Life

Framing the Risk

We are back with Tversky and Kahneman. This time, it is about decision making based on how the risk appears to you. There is one problem statement with two choices. Two groups of participants were selected and given this but in two different formats.

Here is the question in the first format: imagine that the country is bracing for a disease that can kill 600 people. Two programs have been proposed to deal with the illness – program 1 can save 200 people, and program 2 gives 1/3 probability to save all and 2/3 chance to save none. Which of the two do you prefer? 72% of the people chose program 1.

The second group of participants was given the same problem with different framing. Program 3 will lead to 400 people dying, and program 4 has a 1/3 probability that none will die and 2/3 probability that all will die. 78% of the respondents chose program 4!

Risk aversion and risk taking

Identical problems, but the choices are the opposite! The first case sounded like saving lives, and the players chose what appears to be a risk-averse solution. In the second case, the options sounded like losing lives, and people were willing to take the risk and went for the probabilistic solution.

Tversky, A.; Kahneman, D., Science, 1981, 211, 453

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MtDNA Knows It All

You may know that our cell nuclei contain genomic DNA – parts of it possess the codes (genes) that determine all the traits. We obtain this from our parents through some combination.

Enter mitochondrial DNA (mtDNA). It is not your usual type. First, it lies inside mitochondria and not the cell nucleus. Second, it is inherited from the mother alone; fathers do not contribute. Third, it does not recombine. What is so special about this? Well, mtDNA has become the tracer molecule to study relationships between one individual to another.

The absence of recombination and bi-parenting inheritance made these molecules scientists’ pet for tracing the maternal ancestry of human beings. And they traced back thousands and thousands of years and ended up at a single mother who lived ca. 200,000 in Africa. She is called the Mitochondrial Eve. She was not the first human but became the meeting point (common ancestor) when human mtDNAs were all traced back.

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Tiktaalik, the Ancestor that Came out of the Water

If our great grandmother Lucy was the bridge between non-hominins and hominins, Tiktaalik was that extraordinary life that acted as the connection between fishes and four-legged animals. I know it’s not easy to digest that we had fish as our common ancestor!

On the one hand, it was a fish with scales and fins. Unlike the other fishes, Tiktaalik’s fins had bones (corresponds to an upper arm, forearm and wrist) that could enable them to come out from the water and walk. And it had lungs and grills. Above all, Tiktaalik was a fish with a neck.

In his book, the Inner Fish, Neil Shubin, the American palaeontologist and evolutionary biologist, narrates the journey to unearth nature’s best-kept secret for a long time (about 375 million years!) – discovering the missing transitional piece from the life in water to life on land. The possibility of transitional creatures was something Charles Darwin had predicted some 130 years before!

Lucy: wiki
Tiktaalik: wiki
How fins became limbs: nature
A Devonian tetrapod-like fish and the evolution of the tetrapod body plan: nature

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Top Risks Lead to Top Priorities

What should be our top priority in life? Well, it depends on the top risks in life. Depending on whom you ask this question, the answer may vary.

Top priorities

I suspect risk to life comes first. What else can come closer or even be ranked higher? To a large section of the world, it could simply be getting out of poverty. It can be so powerful that individuals may even risk their lives to achieve it for their families and future generations at least. Here, I assume that, at least for the people who read this post, the risk to life is the top one.

Top risks to life

What is the top risk to life? It could be diseases, accidents, extreme weather events, wars, terrorist attacks, etc. Let’s explore this further. According to the World Health Organization (WHO), diseases are the top 10 causes of death and are responsible for 32 out of the 56 million deaths in a year. That is about 60%, according to the 2019 data. And what are they?

Noncommunicable diseases occupied the top seven spots in 2019. Yes, that will change in 2020 and 21, thanks to the COVID-19 pandemic. Deaths due to the current pandemic can reach the top three in 2021, but getting into the top spot is unlikely, at least based on the official records.

The Oscar goes to

The unrivalled winner is cardiovascular diseases (CVDs) – heart attacks and strokes – which cost 18 mln lives in 2019. The risk factors include unhealthy diets, physical inactivity, smoking, and the harmful use of alcohol. And an early warning to watch out for is high blood pressure.

There are three ways to manage the top risk: 1) medication for blood pressure management, 2) regular exercise, and 3) getting into the habit of a healthy diet.

Top 10 causes of death: WHO

Cardiovascular diseases: WHO

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The Confound of Nature Versus Nurture

The outcome of the debate of nature versus nurture is a foregone conclusion. It confused people in the past, but we now know that the problem is an example of confounding. Vaci et al. have published a paper in 2019 in a longitudinal study tracking chess players throughout their careers. And the results showed the importance of numerical intelligence and deliberate practice to master and retain chess skills. Nonlinear interactions between the two suggest that intelligent people benefit more from practice.

The work looked at 90 chess players across their careers – the Elo rating and the number of tournament games played. Three levels of intelligence – verbal, figural and numerical – were followed but found that the numerical has the highest correlation to the performance.

The nonlinearity of behaviour means people of different ages climbed up the rating ladder differently. For 20-year olds, players with an IQ of 120 benefited more from the same amount of practice than ones with IQs of 100 at lower practice regimes. At that stage, more practice of both groups reduced the gap between their performances. At the very high levels of practice, the higher intelligent folks started deviating from others for better performance. The behaviour is represented in the schematic below.

The joint influence of intelligence and practice on skill development throughout the life span: PNAS

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The Probability of 100 posts

Reaching one hundred days is a milestone. The general focus of my posts over these days, and also likely in the near future, has been about understanding risks, differentiating them from perceived risks and making decisions in situations of uncertainty using prior information, also known as Bayesian thinking. It started from the misery of seeing how the responsible agents of society -journalists, the political leadership, or whoever influences the public – ignore critical thinking and present a distorted view of reality.

Probability and evolution

A subplot that is closely associated with probability and randomness is the topic of evolutionary biology. It is hard to comprehend, yet the truth about life is that it moved from one juncture to another through chance. Evolution is misleading if you view the probability from hindsight. Changes happen through random errors, but one at a time, so that every step in the process is a high-probability event. Indeed, getting an error at a specified location during the body’s 30 trillion cell divisions is close to zero, but getting one at an unspecified somewhere is close to one. In other words, the designer has deeper trouble explaining a move than a drunken gambler!

Biases and fallacies

Next up is our biases and fallacies. The title of this post already suggests two of them – survivorship bias and the fallacy of hindsight. The probability of delivering an uninterrupted string of 100 articles in 100 days is small, and I would never have chosen the present title had I missed a post on one of these days. Now that it happened (luck, effort or something else), I claim I’ve accomplished a low-probability event. As long as I have the power to change the blog title until the last minute, I am fine. But scheduling a post today, for 100 days from now, with a caption of 200 days, is risky and, therefore, not a wise thing to do if you are risk-averse.

Deteminism or probability

Why does the subject of probability matter so much when we can understand physical processes in a deterministic sense? We grew up in a deterministic world, i.e. a world that taught us about actions and reactions, causes and effects. However, we also deal with situations where the outcomes are uncertain, which is the realm of probability. The impact of lifestyle on health, growth of wealth in the market, action of viruses on people with varying levels of immunity, the possibility of earthquakes, droughts, the list is endless. You can argue that the complexity of variables and the gaps in the understanding demand stochastic reasoning.

Updation of knowledge and Bayesian thinking

However imperfect it may be, Bayesian thinking is second nature to us. You are watching an NBA match in the last seconds, and your team is trailing by a point. Your team gets two free throws. What is in your mind when Steph Curry comes in for those? Contrast that with Ben Simmons. It is intuitive Bayesian thinking. It is not a surprise that you are more at ease with Curry’s 91% success rate in free throws than Ben, who is at 60%. You may not remember those numbers, but you know it from gut feeling.

Yet, being rational requires constant training. Your innate Baysian is too vulnerable to biases and fallacies. You start missing the base rates, confuse the hypothesis given the evidence with evidence given the hypothesis, or overestimate the prior due to recency bias. Surviving the sea of probability is hard, fighting the wind of lies and the sirens of misinformation. So what do you prefer, put wax in the ears, tie tight to the mast or get the rational power, listen to the music, and persist the voyage?

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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

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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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Police and Colour Sensitivity

We continue the earlier post on interpreting data from an asymmetric sample space.

An estimated 9540 non-Hispanic black people died from police violence during 1980-2018, says a study published in The Lancet last year. In the same period, the number of non-Hispanic White people who met the same fate was 15,200. So, whites are more likely to die from police violence in the US. Right?

Yes, if the population of non-Hispanic blacks and non-Hispanic Whites in the US are equal. But that is not true. As per Wikipedia, the former accounts for 12.3% of the US population and the latter 61.5%. If there is no correlation between death and race, you would expect around 12.3% of deaths for blacks and 61.5% for whites. As that is not apparent from the numbers, we will calculate the odds.

The easier way to do this is to divide 9540 with 12.3 and 15,200 with 61.5 and take ratios. The numbers are 775.6 : 247.2 = 3.1 : 1. In plain English, a non-Hispanic black has a 3.1 times more chance to die from police violence than a non-Hispanic White.

Here we only considered how the mind works while interpreting data when the representation of groups is not symmetric. Studying the reason behind the disparity of either behaviour of people of certain races or the reaction of police in response was not the topic. Statistics rarely tell the cause, but it may suggest a problem that requires a solution.

Fatal Police Violence: The Lancet

Demography in the US: Wiki

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When a ‘feminist’ exposed our education

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Tversky and Kahneman, Psycological Review (1983)

As part of their study, Tversky and Kahneman gave this problem to 142 UBC undergrads to determine which of the two alternative options was more probable.

  • Linda is a bank teller.
  • Linda is a bank teller and is active in the feminist movement.

What is your answer?

The AND rule

Remember the AND rule? You did not need my post to know the rule; we have accepted it happily at school. 1) it appeared logical. 2) since the probability values are always less than or equal to 1, a product of P(A) and some other probability can never be more than P(A) because that other shall always be one or less. 3) Our teacher explained it graphically using Venn diagrams.

None of us had issues with any of these.

Judgements rooted deep 

Yet, 85% of the students selected the second option as the more probable!

Resemblance wins over Extensional

The scientists went to another group of students and asked to choose one statement from the following (far more explicit) options.

  • Argument 1 Linda is more likely to be a bank teller than a feminist bank teller as every feminist bank teller is a bank teller and some bank tellers are not feminists.
  • Argument 2 Linda is more likely to be a feminist bank teller than a bank teller because she resembles an active feminist more than she resembles a bank teller.

The students chose the second (65%) in the majority!

There are more examples of conjunction fallacy in our day-to-day lives. Who knows better to exploit this vulnerability of mind than your insurance agent, who can sell you the life insurance that covers deaths from terrorist attacks when you didn’t want to buy the normal one?

Interestingly, this fallacy is not restricted to stories that use rare but appealing words that trigger our imagination. Students were asked to bet on one of three sequences if a six-sided die, with four green faces and two red faces, is rolled 20 times.
1) RGRRR
2) GRGRRR
3) GRRRRR
Students overwhelmingly chose option 2, forgetting that option 1 is a subset of option 2!

Extensional versus intuitive reasoning: Tversky; Kahneman

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