January 2022

The Heuristics Fight Back

This post supports heuristics as a practical tool for decision making. The proponents of heuristics score a few points when it comes to managing firefighting situations or dealing with the world of randomness, where a deep subject knowledge offers no added advantage. Heuristics suffer from shortcomings that prevent them from helping the world pull out from its biases and fallacies. I will end this article with some observations that I found in the book by Gigerenzer et al.

What is Heuristics?

It is a method of solving practical problems without using extensive rational knowledge. While it is not random guesswork, it can be closer to making educated guesses. It uses the characteristic evolutionary traits of our species in responding to external stimuli. One popular book which comes closer to this description is Blink by Malcolm Gladwell.

Claims of Heuristics

Heuristics claims superior decision quality with a minimum amount of information. They frequently use the adjectives such as simple, practical, minimalist to describe the technique. I will focus on the book of Gigerenzer et al. in the rest of the post. The book is titled, The Simple Heuristics That Make Us Smart.

Toolkits and Workflows

The book opens with an example of managing heart attack victims with the help of a simple checklist. What you see in the list are a few simple questions. They included noting the patient’s systolic blood pressure, age, and heartbeats. Follow this short and sweet classification hierarchy, and you just made a decision.

The book conveniently ignores the origin of how those few vital parameters ended up on the list and what type of history-matching (not the so-called experience) done to those parameters. In other words, the checklist is not something the specialist made up at that moment, however appealing that thought could be. And it doesn’t ignore any quantitative information as the authors appear to claim. Each of the questions in the checklist suggests something about prior knowledge (data), the pillar of Bayesian thinking. It is like claiming pre-cooked meals as an invention to replace a complex cooking process. It is just an illusion to the customer; someone (or a machine) needed to cook somewhere.

Appeal to authority and Appeal to emotions

It is no coincidence that the authors fell into the trap that has been the main criticism against the heuristics – that they can not avoid logical fallacies. The first page itself gives two examples. Starting with a quote attributed to Isaac Newton:

Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.

Then comes the opening sentence:

A man is rushed to a hospital in the throes of a heart attack. The doctor needs to decide quickly whether the victim should be treated as a low-risk or a high-risk patient.

Simple Heuristics That Make Us Smart, Gerd Gigerenzer, Peter M. Todd, and the ABC Research Group

The subject did not require either of the two quoted statements to prove its point. Heuristics is a practical recipe in decision making.

Final verdict 

The book’s proposal to replace the first revolution (computing probabilities etc.) with the second one (adaptive toolbox with fast and frugal heuristics) is rejected! It is pure short-sightedness. Instead of abandoning probability, the alternative proposal may be to promote heuristics as a practical tool. And working side by side with its older sister is no shame.

The quote, “Truth is ever found …” is utter nonsense; sounds nice but far from the truth!

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The problem with Experience

Imagine this: a peaceful city of a million population wakes up with news of a murder. Its inhabitants, not used to such events, naturally get shocked and think of it as a failure of the establishment. The administration recruits a highly specialised cop from an area of another city notorious for criminals. The place was in such a bad shape that it had 10000 people and 100 criminals, and the officer had a lot of experience catching them.

The cop knows the strength of facial recognition systems as he had a high success rate in catching criminals in his old job. He trusts it was because of the high accuracy of the system, i.e. a 1% false-positive rate and a 100% true positivity (if you are a criminal, you are caught). Is recruiting the top cop a good strategy?

The answer depends on how much of the previous experience the cop was willing to forget and learn the reality of the new city. Look at, mathematically, the problem with his background. We use Bayes’ theorem.

Violent City: prevelance of criminal P(C) = 100/10000 = 0.01, P(+ve|C) = 1, P(+ve|nC) = 0.01, P(nc) = 1 – P(C). Chance of the person is a criminal given the facial recognition is matched, P(C|+ve) = (1 x 0.01) / [1 x 0.01 + 0.01 x 0.99] = 0.5 = 50%; he was right half the time.

Peaceful City: prevelance of criminal P(C) = 100/1000000 = 0.0001, P(+ve|C) = 1, P(+ve|nC) = 0.01, P(nc) = 1 – P(C). P(C|+ve) = (1 x 0.0001) / [1 x 0.0001 + 0.01 x 0.9999] = 0.01 = 1%.

The right level of experience

If the officer uses his experience and starts using a facial recognition system to randomly check people, expect him to catch 99 innocent for every potential criminal. Instead, he can use the tool as supporting evidence for those who are caught for other suspicious activities.

Now replace murder with drinking, facial recognition with a breath analyser. The results will be the same as long as the tool is employed for random checking – a lot of innocents are penalised.

The problem with Experience Read More »

The Fallacy of the Inverse

Let us start from where we ended yesterday, the P -> Q problem. Remember the truth table?

PQP -> Q
truetruetrue
truefalsefalse
falsetruetrue
falsefalsetrue

The way to read the truth table is:

If P is true, Q has to be true. It is called direct reasoning. Q false with P true is a violation of the rule, and therefore if Q is false, P has to be false (indirect reasoning). Finally, if P is not true, Q can be true or false. 

Re-look at the earlier rain problem – if it rains, I will take an umbrella. The only thing that is not possible is rain and no umbrella. The statement, it doesn’t rain now, and therefore, I should not have an umbrella [1] is not true; I can have an umbrella, whether it rains or not. Also, the statement, I am carrying an umbrella, and therefore it is raining [2] is also wrong.

The above statements numbered 1 and 2 mark two widespread logical errors. [1] is called the fallacy of the inverse. An example is: if it’s a dog, it has a tail. The fallacy is if it is not a dog, it can not have a tail. But what about a cat?

[2] is called the fallacy of the converse. An example is catholic priests are men. He is a man and, therefore, must be a catholic priest.

From the examples so far, it seems the inverse and converse errors are easy to spot and escape; until you reach more complex situations such as the equation of life! Yes, the Bayesian way of interpreting evidence. Take our famous example, suppose the probability of having a test is positive given the person has the disease (sensitivity of the equipment) is 95% or P(+|D). We know from our earlier discussions that this is just one variable in the equation. We need more data to estimate our ultimate quest, i.e. P(D|+) or the probability of having the disease given the test is positive. Yet, most people jump to conclude that the probability of getting the disease is 95%. Let’s re-phrase the equation to the PQ format. If the person has the disease, there is a 95% chance that the instrument will test +ve (P ->Q). But, the public presumes the converse, i.e. the device has tested +ve, and therefore the person has a 95% chance of having the disease, which is utter nonsense for a rare disease (low prior).

Rules of Inference

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Wason’s trials with logic

Suppose you are shown four cards, each with a number on one side and an alphabet on the other, kept on a table. The symbols on the card facing upwards are D, K, 3, 6. Then there is a rule that says if D is one side, the other side of the card is 3. Which two cards do you need to turn over to verify the rule?

Wason did this study in the 1960s with psychology and statistics students and found a large percentage of them suggesting the cards D and 3 as the leading choices to inspect. It is pointless to turn over 3 as there are no restrictions about what 3 can take on the other side; the rule is on D. The right answer is D and 6. Logical problems such as this are called formal logic as they are set up in certain forms of conditional statements (AND, OR, NOT, IF etc.).

According to Wason, these logics are of the form, if P then Q (P -> Q). P is called the antecedent, and Q is the consequent. The only violation of the rule (P -> Q) here is if P and not Q (P -> !Q). The other combinations, not P and Q (!P -> Q), and not P and not Q (!P -> !Q) are not violations.

To put some meaning to P and Q, consider this one: if it rains (P), I will take an umbrella (P) (P -> Q), the end of the statement. So what all can follow from this? If it doesn’t rain (!P), I may or may not take an umbrella and still, the rule is not broken (!P -> Q and !P -> !Q are possible). But, if it rains, I can not have a situation with no umbrella (P -> !Q is not possible) because I made that statement already. The truth table summarises all the arguments:

P
(rain)		Q
(umbrella)		P -> Q
TrueTrueTrue
TrueFalseFalse
FalseTrueTrue
FalseFalseTrue

Interestingly, these logics are easier to follow in real life. Imagine a simple instruction to the cashier at the shop counter: allow alcohol only if the person is above 18. The employee knows whom to watch out for – the people who carry alcohol to check out and those who appear below 18. Not the man who is holding apple juice. It is ecologic logic or logic in the real world.

Reasoning about a rule: Wason

Rationality: Steven Pinker

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A moth named Biston betularia

Industrial melanism is a term to familiarise. Biston betularia, the “poster moth” of evolution through natural selection, made this word immortal. You may call it a victim of the Industrial Revolution (or the coal pollution of England). However, the transformation of this humble creature provided the most powerful illustration of the theory of evolution and accelerated its inevitable journey towards becoming a theorem.

To give a brief background: Biston betularia is a type of peppered moth that had transformed from its pale (typica) form to black (carbonaria) in the last decades of the nineteenth century, coinciding with the industrial revolution in England. The hypothesis for the observed shift is that the pale varieties became prey to the bird predators as the former had become easily distinguishable on the blackened walls of industrialised cities of England, thanks to the coal revolution (and pollution). Accidental mutant varieties with black shades saved themselves from the lookout of the predators and became the most abundant species in the 20th century and continued until a few decades ago.

We have seen it before but repeating. Polymorphism is where two individuals differ in their DNA sequence, and the less common variant is present in at least one per cent of the people tested. The simplest type of polymorphism is when there is a single-letter change in a genetic sequence. That is called a Single Nucleotide Polymorphism (SNP).

Scientists have recently discovered the locations (the sequence and the genes) of the mutations that caused the change of colour from pale to dark. Further, analysis by statistical inference has found that the transposition happened around 1819, consistent with the actual observation of the change (from the dominance of the pale population to the black).

Noone sees its evolution!

The story of the peppered moth’s evolution is both fascinating and confusing. First, we need to realise that an individual white moth never transforms into a back one in its lifetime; the celebrated illustration (The Road to Homo Sapiens) of Rudolph Zallinger may tell you otherwise. It was a crime, though unknowingly, the artist committed against science that etched this faulty image – of an ape transforming into an upright man – permanently into the human psyche. Evolution is not a conscious conversion of one species to another. For example, the original white-moth-dominated society and the new black-dominated can easily have a hundred generations of separation.

Humans, the moths of glass sponges

We can see a moth’s evolution in front of us because a moth has a short lifetime – a few months at the maximum. In other words, given a few decades, we could see a few hundred life cycles of moths. Human evolution is not visible to humans because we can never see a thousand generations of ourselves unfolding before us. That is why we go after evidence, and science delivers. In doubt, ask a glass sponge who has survived this planet for 10,000 years!

The industrial melanism mutation in British peppered moths: Nature

Polymorphism: NIH

Longest surviving living organisms: wiki

The road to homo sapiens: wiki

A moth named Biston betularia Read More »

Simpson’s Paradox

Continue on the life of asymmetry. Following is the summary statistics of the admission data at Cambridge in 1996 in science, technology, engineering and mathematics (STEM). What is your conclusion?

Accepted
(women)		Accepted
(men)
Total274584

It doesn’t look good, isn’t it? A clear case of gender discrimination. Now, look at the data further.

Applied
(women)		Accepted
(women)		%Applied
(men)		Accepted
(men)		%
Total118427423.1247058423.6

No real difference in the percentage accepted.

Go further deep

Applied
(women)		Accepted
(women)		%Applied
(men)		Accepted
(men)		%
Computer
Science		267272285825
Economics240632651211222
Engineering164523297225226
Medicine416992457814024
Veterinary
Medi cine		33853161802212
Total118427423247058424

Now, this is interesting! Every department accepted a higher proportion of women who applied, yet the overall percentage favoured men. Known as Simpson’s paradox, this reversal of interpretation after accounting for confounding factors is something we should always pay attention to. In this case, women preferred more competitive departments with lower acceptance rates, whereas more men opted for engineering, which had better acceptance rates.

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Myopic Discounting

General preference for short term rewards as against deferred payoff is well known. We have already seen it from the tests done by Prof. Frederick. Subject’s selection for $100 now vs $140 a year later, 30 min massage in 2 weeks vs 45 min massage in November, $3400 this month vs $3800 next month; the list is endless.

The individuals who go for immediate rewards undervalue prizes that are achievable some time in future. Put it differently, they discount the value of the future payoff higher (if it’s money, higher than what is practically achievable from the market) and wait for increasing the benefit until it meets their criteria. The phenomenon is known as temporal discounting. In other words, people with high values of temporal discounting possess myopic discounting.

A study published in The Journal of Neuroscience (2010) used subjects with lesions in their prefrontal cortex to establish the role of the brain in discounting behaviour. Participants included 16 people with brain damage and 20 healthy, as evidenced by MRI and CT images of their brain.

The subjects were given various temporal discounting tasks involving fictitious incentives of money, food, vouchers etc. The results showed a remarkable difference between healthy subjects and the non-healthy. A higher discounting committed by people who damaged their medial orbitofrontal cortex (mOFC) of the brain suggests the importance of mOFC in having clarity about future outcomes in decision making.

Sellitto et al. The Journal of Neuroscience, December 8, 2010, 30(49):16429 –16436.

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It’s not (about) flu, mate

Ever since the pandemic started in early 2020, one thing that polarised society was the severity of covid19. On one extreme were people who panicked over getting infected, and on the other were people who considered it as another spell of flu. What is the truth? Now that we have loads of data, it should be easier to find it out.

What is risk?

There are multiple definitions for the word risk. One of them, more technical, we have seen earlier. It is the product of the likelihood of something to happen and the consequence. The second one is from the oxford learner’s dictionary. The possibility of something bad happening at some time in the future; a situation that could be dangerous or have a bad result.

Who was right?

At the moment, both parties had reasons to believe in what they thought – it was risky to some and not to others. In other words, the risk was not the same for everybody. Look at the wealth of data collected by the CDC on cases in the US.

Age
group		Total18-2940-4950-6465-7475-8485+
% in population10016.412.319.29.64.92
% infected10021.714.418.56.73.31.7
% died1000.8417.622.12627.7
population
(estimated)		33054.140.663.431.716.26.6
no of infected (mln)
(estimated)		7015.210.1134.72.31.2
no of deaths
(estimated)		0.850.0070.0340.150.190.220.23
infection rate
(%)		21.228.124.820.414.814.318
death rate!
(%)		0.260.010.090.250.61.33.3
death/death18-29
(any)		171947109284
death/death18-29
(infected) 		17.52690213441
! The death rate is not the case fatality rate, it is the actual death rate in the population due to covid

Risks are not equal. Take some absolute numbers: the chance of someone dying of covid 19 (entire 2020-21) was about 0.25%. That doesn’t tell the whole story – for an 85-year-old, it is 3.3%. Another way is to calculate the chance of dying after getting infected. Overall it is ca. 1.2%, but for an 85+, it is ca. 20%!

Another type of risk estimate is relative to a younger age group. The relative risk is ca. 300 for an 85+ (any) of dying of covid, whereas once infected, the relative risk of dying is ca. 450.

You are wrong, it’s not flu

Society is connected. Calculating risks based on the least-risky age group is not the way to understand a contagious disease. Once a least-risky person comes home (or a care home), he has every chance of passing it to elders, whose risk was at least two orders of magnitude higher than the giver. For a modern society based on care-for-others, this is not a behaviour to be proud of.

Infectious diseases will come and go. Scientists will also find out cures for present and future pandemics. But, what is sure to remain untreated is human irrationality and ignorance of risks and asymmetry of life.

Demographic trends of cases and death: CDC

Trends in cases: CDC

Risk of Covid19: CDC

It’s not (about) flu, mate Read More »

A bird in the hand

We all know this: “a bird in the hand is worth two in the bush”. It is a timeless proverb that cautioned generations against taking risks and, just as every other proverb, is a monument of simplicity and avoids every rational scrutiny of the present. Whether people believe in this saying or not, there exists a gap in us while estimating the time value of money.

That was what Prof. Shane Frederick found out in the famous Cognitive Reflection Tests (CRT) that he carried out while at MIT. One of his questions was whether the individual goes for $3400 this month versus $3800 next month. The majority of the subjects preferred 3400, leaving the option of getting more than 11% growth in a month. Now compare that with the 2% rate that the world’s best investor could give you!

The results say something about patience and appreciation about rewards at a future date. In that way, it is not so different from the Marshmallow kids!

While my focus was to highlight our attitude towards risk and deferred gratification, I can’t end this piece without quoting the famous 3-item cognitive reflection test. The questions are:

1) If a bat and ball together cost $1.10 in total. The bat costs $1.0 more than the ball. What is the cost of the ball?
2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
3) In a lake, there is a patch of lily pads. Every day, the patch doubles its size. If it takes 48 days for the patch to cover the entire lake, how long would it take to cover half?

The clue to these problems? SLOW DOWN.

Cognitive Reflection Test: Shane Frederick

A bird in the hand Read More »

The Vos Savant Problem

In my opinion, the Monte Hall problem was not about probability. It was about prejudices.

The trouble with reasoning

Logical reasoning has enjoyed an upper hand over experimentation due to historical reasons. Reasoners and philosophers commanded respect in society from very early history. It was understandable, and science, the way we see it today, was in its infancy. Experimentation and computation techniques did not exist. But we continued that habit even when our ability to experiment – physical or computational – has improved exponentially.

I have recently read an article on the Monty Hall problem, and in the end, the author remarked that the topic was still in debate. I wonder who on earth is still wasting their time on something so easy to find experimentally or by performing simulations. Make a cutout, collect a few toys, call your child for help, do a few rounds and note down the outcome. There you are and the great philosophical debate.

Thought experiments are thoughts, not experiments!

Thought experiments, if you can do some, are decent starting points to frame actual experiments and not the end in itself. The trouble with logical reasoning as the primary mode of developing a concept is that it creates an unnecessary but inevitable divide between a minority who could understand and articulate the idea and a large group of others. Evidence that emerges from experiments, on the other hand, is far convincing to communicate to people. The debate then shifts to the validity and representativeness of the experimental conditions and the interpretation of results.

Monte Hall is relevant

The relevance of the Monty Hall problem is that it tells you the existing deep-rooted prejudices and sexism in society. The topic should be discussed but not as an example for budding logical reasoning or the eloquence of mathematical language. If someone doubts the results, which is very ‘logical’, the recommendation should be to conduct experiments or numerical simulations and collect data.

Philosophy, like psychology, has played its role in the grand arena of scientific splendour as the main protagonist. The time has come for them to take the grandpa roles and give the space for experimentation and computation.

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