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# Algorithms to Live By

BY BRIAN CHRISTIAN AND TOM GRIFFITHS

SYNOPSIS
Can computer science teach us the secrets of life? Perhaps not, but it can shed light on how certain everyday processes work and how to exploit them. Algorithms are everywhere, from following a recipe to the order in which you sort your email.
In Algorithms to Live By, programmer and researcher Brian Christian and psychology and cognitive science professor at UC Berkeley Tom Griffiths share the many ways that algorithms shape everything from the way we remember things to how we make big and small decisions.

# TOP 20 INSIGHTS

1) The "37% rule" refers to a series of steps, or algorithms, that someone must follow to make the best decision within a set amount of time. Someone allots 37% of their time to research before they make a decision, then commits to the very next "best choice" they find.

2) The "explore/exploit" trade-off refers to the need to balance the tried and tested with the new and risky. The payoff of this algorithm depends entirely on how much time you have to make decisions. People are more likely to visit their favorite restaurant on their last night in town than risk something new.

3) Developed in 1952 by mathematician Herbert Robins, the "Win-Stay, Lose-Shift" algorithm uses slot machines as a metaphor. Choose a machine at random and play it until you lose. Then switch to another machine; this method was proven to be more reliable than chance.

4) A psychology study found that given choices, people often "over explore" rather than exploit a win. Given 15 opportunities to choose which slot machine would win, 47% used Win-Stay, Lose-Shift strategies, and 22% chose machines randomly instead of staying with a machine that paid out.

5) Hollywood is a prime example of the exploit tactic. The number of movie sequels has steadily increased over the last decade. In both 2013 and 2014, seven of the Top 10 films were either sequels or prequels. The trend is likely to change if new movie ideas draw more box office dollars.

6) The A/B test is similar to the two slot machine scenario in that you stick with the option that performs best. More than 90% of Google's \$50 million in annual revenue is from paid advertisements, which means that explore/exploit algorithms power a large portion of the internet.

7) The Gittins Index provides a framework of odds that assume you have an indefinite amount of time to achieve the best payoff, but the chances reduce the longer you wait. For example: choose a slot machine with a track record of one-to-one wins/losses (50%) over the machine that has won nine out of 18 times.

8) "Upper Confidence Bound" algorithms offer more room for discovery than the "Win-Stay, Lose-Shift" method. This algorithm assigns a value based on what "could be" based on the information available. A new restaurant has a 50/50 chance to provide a good experience because you have never been there.

9) The "Shortest Processing Time" algorithm requires that you complete the quickest tasks first. Divide the importance of the task by how long it will take. Only prioritize a task that takes two times as long if it is two times as important.

10) Laplace's Law calculates the odds that something will occur with only small amounts of data. Count how many times that result has happened, add one, then divide by the number of opportunities plus two. For example: Your softball team plays eight games per season. It has already won two games. 2+1/ 6+2=3/8, or a 37.5% chance you win the next game.

11) The Copernican Principle allows you to predict how long something will last without much of anything about it. The solution is that it will go on as long as it has gone on so far. Based on this principle, Google will reasonably last until 2044 (23 years since 1998 + 23 from 2021).

12) "Power-law distribution" considers that, in life, most things fall below the mean and a few rise above. Two-thirds of the US population makes less than the mean income, but the top 1% make almost ten times the mean. Few movies make "Titanic" level money in the box office, but some do.

13) The "Nash Equilibrium" explores the phenomenon of two-player games and the way that players form strategies that neither wants to change based on what the other person does. This creates stability. In Rock-Paper-Scissors with three options, players adopt a 1/3-1/3-1/3 strategy unless the other person changes tactics, and the process starts again.

14) Human brains have a nearly infinite capacity for memories, but we have a finite amount of time to access them. This results in the "forgetting curve." A study by Hermann Ebbinghaus found that he could recall nonsense syllables 60% of the time after he read them, but it declined to 20% after 800 hours.

15) Ebbinghaus' "forgetting curve" was shown to closely match how often words are used in society. The recurrence of words found in headlines of The New York Times declined at a rate of 15% over 100 days and implied that human brains naturally tune their processes to the world around us.

16) The stock market "flash crash" of May 6, 2010 was caused by an "information cascade." When one person does something different, then other people follow suit, assuming that the first person knows something they don't. This behavior causes people to panic buy or exhibit mob behavior.

17) Sociologist Barry Glassner noted that murders in the United States declined by 20% throughout the 1990s, and yet the mention of gun violence on American news increased by 600%. An information cascade can be caused more by public information than private information.

18) When authors Brian Christian and Tom Griffiths scheduled interviews for the book, they found that experts were more likely to accept a narrow, predetermined window than a wide-open one. It is less challenging to accommodate restraints than find another solution.

19) Believe it or not, randomness is part of life's algorithm, too. Nobel prize-winner Salvador Luria realized that random mutations could produce viral resistance by watching his friend win the jackpot on a slot machine.

20) The best-laid plans are often the simplest. Jason Fried and David Heinemeier Hannson, founders of software company 37signals, use a thick marker when they start to brainstorm because it limits room and forces them to keep it simple and focus on the big picture.

# SUMMARY

## OPTIMAL STOPPING

### LOOK VERSUS LEAP

• Life is full of situations that require us to make the best possible decision in the shortest amount of time. Drivers search for the perfect parking space. Managers search for the best job candidate for a job, and property owners must decide on whether or not to accept a sale offer before the real estate market changes again. This dilemma is called "optimal stopping."

• "Optimal Stopping" problems refer to dilemmas that require the best decision in the shortest amount of time. How do you balance the need to get all the facts with the need to act before it's too late? Common examples include searching for the perfect parking spot, when to rent an apartment before they're all taken and when to hire the best candidate for a job. The latter has been thoroughly examined and discussed by mathematicians since the 1950s.

This problem is known as the "Secretarial Problem."

• If an employer interviews 100 secretary applicants, that person should allocate the first 37% percent of interviews to familiarize themselves with the talent pool and best qualities.

• If they hire the very next applicant that appears to be the "best so far," the company has a 37% chance of that person being the best candidate.

• The odds become greater with fewer applicants.

A renter on the hunt for an apartment in San Francisco might be inclined to take the first available unit due to high demand. If that renter needs to find a new place to live within 30 days, the "Optimal Stopping" algorithm suggests that the renter commit 37% of their time, or 11 days, to explore options without any commitment. On day 12, the renter must be prepared to commit to the first place that they consider to be the "best so far."

### EXPLORE VERSUS EXPLOIT

• Laura Carstensen, a psychology professor at Stanford, hypothesized that people strategically reduce their social circles as they get older. In one study, people were asked if they would rather spend 30 minutes with an immediate family member, an author that wrote a book they read recently or someone they'd met who appeared to share their interests. Older respondents chose the family member, while younger people chose to make new friends.

• When time was added or taken away, however, something interesting happened. If older people were allowed to live 20 years longer, their choices matched those of younger respondents. If younger respondents imagined they were about to move across the country, they chose family members instead.

• Life is full of uncertainty, making the decision process that much more of a struggle at times. To take some of the life or death pressure out of the equation, let's turn instead to something a bit less dire â€“ the casino slot machine.

• Dubbed the "one-armed bandit," slot machines come with various payout odds that have baffled gamblers and fascinated statisticians for centuries. In 1952, mathematician Herbert Robbins proposed a solution to the age-old dilemma of whether you should hold out for the next big win or quit while you're ahead. He called this the Win-Stay, Lose-Shift algorithm.

• Robbins proposed that a person should choose "an arm" at random (explore), then pull it as long as it pays off (exploit). Once the machine fails to pay, the person should move to another one, and so on.

### MINIMAL REGRET

• Sometimes you have to weigh the risk with potential regret to find the solution to your particular problem. Amazon CEO Jeff Bezos had a steady, well-paid job on Wall Street before starting Amazon. The risk of the first online bookstore, he found, was outweighed by the possibility that he might regret not trying, a "regret minimization framework."

• "I knew that when I was 80, I was not going to regret having tried this," Bezos said. "I was not going to regret trying to participate in this thing called the internet that I thought was going to be a really big deal. I knew that if I failed, I wouldn't regret that, but I knew the one thing I might regret is not ever having tried."

• "Upper Confidence Bound" algorithms offer more room for discovery than the "Win-Stay, Lose-Shift" method. This algorithm assigns a value based on what "could be" based on the information available. A new restaurant has a 50/50 chance to provide a good experience because you have never been there.

• Algorithms can't guarantee a life without regret, but they show how our willingness to take risks is reduced by how much time we think (or know) we have to take them. When we are children, we explore our worlds and discover new things with great enthusiasm. As we grow older, we tend to rely on the "tried and true" decisions based on what we've learned, i.e. exploit them.

## PLAN WITH PURPOSE

• Often, those tasks with a due date can be tackled from the nearest deadline to the furthest. If you have multiple tasks due simultaneously, it is best to sort them by how long each will take.

• To approach this type of schedule, especially if you have multiple clients, you can reduce the amount everyone must wait using the Shortest Processing Time algorithm. Simply put, always tackle the quickest task first and so on. Imagine a Monday morning in which you have one big project that takes four days to complete and a smaller project that takes one day. If you deliver the big project first on Thursday (4 days) and the small project on Friday (5 days), your clients will have waited a total of nine days. If you deliver the small project first on Monday (1 day) and the big one on Friday (5 days), your clients will have waited for a total of six days between them. This is known as the "sum of completion times."

• Another approach is to assign a weight to each task, such as how much money it will bring in. Divide each task's weight by how long it will take to complete, then work in the highest to lowest order. For a freelancer or independent contractor, this allows you to determine each task's hourly rate. Divide each project fee by its size and work from the highest hourly rate to the lowest.

## PREDICT THE FUTURE

• Astrophysicist J. Richard Gott III developed the Copernican Principle in 1969 â€“ a method to predict how long something will last. When he visited the Berlin Wall, he wondered how long the wall would last. Since he didn't know how long the wall's life span would be, Gott could assume that, on average, his arrival would be around halfway through. Therefore, he guessed that the wall would stand for another eight years. In this case, the Berlin Wall stood for 20 years, not eight.

• The Copernican Principle isn't perfect â€“ a 90-year-old man is unlikely to live to be 180 â€“ but there are instances where it works well. Long before Gott gave this algorithm a name, statisticians tried to estimate how many tanks the Germans produced each month during World War II. The solution was to double the serial number seen on the tanks and estimate that at least twice as many existed. In this case, they estimated 246 tanks were manufactured each month, compared to the 1,400 suggested by aerial reconnaissance. After the war, German records confirmed the actual number to be 245.

## FORGET ABOUT IT

### YOUR BRAIN WAS DESIGNED TO FORGET

• The human memory seems to be a fickle thing at times, but there is a method to the madness. Hermann Ebbinghaus, a psychologist at the University of Berlin in 1879, studied himself to understand memory better.

• Each day, Ebbinghaus would memorize a list of nonsense syllables and quiz himself. He then created a graph to show how long it took for his memory to fade. The likelihood of recall predictably declined with time, from close to 60% just after reading something to just 20% after 800 hours.

• John Anderson, a psychologist and computer scientist, reexamined Ebbinghaus' work in 1987 to see if he could design computer systems around the human brain. He discovered that our brains forget information when it is no longer relevant to the world around us. Anderson analyzed headlines from The New York Times and found that a word is most likely to reappear right after first being used. The likelihood of seeing it again reduced more over time. Side by side, the appearance of the chart looked nearly identical to Ebbinghaus' data.

## SEEK BALANCEâ€¦ OR NOT

• There is a natural balance in everything, especially in two-player games or scenarios that include at least two competitors. Mathematicians call this phenomenon "equilibrium" because it is stable. Equilibrium is especially evident in poker, where players stick to their strategies unless a significant change occurs.

• Example: In Rock-Paper-Scissors, there are only three options for players to choose from. Players naturally pick a random choice or 1/3 strategy. If one of the players starts to use rock more often, the other play adapts and uses paper. The other player will then balance things out again by changing strategy, i.e. scissors, etc., and the process starts again.

• Mathematician John Nash, immortalized in the book and film "A Beautiful Mind," proved in 1951 that every two-player game has at least one such equilibrium. This discovery earned him the Nobel Prize in 1994 Economics. Often referred to as the "Nash Equilibrium," this principle offers a prediction of the stable long-term outcome of any set of rules or incentives.

• This algorithm is used to plan and shape economic policy and social policy â€“ but sometimes, "stable" does not necessarily mean "good."

• If a town has two shopkeepers that attract the same customers, the first will lose business if they work six days a week while the other works seven. The Nash Equilibrium suggests that if both businesses take a day off, they will both get rest, but both lose business. So, both owners work seven days a week.

## CHANGE THE GAME

• If your friend jumped off a bridge, would you do it, too? The human instinct to copy one another can be a survival trait, like turning to look when you see others do just in case danger lurks nearby. Fads and fashions come and go. Is it better to play it safe or make your own way for better or worse?

• "Whenever you find yourself on the side of the majority, it is time to pause and reflect," said Mark Twain.People tend to make decisions based on assumptions they derive from the actions of someone else. If everyone bought Beanie Babies, they must be valuable, right?

• When this process begins to avalanche out of control, it is called an "Information Cascade." The real estate crisis of 2007-2009 was an example of home prices rising due to demand, only to crash. People assume that because many others do something that urgency exists. (Toilet paper in 2020, for example.) The results can be catastrophic.

• Be wary of cases where public information seems to exceed private information. The representation of events in the media does not match frequency in the world. Sociologist Barry Glassner noted that murders in the United States declined by 20% throughout the 1990s, and yet the mention of gun violence on American news increased by 600%.

• Sometimes, in the face of an Information Cascade, you have to change the game. If you are a Christian shopkeeper or have strong convictions about work-life balance, to close on Sunday is a non-issue. If you see people around you fall into an urgent trend, start to panic buy or become disturbed by sensational newspaper headlines, you can alleviate the stress by inserting more data.

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