant your awareness.
Whereupon counsel on the other side was heard to explain to his client that there were three sorts of liars, the common or garden liar to be found anywhere and everywhere, the damnable liar who is fortunately rather a rara avis in decent society, and lastly the expert, who when giving evidence is always splendidly mendacious. — The Accountant (Lafferty Publications, 1886)
The four commandments
- Thou shall inspect the definitions
We see only a limited set of countries reporting total test numbers and tested individuals (Italy), case counts can hardly be ascribed to regions in instances where standards for public and privately administered tests differ (U.K.). - Thou shall not covet your neighbour’s test kit
In May, in the U.S. alone, over 200 different tests were applying for emergency approval (when the CDC required them to register for use approval). Aside from potential accuracy variability, back in February a Chinese study already found that nasal swabs identified fewer than 74 % of positive cases, at best. A peer-reviewed study on the accuracy of anti-body testing suggests further confirmatory testing is required. - Honour those at the front line
Many, including my younger brother, are not just working long shifts and taking risks, they are your best eyes and ears, observing appropriate best practices early on. Anecdotal reports from business leaders returning from Asia in January and taking measures are abound, ultimately it lead the Grand Duchy to complete the first equipment acquisition mid-February (two weeks before the first reported case). - Thou shall not take the name of statistics in vain
We need to leverage on a fresh pair of a eyes, and recognize that like having a bed made in the morning, your data housekeeping will have rigour fuel a data quality debate.
It’s all about Accuracy and Precision
We would be easily tempted to argue that, ultimately, it is only possible to determine the most appropriate measure ex-post. Luckily, we reminded of the difference between accuracy and precision.
Accuracy is the proximity of measurement results to the true value; precision is the degree to which repeated (or reproducible) measurements under unchanged conditions show the same results.
We remind the avid reader the tests constitute a proxy, which are inescapably imperfect, because of their possible imprecision (e.g. false negatives), and their inaccuracy (e.g. tested population subset is not representative).
We therefore argue that the evidence points to the Grand Duchy outranking it’s neighbouring Kingdom with respect to data accuracy.
A. Positive rate of around 3–12%
This has been reported by the WHO as benchmark of adequate testing
For Belgium (July 7th) it stood at 1.1 % and 0.9 % in Luxembourg (July 13th). (The lower the better)
B. The scale of testing compared to the scale of the outbreak
The daily number of tests (not individuals), indicative of testing efforts
Here Luxembourg not only outranks its neighbour it has the highest number of tests per million inhabitants in the world: 12,477. Belgium reported on the July 9th (four days prior) 659 tests.
The Winner’s Fallacy
Simply looking at the confirmed case count, which stood respectively at 93 and 11 for the Duchy and the Kingdom, ignores testing scale (Trump’s theorem), and corresponding proportionality.
Knowing Luxembourg tests inbound cross-border workers from Belgium, France and Germany, you would also understand that these non-residents can only further worsen the ratio.
The Curse
In the winner’s curse, participants to a competitive bidding assess the value of an item the best they can. Cognitive and emotional causes lead participants in an auction to overpay (price is higher than intrinsic value).
The Cognitive Bias
In a pursuit of valid measures, Luxembourg has become associated to dangers which would be as prevalent in those jurisdictions from where those exact warnings stem. We overpaid by implementing a large-scale testing programme to see our freedom curtailed.
The prize is the defeat of the opponent rather than the health of the populace. — Mark Beckwith, July 19th 2017, The Bishop’s Blog
The Cure
If we stop testing right now, we succumb to the winner’s fallacy. As we learn more about this viral threat, we will most certainly discover more efficient paths to ‘normality’ — until then, as even Trump proudly cites U.S. testing prowesses, it seems to be the best deal to reach our goal.
Many are stubborn in pursuit of the path they have chosen, few in pursuit of the goal. Friedrich Nietzsche
