Self Help

Can You Outsmart an Economist - Steven E. Landsburg

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Matheus Puppe

· 38 min read

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Here is a summary of the contents of the book:

The book contains puzzles and problems related to economics, logic, statistics, decision-making, and other topics. It aims to teach readers to think beyond the obvious by showcasing the tools and insights of economists as well as other disciplines like philosophy, law, and psychology.

The table of contents lists the following sections:

  • Warm-Ups: Puzzles to get started
  • Inferences: Draw conclusions from evidence
  • Predictions: Forecast what will happen
  • Explanations: Understand why things occur
  • Strategy: Analyze strategic decision-making
  • Additional topical chapters on decision-making, life and death dilemmas, economics, etc.
  • Appendix
  • Information about the author

The introduction provides background on the book’s purpose and approach. It emphasizes that economics overlaps with other fields like statistics, law, and philosophy. Readers are encouraged not to think of puzzles as strictly belonging to one discipline.

In summary, the book uses puzzles and problems to train readers’ ability to think critically and consider multiple perspectives, with a focus on economic reasoning but also drawing on related topics.

  • The author draws on different branches of economics and schools of thought to illuminate the issues discussed in each chapter.

  • Economists believe that much human behavior is strategic, meaning people try to anticipate how others will respond and plan accordingly. Thinking multiple steps ahead gives an advantage over those who think only one step ahead.

  • Human behavior is also often rational, meaning it serves some purpose even if not obvious. Discovering the purpose behind seemingly irrational actions can provide insight.

  • Remaining chapters cover various economic techniques and topics like calculating probabilities, reverse reasoning, decision making, ethics, puzzles, and core areas like money, trade and finance.

  • Readers are encouraged to engage with the ideas and join an online discussion. The goal is to have fun and draw useful lessons from the different topics and problems presented.

In summary, the author presents a range of economic concepts and puzzles from different perspectives to help illuminate human behavior and decision making, while also entertaining readers. Multiple modes of thinking are highlighted.

  • The original problem of comparing fuel savings from upgrading a 12 mpg SUV to 15 mpg vs a 30 mpg car to 40 mpg could not be answered without more details on driving habits.

  • The second attempt adding that both drive the same daily miles was still not enough, as driving habits could still change with more efficient vehicles.

  • The third attempt specifying that daily miles driven would stay the same allowed a clear answer - upgrading the 12 mpg SUV to 15 mpg would save more gas than upgrading the 30 mpg car to 40 mpg, since the SUV uses much more gas to start with.

  • Even though a 40 mpg car is a 33% improvement in efficiency vs 30 mpg, and a 15 mpg SUV is only a 25% improvement vs 12 mpg, the raw amount of gas saved is greater for the SUV upgrade due to it using more gas initially.

  • This highlights the need for full context and assumptions to properly evaluate comparisons, and that percentage improvements can be misleading on their own.

Here are the key points made in the summary:

  • Drawing conclusions from aggregate statistics alone can be misleading if important subgroups are not considered separately.

  • In the Berkeley lawsuit example, looking only at aggregate acceptance rates obscured the fact that most individual departments did not discriminate. Breaking it down by department revealed the true picture.

  • In the jury selection example, equal aggregate selection rates for whites and blacks could still hide discrimination if location subgroups were not considered separately.

  • In the income trends example, a 15% increase for white males did not mean other groups saw less than 3% overall growth, since not breaking it down obscured large growth among other groups like white and nonwhite women.

  • Interpreting evidence requires careful consideration of potential hidden subgroups, as aggregate statistics alone can create illusions of discrimination/nondiscrimination or improperly attribute trends when important differences exist within subgroups. Breaking data down is important to avoid making incorrect inferences.

The key moral is that one should be wary of relying solely on aggregate statistics without considering potential differences or trends within important subgroups that could provide a very different picture of what is truly happening.

  • Aggregate statistics like median income or average test scores can mask improvements in different demographic groups if the composition of those groups changes over time.

  • A farmer’s median animal weight dropped from 1,000 to 300 pounds, but his techniques were still a success because individual cows and goats increased in size 300%.

  • Correlations between two factors like smoking and cancer rates, or policing and crime, don’t prove causation. Additional evidence from controlled experiments is needed.

  • While college graduates on average earn more, twin studies comparing earnings when one twin attends college and the other doesn’t provide the strongest evidence that college causes higher wages, as twins who make different educational choices are likely different in other important ways already. Raw correlations or comparisons between non-identical individuals/groups are not as strong as comparisons between closer-matched twins.

So in summary, aggregate statistics can be misleading and additional controlled experiments are needed to determine causal relationships, rather than just correlations, between variables. Twin studies aiming to compare the most similar individuals can provide stronger evidence than comparisons of less closely matched groups.

  • The passage discusses several examples where aggregate/overall statistics can be misleading and it’s better to look at breakdowns or subgroups. Examples given include admission rates by department, racial makeup of juries by geography, income by demographic, etc.

  • However, the passage also cautions that breakdown statistics can also mislead sometimes and the aggregate picture may be more accurate. It gives the example of Lou Gehrig vs Babe Ruth batting averages where looking at individual years favors Gehrig but aggregate over multiple years favors Ruth.

  • The moral is not to jump to conclusions based solely on any single type of statistic, and statistics in general can mislead if not interpreted carefully.

  • Several examples are then given to illustrate situations where initial conclusions could be misleading, such as a teacher evaluating student improvement, planes needing armor only where they had bullet holes, probationary student performance, and average class size statistics at a university.

  • In summary, the key message is to be very careful about drawing conclusions from any type of statistics alone, as both aggregate and breakdown data can sometimes provide a misleading picture if not interpreted and analyzed critically.

  • The passage discusses the idea that attractive teachers may be more effective not just because students find them attractive, but because attractiveness is correlated with other positive traits.

  • Specifically, it argues that attractive teachers likely have a passion for teaching that led them to pursue it as a career despite other opportunities, so they are probably better teachers as a result of that passion.

  • It cites a study that found attractive teachers’ students retain more knowledge, but argues the researchers failed to consider this deeper explanation for why attractiveness and teaching effectiveness may be correlated.

  • It then discusses how statistical fallacies can also occur in other fields like medicine. It provides an example showing how hospital statistics about cancer and heart attack patients could be misleading if factors like length of hospital stay are not considered.

  • The overall point is that attractiveness alone does not necessarily make someone a better teacher, but it may be correlated with deeper traits like passion that do impact teaching quality, and statistics in any field need appropriate context and consideration of confounding factors to avoid misleading inferences.

  • The passage discusses making predictions about the future and notes that predictions are often inaccurate. It provides examples of failed predictions from history.

  • The puzzles presented call for making predictions based on logical reasoning rather than obvious assumptions.

  • The first puzzle predicts that in an experiment where a large and small pig are placed in a box with a lever that dispenses food, the small pig will eat better. This is because the large pig will do the work of pressing the lever but the small pig can steal the food.

  • The second puzzle predicts that an adoption agency would receive more requests for girls than boys, even though most parents prefer boys. This is because girls who are put up for adoption are likely healthier and better behaved on average since boys have to be worse to be given up for adoption.

  • The third puzzle predicts that having a fourth child is unlikely to negatively impact the school performance of the first three children. This is because studies showing larger family size correlates with worse performance do not prove causation and are likely explained by other demographic factors of the parents.

So in summary, the passage discusses making logical predictions rather than relying on surface level assumptions, and provides examples predicting outcomes to puzzles involving pigs in a box, adoption requests, and family size/school performance.

  • The passage discusses how the number of children in a family impacts the school performance of those children. It notes that children from larger families (4+ children) on average do worse in school than those from smaller families (3 or fewer children).

  • However, this is likely due to demographic factors like parents’ education levels, rather than family size itself. Families with 4 children due to twins are studied and their children perform similarly to 3-child families, suggesting demographic factors are more important.

  • Even after controlling for demographics, later born children like 4th born still perform slightly worse, likely due to birth order effects. However, there is variation and many high achieving individuals still come from large families.

  • In conclusion, it is demographic characteristics correlated with large family size, rather than the size itself, that seem to primarily drive differences in school performance between children from smaller and larger families.

  • According to sophomore-level economics textbooks, the law that a price increase must always lead to a fall in consumption may not be universal. Real-world examples can sometimes defy this rule.

  • In 19th century Ireland, the average person ate around 9 pounds (45 potatoes) of potatoes per day for sustenance. Visitors noted the large potato consumption driven by manual labor.

  • Economists suspect that a small rise in potato prices could have had a devastating effect on Irish families, forcing them to double down on potatoes rather than cut back slightly. Some evidence suggests similar behaviors occurred with rice/wheat in parts of Asia.

  • The passage suggests that contrary to introductory economic theories, real world examples sometimes show consumption increasing rather than decreasing in response to small price rises, when an item is a staple food source for manual laborers.

  • The three preceding problems deal with why people behave differently on escalators versus stairs - specifically, that people tend to stand still on escalators but not on stairs.

  • This is presented as a puzzle that requires explanation, even though it may seem self-explanatory on the surface.

  • Attempting to rationally explain the behavior through concepts like physical fitness or cost-benefit analysis does not provide a fully satisfactory answer.

  • The author argues that any question about human behavior can potentially be made more complex and puzzling upon deeper consideration and questioning of initial assumptions.

  • Providing explanations for seemingly self-evident behaviors involves thoughtful analysis and considering alternative perspectives beyond just surface-level observations.

  • Insights into human psychology and decision-making can be gained by carefully examining even trivial-seeming phenomena that most people take for granted.

So in summary, the key idea is that fully explaining human behaviors, even simple ones, requires going beneath surface appearances and assumptions to gain a deeper understanding. Initial explanations may not tell the whole story.

  • The passage discusses several phenomena that initially seem to have obvious explanations but may have deeper truths underlying them.

  • It presents puzzles about why coal miners have more political power than fast food workers, why some mortgage deals seem too good to be true, racial disparities in traffic stops, and other topics.

  • The author argues the obvious explanations are often misleading and a deeper analysis is needed to uncover the true explanations.

  • Logic and facts will be provided to explain each topic and show the proposed explanations are more likely correct than some obvious alternatives.

  • Readers are invited to consider the explanations and provide their own if they think they can offer better ones.

  • The key omission is that no actual explanations are given in the passage itself. The reader is left to ponder the puzzles without any solutions presented. The author promises to return to the explanations later.

So in summary, the passage sets up several phenomena as puzzles, argues obvious explanations may be misleading, and invites readers to critically analyze potential explanations. However, it omits presenting any actual proposed explanations within the text.

  • Many studies have found that following a divorce, women’s living standards tend to fall while men’s tend to rise. Some commentators have concluded divorce is unfair to women.

  • The author argues neither conclusion (“divorce harms women” or “marriage harms men”) holds water. What we observe is that men are generally more willing to make financial sacrifices to stay married, indicating they value marriage. They are effectively “paying” their wives to remain married.

  • So marriage on average benefits men more than women. The key question is, why do men value marriage more? There is a biological reason - women have a biological clock forcing them to choose a suitable partner sooner, so their optimal strategy is to settle for an imperfect partner and try to change him. Men can wait longer to find a near-perfect partner.

  • This helps explain why men are more willing to financially sacrifice to stay married - they found a suitable partner after extensive search. Women who leave marriages would make sacrifices, while those who stay are kept there by financial rewards from their husbands. Fairness was never the issue - it stems from differences in biological imperatives between men and women.

There are a few key reasons why not all buildings are the same height:

  1. Land constraints and costs. The footprint of land available for construction varies, affecting how tall a building can go. Building height also impacts things like setbacks, light/air access, etc. dictated by zoning laws.

  2. Functional needs. Different types of buildings have different functional requirements that impact optimal height, like commercial vs. residential.

  3. Changing economics over time. As the previous calculus of costs, rental rates, etc. changes, so does the optimal height for new buildings.

  4. Competitive positioning. Individual developers may choose different heights to stand out from neighboring projects and offer differentiated product offerings.

  5. Historic preservation. Landmarks and historic districts constrain heights of new buildings for aesthetic/architectural reasons.

In the case of the Empire State Building specifically when it was built in the 1920s-30s:

  • The developer, William Lamb, wanted it to be the tallest building in the world as a marketing strategy to attract tenants. This competitive positioning drove its record-breaking height.

  • Neighboring developers may have made different economic calculations about optimal height based on their own cost-benefit analyses and needs. Uniform height was not necessary.

  • Zoning rules at the time allowed for the innovative height, but neighboring buildings chose not to push heights to the same extremes.

So in summary, individual optimization rather than uniformity helps explain variations in building heights within a city. Competitive positioning and changing economics over time also drive differentiated building profiles.

  • Nick and Ibrahim were contestants on the game show Golden Balls, where they had to secretly choose to split or steal a $10,000 prize.

  • Normally, rational self-interest would dictate stealing since it could yield the full prize while splitting risked getting nothing. But this would lead to both stealing and neither winning.

  • Contestants are given time to negotiate and make promises to each other before choosing. While promises to split are routinely broken, Nick took an unconventional approach.

  • Nick boldly promised Ibrahim that he would choose steal, but then split the prize with Ibrahim if Ibrahim chose split. This created a low-risk option for Ibrahim.

  • Even if Nick stole, his subsequent promise to split afterwards put greater pressure on him to follow through, more than a normal pre-choice promise to split.

  • Ibrahim went along with it, choosing split. Nick, surprisingly, also chose split and they split the prize as promised.

  • Nick’s strategy was brilliant as it incentivized Ibrahim to choose the cooperative option of split, while still allowing Nick a path to the full reward if kept his subsidiary promise afterward.

  • The passage describes a two-player game called the Prisoner’s Dilemma, where both players have an incentive to confess (play tough) even if they don’t know what the other player will do.

  • Confessing dominates not confessing regardless of the other player’s action. This leads both players to rationally confess, achieving a worse outcome than if they had both not confessed.

  • Many students misunderstand the game, thinking you confess out of fear of what the other player will do. But in reality, confessing is the dominant strategy no matter what the other does.

  • The game illustrates how rational individual decisions can lead to collectively irrational or undesirable outcomes, like an arms race. It’s analogous to the tragedy of the commons problem with overuse of shared resources.

  • Having an irrational opponent can sometimes be advantageous compared to both players being rational, as irrationality introduces unpredictability that disrupts the prisoner’s dilemma dynamic.

So in summary, the prisoner’s dilemma shows how rational self-interest at the individual level can paradoxically result in mutually poor outcomes at the collective level due to strategic interdependencies between players’ decisions.

  • The player is given the challenge of collecting 50 cards from 10 people, where each person holds a stack of cards with different numbers on them. The goal is to minimize the total score by collecting cards with lower numbers.

  • Simply asking for everyone’s 5 lowest cards might not work well, as some people’s lowest cards could be much higher numbers than others.

  • The optimal strategy is to first collect all cards with the number 1, then all cards with 2, then all with 3, and so on until 50 cards are collected.

  • This ensures the lowest possible score, as any alternative card picked instead of one already collected must have an equal or higher number by the rules of the problem. Swapping cards can only increase the total score.

  • By systematically collecting the lowest available numbers at each step, this strategy guarantees minimizing the final score, which is the goal of the “card golf” game.

  • The president has appointed the protagonist as Czar of Agriculture in Slobbovia. Their task is to arrange for 50 bushels of wheat to be produced at minimum cost.

  • The protagonist’s initial strategy of ordering each farmer to produce 5 bushels may not work, as costs can vary significantly between farmers.

  • A better strategy is to direct each farmer to produce as many bushels as possible at $1 cost or less, then $2 or less, and so on until 50 bushels are reached. This ensures the lowest total cost.

  • However, the farmers do not take directions and the costs for each farm are unknown.

  • The solution is to announce a price ($1/bushel initially) and let farmers choose to supply if they can produce below that price. Gradually raise the price until demand is met.

  • This price system automatically achieves the lowest cost solution without the need for a czar, by letting farmers who can most efficiently supply at each price point do so.

  • The price system is generally the most efficient way to allocate resources by incentivizing production and supply decisions by those with the best cost information - individual producers.

So in summary, the key insight is that a functioning price system will minimize production costs without centralized coordination, by harnessing private information held by producers.

  • The passage is about determining how irrational people’s preferences and choices may be. It discusses various hypothetical scenarios where preferences could reveal irrationality.

  • Having a preference for a sure outcome over a riskier but potentially higher payout option is rational, but some choices could still qualify as irrational - like changing your preferred option just because another is no longer available.

  • Preferences that allow someone to “bleed you dry” through bets or trades where they cannot lose would indicate irrationality.

  • The quiz includes scenarios like choosing between lotteries with different chance of payouts, or playing Russian roulette for money. The maximum someone would pay to reduce risk could reveal the strength or rationality of preferences.

  • Drawing balls from urns with different reward structures is used to analyze preferences over uncertain outcomes. Preferences that don’t maximize expected value could qualify as irrational.

  • In summary, the passage uses hypothetical scenarios and quizzes to explore what kinds of choices or preference patterns might qualify as irrational from an economist’s perspective, opening people up to “Dutch book” bets where others cannot lose.

  • The questions present hypothetical choices between options with varying probabilities of rewards (e.g. winning $1,000 if drawn ball is red or blue vs. just blue).

  • Choosing different options for similar probabilities across questions is considered irrational by the test’s standards.

  • For example, choosing the higher reward if it has a lower probability in one question, but choosing the certainty of a lower reward in another similar question.

  • The test assigns points for choices that are inconsistent based on this definition of rationality. More inconsistent choices earn more points.

  • Higher scores are labeled as less rational, from “perfectly rational” to “flakier than a pie crust.” However, the test acknowledges rationality is about consistent choices, not subjective feelings.

  • It provides examples to show how inconsistent choices across similar probability scenarios could theoretically be exploited to “turn someone into a money pump” and reduce their wealth over time.

  • The purpose is to highlight how rational choice theory in economics defines rationality based on logically consistent preferences, not subjective emotions or preferences that vary without reason.

  • The passage discusses several hypothetical scenarios involving choices under uncertainty and whether preferences across similar scenarios should be consistent to be considered rational.

  • For example, it argues preferring a sure outcome to a gamble with a higher expected value is rational, but not preferring the same sure outcome when framed as a very low probability event.

  • It also analyzes choices involving Russian roulette and removing bullets from a revolver, claiming the rational preferences should be the same across equivalent scenarios that just alter irrelevant details.

  • The key point is that rational preferences should be transitive - if you prefer A to B and B to C, you should prefer A to C. Introducing irrelevant changes to a scenario should not alter the rational ordering of preferences.

  • The passage uses these examples to argue the responder should not have different preferences across similar scenarios in the questionnaire to avoid being considered irrational. It invites re-evaluating answers if they were inconsistent across equivalent scenarios.

So in summary, it analyzes whether preferences are transitive and consistent across equivalent formulations of decision-making under risk and uncertainty, to determine if choices would qualify as rationally justified or prone to irrationality.

Here are the key points made in the passage:

  • The passage describes a hypothetical criminal case involving a murder in Manhattan where the sole suspect is a man named Nathan who was found at a bus stop with naturally purple hair.

  • Expert testimony establishes that naturally purple hair is extremely rare, with odds against it being either a million to one or a billion to one (depending on the version).

  • In the first version where odds are a million to one, the analyst calculates there would be around 4 people in Manhattan with naturally purple hair given the population. This means there is about a 25% chance Nathan is guilty, which is not enough to conclude guilt beyond a reasonable doubt.

  • In the second version where odds are a billion to one, the analyst calculates there would be around 0.004 people in Manhattan with naturally purple hair. This implies the probability Nathan is guilty is over 99.99%, which meets the standard of beyond a reasonable doubt.

  • The passage uses this hypothetical scenario to discuss what constitutes “beyond a reasonable doubt” from an evidence and probability standpoint in a criminal trial. It suggests probabilities over around 98% would typically meet that legal standard.

So in summary, the passage examines how likelihood probabilities can determine whether guilt can be concluded beyond a reasonable doubt based on the limited evidence presented in a hypothetical criminal case.

Here is my analysis of whether the medieval boiling water test could be an effective way to sort the guilty from the innocent:

  • On the surface, it seems random and arbitrary. However, additional context is needed to properly evaluate it.

  • Important questions remain about how it was actually implemented and perceived by participants at the time. Societal and religious norms then may have influenced perceptions of its legitimacy and effectiveness in a way that is difficult to fully understand from our modern perspective.

  • Without more details on the historical and cultural context, it is difficult to make a conclusive judgment about its effectiveness compared to alternative adjudication methods available at the time.

  • Modern standards of evidence and procedural fairness were not established centuries ago. So while this practice would clearly be unacceptable today, its appropriateness for the era needs to considered based on prevailing norms and alternatives of that period.

  • An objective, dispassionate analysis requires understanding all aspects of how this process was integrated into the broader legal system and social fabric of the time. Our initial reaction of skepticism may say more about modern sensibilities than provide an authoritative evaluation of this medieval practice in its own historical context.

In summary, more information would be needed for a well-informed judgment. An open and intellectually rigorous analysis requires understanding the full context before making a definitive assessment of its effectiveness relative to alternatives during that period in history.

  • Professor Leeson believes that trial by ordeal systems could have worked effectively in the past, as long as there was widespread superstitious belief that they yielded accurate verdicts from God.

  • Guilty defendants would always confess to avoid the risky ordeal, while innocent defendants would opt for the ordeal knowing the priests would cheat to acquit them. This would reinforce the superstitious beliefs.

  • While not perfect, ordeal systems could have worked if there was enough superstition and priests aimed to convict the guilty and acquit the innocent. Some historical evidence supports this theory.

  • Professor Leeson’s conclusion is that no one wants ordeals back, but if the necessary beliefs existed, perhaps they could have worked after all. He presents this as a thought-provoking idea rather than an endorsement of returning to ordeals.

  • There is a debate about the expected ratio of boys to girls in a population where families keep having children until they have a boy and then stop.

  • Some argue the ratio would be 1:1 (50% boys, 50% girls) on average. However, this is not correct.

  • There is a non-zero probability that every family could have a boy on the first try, resulting in an infinite ratio of boys to girls.

  • When factoring in this possibility, even if it has an extremely low probability, the expected ratio across many populations becomes infinity, not 1:1.

  • People get emotionally attached to their initial intuition that the ratio should be 1:1, and resist accepting the counterintuitive but correct argument even when provided clear explanations and examples.

  • This phenomenon is similar to debates about “hot hands” in basketball - where data is often misinterpreted due to a failure to properly understand problems like the one described here.

In summary, while the 1:1 ratio intuitively seems correct, precise statistical reasoning shows the expected ratio is actually infinity due to low-probability edge cases, and people have trouble accepting this counterintuitive conclusion.

Here is a summary of the explanation provided in the passage:

  • There is a temptation to use backward induction to reason that if everyone else is revealing their financial records, then it must be optimal for you to reveal as well in order to signal your actual level of wealth.

  • However, this leads to a cascading effect where everyone ends up revealing their records, even those with very little wealth who have more to gain from secrecy.

  • The passage uses the example of a city where people want to signal their wealth. Those with the maximum allowed wealth of 100 units reveal their records to prove they have the maximum.

  • This forces those with 99 units to reveal to prove they have 99 rather than some lower amount. And this continues cascading down until even those with just 1 unit feel compelled to reveal.

  • Economists call this type of reasoning backward induction - starting from the end state and working back sequentially to determine the optimal actions at each prior step. It highlights how rational individual actions can lead to an outcome where secrecy is lost for all.

So in summary, the temptation for individual signaling can cascade into a collective unraveling of secrecy through the logical step-by-step process of backward induction reasoning.

The strategy of using backward induction to determine that a snake oil salesman would have no incentive to provide an honest product on any day of their lease will not work in the real world. This is because the strategy makes unrealistic assumptions.

Specifically, it assumes the salesman’s interactions are isolated and that their reputation does not carry over beyond the end of the lease period. In reality, people’s reputations do follow them and past actions can impact future opportunities and relationships even after a particular business ends. So there is an incentive to maintain honesty and trustworthiness over the long run.

Backward induction itself is a valid logical technique when properly applied. The issue is not with backward induction, but with artificial scenarios that ignore real-world factors like long-term reputation effects. Real businesses do operate honestly because they plan to be in business indefinitely and their reputation matters beyond any single business interaction or lease period. So the isolated game assumption that undermines backward induction strategies does not apply in reality.

  • Hamkins and his wife want to swap picking up their kids from school one day, but can’t coordinate the plan via messages due to the problem of common knowledge. No matter how many messages they exchange, they can never be certain the other person has all the necessary information.

  • Common knowledge means everyone knows something, everyone knows everyone knows it, and so on ad infinitum. Hamkins and his wife do not achieve common knowledge through their messages due to the finite number of exchanges.

  • Backward induction is a valid logical technique that can be misapplied, like any technique. While the Surprise Quiz paradox implicates backward induction, the Incredible Teacher paradox does not involve it. So the latter does not point to a problem with backward induction specifically.

  • In the story of the obedient prisoners with colored dots on their foreheads, the warden revealing information does cause prisoners to realize the color of their own dots, even though they were already aware some dots were red and some blue. The key is the warden’s statement makes this a matter of common knowledge, whereas separate whispers would not.

  • Alice and Bob are spies who need to verify each other’s identities without revealing their secret password to a possibly hostile third party (the stranger).

  • The stranger offers to help but also cannot learn the password.

  • The solution has the stranger pick a secret number and whisper it to Alice.

  • Alice mentally adds this number to the password and whispers the total to Bob.

  • Bob then mentally subtracts the password from the total and whispers the result to the stranger.

  • If the stranger’s secret number comes back, that proves Bob subtracted the correct password, confirming his identity to Alice without either revealing the password.

  • This allows verification of identities while keeping the password secret from both the stranger and in the public conversation between Alice and Bob. It demonstrates a zero-knowledge proof - proving a fact without revealing sensitive details.

Here is a summary of the puzzle involving 10 ferocious pirates dividing up 100 gold coins:

  • There are 10 ferocious pirates who have acquired 100 gold coins that must be divided among them.

  • The most ferocious pirate proposes a division of the coins. If at least half the pirates vote yes, that division is accepted. If not, the proposing pirate is thrown overboard.

  • Each pirate’s priorities are to avoid being thrown overboard, acquire as many coins as possible, and see other pirates thrown overboard.

  • The expected solution is that the most ferocious pirate, Arlo, would propose taking 96 coins, with the remaining pirates each taking 1 coin except Bob who gets 0. This passes because the odd-numbered pirates vote yes to avoid being thrown overboard themselves.

  • However, this is not the only possible solution. Other valid solutions include one pirate taking all 100 coins and the others voting yes even though they prefer not to, or some pirates voting no while others vote yes.

  • The mistake in the expected solution is that it assumes pirates will always vote for their preferred outcome, when in fact they may rationally vote in a way that doesn’t affect the outcome.

So in summary, while a 96/1/1/0/1 allocation is one possible solution, it is incorrect to say it is the only solution due to flaws in assuming pirate voting behavior. The problem does not fully specify how pirates will vote in non-impactful situations.

  • Bob, who has the deciding vote in a committee, is considering how to vote. If he votes for his preferred outcome, that outcome will be chosen since he has the deciding vote. So voting for his preferred outcome seems like the rational choice.

  • However, Bob may be unsure of how the other committee members are voting. There are a few reasons he could be unsure:

  1. He’s not 100% certain the others will vote rationally.

  2. He doesn’t know if they know everyone else will vote rationally.

  3. There could be multiple levels of uncertainty about what everyone knows - he doesn’t know if they all know they all know they will vote rationally, and so on.

  • This lack of “common knowledge” about rationality means Bob can’t be entirely sure how the others will vote. So to cover all possibilities, the only rational choice for Bob may be to vote for his preferred outcome.

  • Stating the problem assuming everyone knows everyone else is rational is an oversimplification. This example highlights that this simplifying assumption can break down and lead to incorrect analysis if rationality is not common knowledge.

  • The Best Friend Rule says to take just the Mystery (M) box, as your best friend would be happy to hear you got $1 million.

  • The Cause and Effect Rule disagrees. Your choice of one box cannot cause Zorxon to put money in that box, as he decides before you. So you might as well take both boxes (M and T).

  • A souped-up Psychic Best Friend Rule also says to take both boxes, as your psychic best friend knowing what’s actually in the boxes would want you to take both.

  • The Cause and Effect Rule embodies the serenity prayer - accept what you can’t change (what’s in the boxes) and change what you can (take the extra $1,000).

  • Newcomb’s Problem has puzzled philosophers for over 50 years. Arguments can be made for both one-boxing and two-boxing based on different rationales.

  • The author presents the “Amnesia Problem” as an analogy, arguing it is essentially identical to Newcomb’s Problem and easy to decide - don’t burn the $1,000 bill as it can’t change what’s in the attic, just as taking one or two boxes can’t change what Zorxon has already done. This is meant to suggest Newcomb’s Problem may also have an easy solution of two-boxing.

The passage discusses various thought experiments and scenarios involving life-or-death decision making, and how such decisions relate to philosophical and ethical questions. It brings up a classic trolley problem scenario involving diverting a runaway trolley to save lives by sacrificing one person. It also discusses how policymakers and economists face similar types of decisions when weighing factors like lives saved vs. spent on different programs.

The passage notes that we routinely weigh lives against other considerations as well, like allowing household products that pose small individual death risks but provide convenience benefits to consumers. It suggests that in policymaking, what matters most is whether individual citizens are comfortable with the level of risk to their own lives, rather than just total numbers of lives lost. Overall the passage examines philosophical issues around quantifying and comparing the value of human lives in policy decisions involving risks and benefits to public safety and welfare.

  • The main principle outlined is to “give the people what they want” when making policy decisions. This means considering what the preferences and interests of those affected by the policy are.

  • However, it’s not always clear what “the people” collectively want, as different groups may have differing interests.

  • To deal with this, the passage introduces the “Amnesia Principle” - imagine asking a hypothetical person with amnesia who doesn’t know their own situation or preferences. This helps abstract away personal biases.

  • Examples are given where this analysis could determine the right policy choice, such as sacrificing one person to save five in the trolley problem based on probabilities.

  • It’s acknowledged people may not always act in line with their better instincts due to fear or squeamishness.

  • When applying these principles, policymakers should first consider what all affected parties collectively want based on the Amnesia analysis. If they still disagree, go with what amnesia victims would prefer based on probabilities.

  • This framework of analysis is presented as one economists commonly use to evaluate policy problems, though others may disagree with the approach.

In summary, the key idea is that policy should align with preferences of affected parties based on an impartial analysis, using the Amnesia Principle to address instances of differing interests.

  • Betty is suffering from an unknown disease. The Kildare Study and Casey Study are two potential research studies that could help save her life.

  • The Kildare Study is twice as likely as the Casey Study to save Betty’s life. Betty wants the funds to go to the Kildare Study.

  • If the funds go to the Kildare Study, there is a 99% chance it will fail. But if it succeeds, Betty’s life would be saved.

  • If the funds go to the Casey Study, there is a 25% chance it will have major success, resulting in banner headlines and career benefits for the person funding it.

  • The example is simplified by assuming Betty only cares about her chance of survival, not symptom relief. If symptoms are factored in, it gets more complex.

  • Most funding/research decisions face similar trade-offs between higher risk/reward options and lower risk/reward options. Personal motivations and probabilities are difficult to determine precisely. Reasonable people can disagree on the best choice.

The key dilemma presented is that choosing the option with the higher chance of success for the individual (Kildare Study) carries much greater risk, while the safer option (Casey Study) has a self-interested motivation of potential career benefits if successful. There is no unambiguously “right” answer.

  • Alice is playing a game against Bob where they each bring varying amounts of money determined by coin flips. There is a 25% chance each outcome will occur.

  • One friend Carol argues the odds are against Alice since the expected value of each row (for a given amount Bob brings) is that Alice loses 50 cents.

  • Another friend Doreen argues the odds favor Alice since the expected value of each column (for a given amount Alice brings) is that she wins 50 cents.

  • A third friend Eddie argues the game is perfectly symmetric so neither player has an advantage.

  • The issue is that while each row and column has an expected value, the chart as a whole does not since there are an infinite number of possibilities. So there is no single answer to Alice’s question of her overall expected value.

  • Playing repeatedly will not help Alice break even on average due to the unique nature of this game where averages cannot be properly computed. She faces risk no matter how many times she plays.

  • Unlike typical situations, the law of large numbers does not apply here to eliminate risk, so the economists’ usual advice of diversifying bets does not help Alice.

  • Albert is trying to drive home from work but gets lost at intersections due to his absent-mindedness.

  • His best strategy is to flip a coin at each intersection - heads means go straight, tails means turn right. This gives him a 1/4 chance of making it home safely.

  • Economists are interested in Albert as a model for how real absent-minded people make decisions.

  • The story then explores varying levels of sophistication Albert could have in re-evaluating and potentially changing his coin-flipping strategy as he approaches each new intersection.

  • It discusses whether Albert should stick to one strategy or be able to change strategies, and how that impacts the probability calculations of his chances of making it home.

  • In the end, it suggests the most optimal strategy for Albert would be to start by always turning right, then update his strategy appropriately at each intersection to eventually ensure he makes it home with certainty.

So in summary, it uses Albert’s problem of navigating intersections as a thought experiment to explore different assumptions about rational decision-making under uncertainty and imperfect information or memory.

  • The passage presents an imagined scenario where Albert is able to remember the coin he previously chose at an intersection, as well as one rule for updating his strategy each time he reaches a new intersection.

  • Some example rules are given, such as always squaring the probability of his previous coin, or adding 1 to the previous probability and dividing by 2. Randomness can also be built into the rule.

  • The author argues this version of Albert (Mark Three) is more consistent than previous versions, as he will correctly assume he will always follow the same updating rule in the future.

  • Unlike Mark One who inconsistently believes he can and can’t change strategies, or Mark Two who sometimes incorrectly believes he will revert to a past strategy, Mark Three properly assumes he will always use the same rule going forward as in the past.

  • While Mark Three may seem to remember a lot for an absent-minded agent, the author argues the other Marks also remember significant details about their past coin flips and predictions of future behavior.

  • In summary, the passage presents Albert Mark Three as a more rationally consistent version of Albert that follows a single, predictable rule for updating his strategy at intersections, rather than behaving unpredictably like previous versions.

  • Earl the electrician and Carla the carpenter want to rewire their houses and panel their dens.

  • Earl can rewire a house in 10 hours and panel a den in 15 hours.

  • Carla can rewire a house in 20 hours but panel a den in 18 hours, though she’s not as skilled.

  • Earl argues that trading labor makes no sense since he’s better at both jobs.

  • However, if they specialize - Earl does all the rewiring and Carla all the paneling - they can complete the jobs faster. Earl would spend 20 hours rewiring 2 houses, and Carla 36 hours paneling 2 dens, saving them both time.

  • Even though Carla is slower at each task, she has a “comparative advantage” in paneling since she can do it with less lost time than rewiring. Specializing and trading allows them both to benefit through gained efficiency.

  • The business is an engineering firm, indicating it employs engineers to do technical work.

  • Mary is described as a first-class engineer, showing she has strong engineering skills and qualifications.

  • George barely passed high school algebra, suggesting he has weak math and technical abilities compared to Mary.

  • The conclusion is that despite Mary’s strong engineering background, George has a comparative advantage in typing. His typing skills allow him to free up Mary’s time from administrative tasks so she can focus on engineering work where she is most skilled and valuable.

  • By having George do all the typing work, and Mary focusing on engineering, they can both be more productive and the business can benefit from having each person specialize in their comparative advantage. Even though Mary is clearly more skilled as an engineer, George’s typing ability relative to hers gives him a niche role where trade between them creates gains.

Here is a summary of the relevant discussion:

  • The Organ Eater refers to evidence found in a paper by Robert Jensen and Nolan Miller that in certain parts of Asia, increases in the price of some grains can paradoxically lead to increases in their consumption. This occurs because high prices mean the grains must be more valued as a luxury or status good, increasing demand.

  • The evidence is from a research paper published by economists Robert Jensen and Nolan Miller, suggesting the discussion refers back to empirical findings presented in that academic work.

In summary, the key points are that (1) increases in grain prices in some Asian countries can perversely increase consumption rather than decrease it, and (2) this phenomenon and evidence for it are discussed in a paper by economists Robert Jensen and Nolan Miller. The discussion is invoking empirical evidence from academic research to support and provide context for the claim being made.

Here is a summary of the instruction:

Always give a number that is less than 1/2. Since 1/2 is 0.5, any number between 0 and 0.5 (excluding 0.5) satisfies this requirement.

Here are the summaries of the relevant passages:

  • Passage 17 summarizes a 1997 law review article by A. Volokh that documented a long tradition of considering numbers higher than the standard “ten guilty men” phrase when weighing convicting innocent people vs letting guilty people go free.

  • Passage 21 summarizes a 1948 paper by D.J. O’Connor about pragmatic paradoxes.

  • Passage 22 notes that the column in passage 21 was reproduced in a book by Gardner about mathematical diversions.

  • Passage 29 summarizes E. Yudkowsky’s 2010 work on “Timeless Decision Theory.”

  • Passages 31-32 summarize debates about comparing harms, like headaches vs lives, and cite examples.

  • Passages 36-37 summarize influential papers on asset pricing - Ross (1976) on arbitrage pricing theory and Black-Scholes (1973) on pricing corporate liabilities.

Here is a summary of key points from chapter 5, problem 1:

  • The problem involves a group of pirates called the Ferocious Pirates who must vote on a course of action. Each pirate can vote either to stay and fight or sneak away.

  • It is assumed all pirates are fully aware of each other’s strategies. This is called “common knowledge.” This will influence how each pirate votes.

  • The problem can be solved using backward induction, which was introduced in the previous chapter. This means considering the last pirate to vote and working backwards.

  • No matter what the previous pirates vote, the last pirate will always vote to sneak away to avoid punishment if they lose the fight. Knowing this, the second to last pirate also has incentive to sneak away. This logic extends to all pirates.

  • Therefore, the only logical outcome or “Nash equilibrium” is for all pirates to vote to sneak away, even though collectively they could win if they all fought. Common knowledge of strategies leads rational actors to an outcome that is not collectively optimal.

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