# Tag: Probability

### “[K]nowledge is indeed highly subjective, but we can quantify it with a bet. The amount we wager shows how much we believe in something.”

— Sharon Bertsch McGrayne

The quality of your life will, to a large extent, be decided by whom you elect to spend your time with. Supportive, caring, and funny are great attributes in friends and lovers. Unceasingly negative cynics who chip away at your self-esteem? We need to jettison those people as far and fast as we can.

The problem is, how do we identify these people who add nothing positive — or not enough positive — to our lives?

Few of us keep relationships with obvious assholes. There are always a few painfully terrible family members we have to put up with at weddings and funerals, but normally we choose whom we spend time with. And we’ve chosen these people because, at some point, our interactions with them felt good.

How, then, do we identify the deadweight? The people who are really dragging us down and who have a high probability of continuing to do so in the future? We can apply the general thinking tool called Bayesian Updating.

Bayes's theorem can involve some complicated mathematics, but at its core lies a very simple premise. Probability estimates should start with what we already know about the world and then be incrementally updated as new information becomes available. Bayes can even help us when that information is relevant but subjective.

How? As McGrayne explains in the quote above, from The Theory That Would Not Die, you simply ask yourself to wager on the outcome.

Let’s take an easy example.

You are going on a blind date. You’ve been told all sorts of good things in advance — the person is attractive and funny and has a good job — so of course, you are excited. The date starts off great, living up to expectations. Halfway through you find out they have a cat. You hate cats. Given how well everything else is going, how much should this information affect your decision to keep dating?

Quantify your belief in the most probable outcome with a bet. How much would you wager that harmony on the pet issue is an accurate predictor of relationship success? Ten cents? Ten thousand dollars? Do the thought experiment. Imagine walking into a casino and placing a bet on the likelihood that this person’s having a cat will ultimately destroy the relationship. How much money would you take out of your savings and lay on the table? Your answer will give you an idea of how much to factor the cat into your decision-making process. If you wouldn’t part with a dime, then I wouldn’t worry about it.

This kind of approach can help us when it comes to evaluating our interpersonal relationships. Deciding if someone is a good friend, partner, or co-worker is full of subjective judgments. There is usually some contradictory information, and ultimately no one is perfect. So how do you decide who is worth keeping around?

Let’s start with friends. The longer a friendship lasts, the more likely it is to have ups and downs. The trick is to start quantifying these. A hit from a change in geographical proximity is radically different from a hit from betrayal — we need to factor these differently into our friendship formula.

This may seem obvious, but the truth is that we often give the same weight to a wide variety of behaviors. We’ll says things like “yeah, she talked about my health problems when I asked her not to, but she always remembers my birthday.” By treating all aspects of the friendship equally, we have a hard time making reasonable estimates about the future value of that friendship. And that’s how we end up with deadweight.

For the friend who has betrayed your confidence, what you really want to know is the likelihood that she’s going to do it again. Instead of trying to remember and analyze every interaction you’ve ever had, just imagine yourself betting on it. Go back to that casino and head to the friendship roulette wheel. Where would you put your money? All in on “She can’t keep her mouth shut” or a few chips on “Not likely to happen again”?

Using a rough Bayesian model in our heads, we’re forcing ourselves to quantify what “good” is and what “bad” is. How good? How bad? How likely? How unlikely? Until we do some (rough) guessing at these things, we’re making decisions much more poorly than we need to be.

The great thing about using Bayes’s theorem is that it encourages constant updating. It also encourages an open mind by giving us the chance to look at a situation from multiple angles. Maybe she really is sorry about the betrayal. Maybe she thought she was acting in your best interests. There are many possible explanations for her behavior and you can use Bayes’s theorem to integrate all of her later actions into your bet. If you find yourself reducing the amount of money you’d bet on further betrayal, you can accurately assume that the probability she will betray your trust again has gone down.

Using this strategy can also stop the endless rounds of asking why. Why did that co-worker steal my idea? Who else do I have to watch out for? This what-if thinking is paralyzing. You end up self-justifying your behavior through anticipating the worst possible scenarios you can imagine. Thus, you don’t change anything, and you step further away from a solution.

In reality, who cares? The why isn’t important; the most relevant task for you is to figure out the probability that your coworker will do it again. Don’t spend hours analyzing what to do, get upset over the doomsday scenarios you have come up with, or let a few glasses of wine soften the experience.

Head to your mental casino and place the bet, quantifying all the subjective information in your head that is messy and hard to articulate. You will cut through the endless “but maybes” and have a clear path forward that addresses the probable future. It may make sense to give him the benefit of the doubt. It may also be reasonable to avoid him as much as possible. When you figure out how much you would wager on the potential outcomes, you’ll know what to do.

Sometimes we can’t just get rid of people who aren’t good for us — family being the prime example. But you can also use Bayes to test how your actions will change the probability of outcomes to find ways of keeping the negativity minimal. Let’s say you have a cousin who always plans to visit but then cancels. You can’t stop being his cousin and saying “you aren’t welcome at my house” will cause a big family drama. So what else can you do?

Your initial equation — your probability estimate — indicates that the behavior is likely to continue. In your casino, you would comfortably bet your life savings that it will happen again. Now imagine ways in which you could change your behavior. Which of these would reduce your bet? You could have an honest conversation with him, telling him how his actions make you feel. To know if he’s able to openly receive this, consider whether your bet would change. Or would you wager significantly less after employing the strategy of always being busy when he calls to set up future visits?

And you can dig even deeper. Which of your behaviors would increase the probability that he actually comes? Which behaviors would increase the probability that he doesn’t bother making plans in the first place? Depending on how much you like him, you can steer your changes to the outcome you’d prefer.

Quantifying the subjective and using Bayes’s theorem can help us clear out some of the relationship negativity in our lives.

## Philip Tetlock on The Art and Science of Prediction

This is the sixth episode of The Knowledge Project, a podcast aimed at acquiring wisdom through interviews with fascinating people to gain insights into how they think, live, and connect ideas.

***

On this episode, I'm happy to have Philip Tetlock, professor at the University of Pennsylvania. He's the co-leader of The Good Judgement Project, which is a multi-year forecasting study. He's also the author of Superforecasting: The Art and Science of Prediction and Expert Political Judgment: How Good Is It? How Can We Know?

The subject of this interview is how we can get better at the art and science of prediction. We dive into what makes some people better at making predictions and how we can learn to improve our ability to guess the future. I hope you enjoy the conversation as much as I did.

***

Listen

***

## Show Notes

Transcript:
A complete transcript is available for members.

Books Mentioned

## Mental Model: Misconceptions of Chance

We expect the immediate outcome of events to represent the broader outcomes expected from a large number of trials. We believe that chance events will immediately self-correct and that small sample sizes are representative of the populations from which they are drawn. All of these beliefs lead us astray.

***

Our understanding of the world around us is imperfect and when dealing with chance our brains tend to come up with ways to cope with the unpredictable nature of our world.

“We tend,” writes Peter Bevelin in Seeking Wisdom, “to believe that the probability of an independent event is lowered when it has happened recently or that the probability is increased when it hasn't happened recently.”

In short, we believe an outcome is due and that chance will self-correct.

The problem with this view is that nature doesn't have a sense of fairness or memory. We only fool ourselves when we mistakenly believe that independent events offer influence or meaningful predictive power over future events.

Furthermore we also mistakenly believe that we can control chance events. This applies to risky or uncertain events.

Chance events coupled with positive reinforcement or negative reinforcement can be a dangerous thing. Sometimes we become optimistic and think our luck will change and sometimes we become overly pessimistic or risk-averse.

How do you know if you're dealing with chance? A good heuristic is to ask yourself if you can lose on purpose. If you can't you're likely far into the chance side of the skill vs. luck continuum. No matter how hard you practice, the probability of chance events won't change.

“We tend,” writes Nassim Taleb in The Black Swan, “to underestimate the role of luck in life in general (and) overestimate it in games of chance.”

We are only discussing independent events. If events are dependent, where the outcome depends on the outcome of some other event, all bets are off.

***

## Misconceptions of Chance

Daniel Kahneman coined the term misconceptions of chance to describe the phenomenon of people extrapolating large-scale patterns to samples of a much smaller size. Our trouble navigating the sometimes counterintuitive laws of probability, randomness, and statistics leads to misconceptions of chance.

Kahneman found that “people expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short.”

In the paper Belief in the Law of Small Numbers, Kahneman and Tversky reflect on the results of an experiment, where subjects were instructed to generate a random sequence of hypothetical tosses of a fair coin.

They [the subjects] produce sequences where the proportion of heads in any short segment stays far closer to .50 than the laws of chance would predict. Thus, each segment of the response sequence is highly representative of the “fairness” of the coin.

Unsurprisingly, the same nature of errors occurred when the subjects, instead of being asked to generate sequences themselves, were simply asked to distinguish between random and human generated sequences. It turns out that when considering tosses of a coin for heads or tails people regard the sequence H-T-H-T-T-H to be more likely than the sequence H-H-H-T-H-T, which does not appear random, and also more likely than the sequence H-H-H-H-T-H. In reality, each one of those sequences has the exact same probability of occurring. This is a misconception of chance.

The aspect that most of us find so hard to grasp about this case is that any pattern of the same length is just as likely to occur in a random sequence. For example, the odds of getting 5 tails in a row are 0.03125 or simply stated 0.5 (the odds of a specific outcome at each trial) to the power of 5 (number of trials).

The same probability rule applies for getting the specific sequences of HHTHT or THTHT – where each sequence is obtained by once again taking 0.5 (the odds of a specific outcome at each trial) to the power of 5 (number of trials), which equals 0.03125.

This probability is true for sequences – but it implies no relation between the odds of a specific outcome at each trial and the representation of the true proportion within these short sequences.

Yet it’s still surprising. This is because people expect that the single event odds will be reflected not only in the proportion of events as a whole but also in the specific short sequences we encounter. But this is not the case. A perfectly alternating sequence is just as extraordinary as a sequence with all tails or all heads.

In comparison, “a locally representative sequence,” Kahneman writes, in Thinking, Fast and Slow, “deviates systematically from chance expectation: it contains too many alternations and too few runs. Another consequence of the belief in local representativeness is the well-known gambler’s fallacy.”

***

## Gambler’s Fallacy

There is a specific variation of the misconceptions of chance that Kahneman calls the Gambler’s fallacy (elsewhere also called the Monte Carlo fallacy).

The gambler's fallacy implies that when we come across a local imbalance, we expect that the future events will smoothen it out. We will act as if every segment of the random sequence must reflect the true proportion and, if the sequence has deviated from the population proportion, we expect the imbalance to soon be corrected.

Kahneman explains that this is unreasonable – coins, unlike people, have no sense of equality and proportion:

The heart of the gambler's fallacy is a misconception of the fairness of the laws of chance. The gambler feels that the fairness of the coin entitles him to expect that any deviation in one direction will soon be cancelled by a corresponding deviation in the other. Even the fairest of coins, however, given the limitations of its memory and moral sense, cannot be as fair as the gambler expects it to be.

He illustrates this with an example of the roulette wheel and our expectations when a reasonably long sequence of repetition occurs.

After observing a long run of red on the roulette wheel, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red.

In reality, of course, roulette is a random, non-evolving process, in which the chance of getting a red or a black will never depend on the past sequence. The probabilities restore after each run, yet we still seem to take the past moves into account.

Contrary to our expectations, the universe does not keep accounting of a random process so streaks are not necessarily tilted towards the true proportion. Your chance of getting a red after a series of blacks will always be equal to that of getting another red as long as the wheel is fair.

The gambler’s fallacy need not to be committed inside the casino only. Many of us commit it frequently by thinking that a small, random sample will tend to correct itself.

For example, assume that the average IQ at a specific country is known to be 100. And for the purposes of assessing intelligence at a specific district, we draw a random sample of 50 persons. The first person in our sample happens to have an IQ of 150. What would you expect the mean IQ to be for the whole sample?

The correct answer is (100*49 + 150*1)/50 = 101. Yet without knowing the correct answer, it is tempting to say it is still 100 – the same as in the country as a whole.

According to Kahneman and Tversky such expectation could only be justified by the belief that a random process is self-correcting and that the sample variation is always proportional. They explain:

Idioms such as “errors cancel each other out” reflect the image of an active self-correcting process. Some familiar processes in nature obey such laws: a deviation from a stable equilibrium produces a force that restores the equilibrium.

Indeed, this may be true in thermodynamics, chemistry and arguably also economics. These, however, are false analogies. It is important to realize that the laws governed by chance are not guided by principles of equilibrium and the number of random outcomes in a sequence do not have a common balance.

“Chance,” Kahneman writes in Thinking, Fast and Slow, “is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not “corrected” as a chance process unfolds, they are merely diluted.”

***

## The Law of Small Numbers

Misconceptions of chance are not limited to gambling. In fact, most of us fall for them all the time because we intuitively believe (and there is a whole best-seller section at the bookstore to prove) that inferences drawn from small sample sizes are highly representative of the populations from which they are drawn.

By illustrating people's expectations of random heads and tails sequences, we already established that we have preconceived notions of what randomness looks like. This, coupled with the unfortunate tendency to believe in self-correcting process in a random sample, generates expectations about sample characteristics and representativeness, which are not necessarily true. The expectation that the patterns and characteristics within a small sample will be representative of the population as a whole is called the law of small numbers.

Consider the sequence:

1, 2, 3, _, _, _

What do you think are the next three digits?

The task almost seems laughable, because the pattern is so familiar and obvious – 4,5,6. However, there is an endless variation of different algorithms that would still fit the first three numbers, such as the Fibonacci sequence (5, 8, 13), a repeated sequence (1,2,3), a random sequence (5,8,2) and many others. Truth is, in this case there simply is not enough information to say what the rules governing this specific sequence are with any reliability.

The same rule applies to sampling problems – sometimes we feel we have gathered enough data to tell a real pattern from an illusion. Let me illustrate this fallacy with yet another example.

Imagine that you face a tough decision between investing in the development of two different product opportunities. Let’s call them Product A or Product B. You are interested in which product would appeal to the majority of the market, so you decide to conduct customer interviews. Out of the first five pilot interviews, four customers show a preference for Product A. While the sample size is quite small, given the time pressure involved, many of us would already have some confidence in concluding that the majority of customers would prefer Product A.

However, a quick statistical test will tell you that the probability of a result just as extreme is in fact 3/8, assuming that there is no preference among customers at all. This in simple terms means that if customers had no preference between Products A and B, you would still expect 3 customer samples out of 8 to have four customers vouching for Product A.

Basically, a study of such size has little to no predictive validity – these results could easily be obtained from a population with no preference for one or the other product. This, of course, does not mean that talking to customers is of no value. Quite the contrary – the more random cases we examine, the more reliable and accurate the results of the true proportion will be. If we want absolute certainty we must be prepared for a lot of work.

There will always be cases where a guesstimate based on a small sample will be enough because we have other critical information guiding the decision-making process or we simply do not need a high degree of confidence. Yet rather than assuming that the samples we come across are always perfectly representative, we must treat random selection with the suspicion it deserves. Accepting the role imperfect information and randomness play in our lives and being actively aware of what we don’t know already makes us better decision makers.

## 13 Practical Ideas That Have Helped Me Make Better Decisions

This article is a collaboration between Mark Steed and myself. He did most of the work. Mark was a participant at the last Re:Think Decision Making event as well as a member of the Good Judgment Project. I asked him to put together something on making better predictions. This is the result.

We all face decisions. Sometimes we think hard about a specific decision, other times, we make decisions without thinking. If you've studied the genre you’ve probably read Taleb, Tversky, Kahneman, Gladwell, Ariely, Munger, Tetlock, Mauboussin and/or Thaler. These pioneers write a lot about “rationality” and “biases”.

Rationality dictates the selection of the best choice among however many options. Biases of a cognitive or emotional nature creep in and are capable of preventing the identification of the “rational” choice. These biases can exist in our DNA or can be formed through life experiences. The mentioned authors consider biases extensively, and, lucky for us, their writings are eye-opening and entertaining.

Rather than rehash what brighter minds have discussed, I’ll focus on practical ideas that have helped me make better decisions. I think of this as a list of “lessons learned (so far)” from my work in asset management and as a forecaster for the Good Judgment Project. I’ve held back on submitting this given the breadth and depth of the FS readers, but, rather than expect perfection, I wanted to put something on the table because I suspect many of you have useful ideas that will help move the conversation forward.

1. This is a messy business. Studying decision science can easily motivate self-loathing. There are over one-hundred cognitive biases that might prevent us from making calculated and “rational” decisions. What, you can’t create a decision tree with 124 decision nodes, complete with assorted probabilities in split seconds? I asked around, and it turns out, not many people can. Since there is no way to eliminate all the potential cognitive biases and I don’t possess the mental faculties of Dr. Spock or C-3PO, I might as well live with the fact that some decisions will be more elegant than others.

2. We live and work in dynamic environments. Dynamic environments adapt. The opposite of dynamic environments are static environments. Financial markets, geopolitical events, team sports, etc. are examples of dynamic “environments” because relationships between agents evolve and problems are often unpredictable. Changes from one period are conditional on what happened the previous period. Casinos are more representative of static environments. Not casinos necessarily, but the games inside. If you play Roulette, your odds of winning are always the same and it doesn’t matter what happened the previous turn.

3. Good explanatory models are not necessarily good predictive models. Dynamic environments have a habit of desecrating rigid models. While blindly following an elegant model may be ill-advised, strong explanatory models are excellent guideposts when paired with sound judgment and intuition. Just as I’m not comfortable with the automatic pilot flying a plane without a human in the cockpit, I’m also not comfortable with a human flying a plane without the help of technology. It has been said before, people make models better and models make people better.

4. Instinct is not always irrational.  The rule of thumb, otherwise known as heuristics, provide better results than more complicated analytical techniques. Gerd Gigerenzer, is the thought leader and his book Risk Savvy: How to Make Good Decisions is worth reading. Most literature despises heuristics, but he asserts intuition proves superior because optimization is sometimes mathematically impossible or exposed to sampling error. He often uses the example of Harry Markowitz, who won a Nobel Prize in Economics in 1990 for his work on Modern Portfolio Theory. Markowitz discovered a method for determining the “optimal” mix of assets. However, Markowitz himself did not follow his Nobel prize-winning mean-variance theory but instead used a 1/N heuristic by spreading his dollars equally across N number of investments. He concluded that his 1/N strategy would perform better than a mean-optimization application unless the mean-optimization model had 500 years to compete.  Our intuition is more likely to be accurate if it is preceded by rigorous analysis and introspection. And simple rules are more effective at communicating winning strategies in complex environments. When coaching a child’s soccer team, it is far easier teaching a few basic principles, than articulating the nuances of every possible situation.

5. Decisions are not evaluated in ways that help us reduce mistakes in the future. Our tendency is to only critique decisions where the desired outcome was not achieved while uncritically accepting positive outcomes even if luck, or another factor, produced the desired result. At the end of the day I understand all we care about are results, but good processes are more indicative of future success than good results.

6. Success is ill-defined. In some cases this is relatively straightforward. If the outcome is binary, either it did, or did not happen, success is easy to identify. But this is more difficult in situations where the outcome can take a range of potential values, or when individuals differ on what the values should be.

7. We should care a lot more about calibration. Confidence, not just a decision, should be recorded (and to be clear, decisions should be recorded). Next time you have a major decision, ask yourself how confident you are that the desired outcome will be achieved. Are you 50% confident? 90%? Write it down. This helps with calibration. For all decisions in which you are 50% confident, half should be successes. And you should be right nine out of ten times for all decisions in which you are 90% confident. If you are 100% confident, you should never be wrong. If you don’t know anything about a specific subject then you should be no more confident than a coin flip. It’s amazing how we will assign high confidence to an event we know nothing about. Turns out this idea is pretty helpful. Let’s say someone brings an idea to you and you know nothing about it. Your default should be 50/50; you might as well flip a coin. Then you just need to worry about the costs/payouts.

8. Probabilities are one thing, payouts are another. You might feel 50/50 about your chances but you need to know your payouts if you are right. This is where the expected value comes in handy. It’s the probability of being right multiplied by the payout if you are right, plus the probability of being wrong multiplied by the cost. E= .50(x) + .50(y). Say someone on your team has an idea for a project and you decided there is a 50% chance that it succeeds and, if it does, you double your money, if it doesn’t, you lose what you invested. If the project required \$10mm, then the expected outcome is calculated as .50*20 + .50*0 = 10, or \$10mm. If you repeat this process a number of times, approving only projects with a 2:1 payout and 50% probability of success you would likely end up with the same amount you started with. Binary outcomes that have a 50/50 probability should have a double-or-nothing payout. This is even more helpful given #7 above. If you were tracking this employee’s calibration you would have a sense as to whether their forecasts are accurate. As a team member or manager, you would want to know if a specific employee is 90% confident all the time but only 50% accurate. More importantly, you would want to know if a certain team member is usually right when they express 90% or 100% confidence. Use a Brier Score to track colleagues but provide an environment to encourage discussion and openness.

10. Improving estimations of probabilities and payouts is about polishing our 1) subject matter expertise and 2) cognitive processing abilities. Learning more about a given subject reduces uncertainty and allows us to move from the lazy 50/50 forecast. Say you travel to Arizona and get stung by a scorpion. Rather than assume a 50% probability of death you can do a quick internet search and learn no one has died from a scorpion bite in Arizona since the 1960s. Overly simplistic, but, you get the picture. Second, data needs to be interpreted in a cogent way. Let’s say you work in asset management and one of your portfolio managers has made three investments that returned -5%, -12% and 22%. What can you say about the manager (other than two of the three investments lost money)? Does the information allow you to claim the portfolio manager is a bad manager? Does the information allow you to claim you can confidently predict his/her average rate of return? Unless you’ve had some statistics, it might not be entirely clear what clinical conclusions you can draw. What if you flipped a coin three times and came up with tails on two of them? That wouldn’t seem so strange. Two-thirds is the same as 66%. If you tossed the coin one-hundred times and got 66 tails, that would be a little more interesting. The more observations, the higher our confidence should be. A 95% confidence interval for the portfolio manager’s average return would be a range between -43% and 45%. Is that enough to take action?

11. Bayesian analysis is more useful than we think. Bayesian thinking helps direct given false/true positives and false/true negatives. It’s the probability of a hypothesis given some observed data. For example, what’s the likelihood of X (this new hire will place in the top 10% of the firm) given Y (they graduated from an Ivy League school)? A certain percentage of employees are top-performing employees, some Ivy League grads will be top-performers (others not) and some non-Ivy League grads will be top-performers (others not). If I’m staring at a random employee trying to guess whether they are a top-performing employee all I have are the starting odds, and, if only the top 10% qualify, I know my chances are 1 in 10. But I can update my odds if supplied information regarding their education. Here’s another example. What is the likelihood a project will be successful (X) given it missed one of the first two milestones (Y)?. There are lots of helpful resources online if you want to learn more but think of it this way (hat tip to Kalid Azad at Better Explained); original odds x the evidence adjustment = your new odds. The actual equation is more complicated but that is the intuition behind it. Bayesian analysis has its naysayers. In the examples provided, the prior odds of success are known, or could easily be obtained, but this isn’t always true. Most of the time subjective prior probabilities are required and this type of tomfoolery is generally discouraged. There are ways around that, but no time to explain it here.

12. A word about crowds. Is there a wisdom of crowds? Some say yes, others say no. My view is that crowds can be very useful if individual members of the crowd are able to vote independently or if the environment is such that there are few repercussions for voicing disagreement. Otherwise, I think signaling effects from seeing how others are “voting” is too much evolutionary force to overcome with sheer rational willpower. Our earliest ancestors ran when the rest of the tribe ran. Not doing so might have resulted in an untimely demise.

13. Analyze your own motives. Jonathan Haidt, author of The Righteous Mind: Why Good People Are Divided by Politics and Religion, is credited with teaching that logic isn’t used to find truth, it’s used to win arguments. Logic may not be the only source of truth (and I have no basis for that claim). Keep this in mind as it has to do with the role of intuition in decision making.

Just a few closing thoughts.

We are pretty hard on ourselves. My process is to make the best decisions I can, realizing not all of them will be optimal. I have a method to track my decisions and to score how accurate I am. Sometimes I use heuristics, but I try to keep those to within my area of competency, as Munger says. I don’t do lists of pros and cons because I feel like I’m just trying to convince myself, either way.

If I have to make a big decision, in an unfamiliar area, I try to learn as much as I can about the issue on my own and from experts, assess how much randomness could be present, formulate my thesis, look for contradictory information, try and build downside protection (risking as little as possible) and watch for signals that may indicate a likely outcome. Many of my decisions have not worked out, but most of them have. As the world changes, so will my process, and I look forward to that.

Have something to say? Become a member: join the slack conversation and chat with Mark directly.

## The Lucretius Problem

It's always good to re-read books and to dip back into them periodically. When reading a new book, I often miss out on crucial information (especially books that are hard to categorize with one descriptive sentence). When you come back to a book after reading hundreds of others you can't help but make new connections with the old book and see it anew.

It has been a while since I read Anti-fragile. In the past I've talked about an Antifragile Way of Life, Learning to Love Volatility, the Definition of Antifragility , Antifragile life of economy, and the Noise and the Signal.

But upon re-reading Antifragile I came across the Lucretius Problem and I thought I'd share an excerpt. (Titus Lucretius Carus was a Roman poet and philosopher, best-known for his poem On the Nature of Things). Taleb writes:

Indeed, our bodies discover probabilities in a very sophisticated manner and assess risks much better than our intellects do. To take one example, risk management professionals look in the past for information on the so-called ​worst-case scenario ​and use it to estimate future risks – this method is called “stress testing.” They take the worst historical recession, the worst war, the worst historical move in interest rates, or the worst point in unemployment as an exact estimate for the worst future outcome​. But they never notice the following inconsistency: this so-called worst-case event, when it happened, exceeded the worst [known] case at the time.

I have called this mental defect the Lucretius problem, after the Latin poetic philosopher who wrote that the fool believes that the tallest mountain in the world will be equal to the tallest one he has observed. We consider the biggest object of any kind that we have seen in our lives or hear about as the largest item that can possibly exist. And we have been doing this for millennia.

Taleb brings up an interesting point, which is that our documented history can blind us. All we know is what we have been able to record.

We think because we have sophisticated data collecting techniques that we can capture all the data necessary to make decisions. We think we can use our current statistical techniques to draw historical trends using historical data without acknowledging the fact that past data recorders had fewer tools to capture the dark figure of unreported data. We also overestimate the validity of what has been recorded before and thus the trends we draw might tell a different story if we had the dark figure of unreported data.

Taleb continues:

The same can be seen in the Fukushima nuclear reactor, which experienced a catastrophic failure in 2011 when a tsunami struck. It had been built to withstand the worst past historical earthquake, with the builders not imagining much worse— and not thinking that the worst past event had to be a surprise, as it had no precedent. Likewise, the former chairman of the Federal Reserve, Fragilista Doctor Alan Greenspan, in his apology to Congress offered the classic “It never happened before.” Well, nature, unlike Fragilista Greenspan, prepares for what has not happened before, assuming worse harm is possible.

So what do we do and how do we deal with the blindness?

Taleb provides an answer which is to develop layers of redundancy to act as a buffer against oneself. We overvalue what we have recorded and assume it tells us the worst and best possible outcomes. Redundant layers are a buffer against our tendency to think what has been recorded is a map of the whole terrain. An example of a redundant feature could be a rainy day fund which acts as an insurance policy against something catastrophic such as a job loss that allows you to survive and fight another day.

Antifragile is a great book to read and you might learn something about yourself and the world you live in by reading it or in my case re-reading it.

## Fooled By Randomness

I don't want you to make the same mistake I did.

I waited too long before reading Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Taleb. He wrote the book before the Black Swan and Antifragile, which propelled him into intellectual celebrity. Interestingly, Fooled by Randomness contains semi-explored gems of the ideas that would later go on to become the best-selling books The Black Swan and Antifragile.

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Hindsight Bias

Part of the argument that Fooled by Randomness presents is that when we look back at things that have happened we see them as less random than they actually were.

It is as if there were two planets: the one in which we actually live and the one, considerably more deterministic, on which people are convinced we live. It is as simple as that: Past events will always look less random than they were (it is called the hindsight bias). I would listen to someone’s discussion of his own past realizing that much of what he was saying was just backfit explanations concocted ex post by his deluded mind.

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The Courage of Montaigne

Writing on Montaigne as the role model for the modern thinker, Taleb also addresses his courage:

It certainly takes bravery to remain skeptical; it takes inordinate courage to introspect, to confront oneself, to accept one’s limitations— scientists are seeing more and more evidence that we are specifically designed by mother nature to fool ourselves.

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Probability

Fooled by Randomness is about probability, not in a mathematical way but as skepticism.

In this book probability is principally a branch of applied skepticism, not an engineering discipline. …

Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance. Outside of textbooks and casinos, probability almost never presents itself as a mathematical problem or a brain teaser. Mother nature does not tell you how many holes there are on the roulette table , nor does she deliver problems in a textbook way (in the real world one has to guess the problem more than the solution).

Outside of textbooks and casinos, probability almost never presents itself as a mathematical problem” which is fascinating given how we tend to solve problems. In decisions under uncertainty, I discussed how risk and uncertainty are different things, which creates two types of ignorance.

Most decisions are not risk-based, they are uncertainty-based and you either know you are ignorant or you have no idea you are ignorant. There is a big distinction between the two. Trust me, you'd rather know you are ignorant.

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Randomness Disguised as Non-Randomness

The core of the book is about luck that we understand as skill or “randomness disguised as non-randomness (that is determinism).”

This problem manifests itself most frequently in the lucky fool, “defined as a person who benefited from a disproportionate share of luck but attributes his success to some other, generally very precise, reason.”

Such confusion crops up in the most unexpected areas, even science, though not in such an accentuated and obvious manner as it does in the world of business. It is endemic in politics, as it can be encountered in the shape of a country’s president discoursing on the jobs that “he” created, “his” recovery, and “his predecessor’s” inflation.

These lucky fools are often fragilistas — they have no idea they are lucky fools. For example:

[W]e often have the mistaken impression that a strategy is an excellent strategy, or an entrepreneur a person endowed with “vision,” or a trader a talented trader, only to realize that 99.9% of their past performance is attributable to chance, and chance alone. Ask a profitable investor to explain the reasons for his success; he will offer some deep and convincing interpretation of the results. Frequently, these delusions are intentional and deserve to bear the name “charlatanism.”

This does not mean that all success is luck or randomness. There is a difference between “it is more random than we think” and “it is all random.”

Let me make it clear here : Of course chance favors the prepared! Hard work, showing up on time, wearing a clean (preferably white) shirt, using deodorant, and some such conventional things contribute to success— they are certainly necessary but may be insufficient as they do not cause success. The same applies to the conventional values of persistence, doggedness and perseverance: necessary, very necessary. One needs to go out and buy a lottery ticket in order to win. Does it mean that the work involved in the trip to the store caused the winning? Of course skills count, but they do count less in highly random environments than they do in dentistry.

No, I am not saying that what your grandmother told you about the value of work ethics is wrong! Furthermore, as most successes are caused by very few “windows of opportunity,” failing to grab one can be deadly for one’s career. Take your luck!

That last paragraph connects to something Charlie Munger once said: “Really good investment opportunities aren't going to come along too often and won't last too long, so you've got to be ready to act. Have a prepared mind.

Taleb thinks of success in terms of degrees, so mild success might be explained by skill and labour but outrageous success “is attributable variance.”

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Luck Makes You Fragile

One thing Taleb hits on that really stuck with me is that “that which came with the help of luck could be taken away by luck (and often rapidly and unexpectedly at that). The flipside, which deserves to be considered as well (in fact it is even more of our concern), is that things that come with little help from luck are more resistant to randomness.” How Antifragile.

Taleb argues this is the problem of induction, “it does not matter how frequently something succeeds if failure is too costly to bear.”

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Noise and Signal

We are confused between noise and signal.

…the literary mind can be intentionally prone to the confusion between noise and meaning, that is, between a randomly constructed arrangement and a precisely intended message. However, this causes little harm; few claim that art is a tool of investigation of the Truth— rather than an attempt to escape it or make it more palatable. Symbolism is the child of our inability and unwillingness to accept randomness; we give meaning to all manner of shapes; we detect human figures in inkblots.

All my life I have suffered the conflict between my love of literature and poetry and my profound allergy to most teachers of literature and “critics.” The French thinker and poet Paul Valery was surprised to listen to a commentary of his poems that found meanings that had until then escaped him (of course, it was pointed out to him that these were intended by his subconscious).

If we're concerned about situations where randomness is confused with non randomness should we also be concerned with situations where non randomness is mistaken for randomness, which would result in signal being ignored?

First, I am not overly worried about the existence of undetected patterns. We have been reading lengthy and complex messages in just about any manifestation of nature that presents jaggedness (such as the palm of a hand, the residues at the bottom of Turkish coffee cups, etc.). Armed with home supercomputers and chained processors, and helped by complexity and “chaos” theories, the scientists, semiscientists, and pseudoscientists will be able to find portents. Second, we need to take into account the costs of mistakes; in my opinion, mistaking the right column for the left one is not as costly as an error in the opposite direction. Even popular opinion warns that bad information is worse than no information at all.

If you haven't yet, pick up a copy of Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. Don't make the same mistake I did and wait to read this important book.

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