7. See Gladwell (1999).
8. Naturally, how many friends you count people as having depends a lot on how you define “friendship,” a concept that has always been ambiguous, and is even more so now in the era of social networking sites, where you can “friend” someone you don’t even know. The result is that what we might call “true” friendship has become difficult to distinguish from mere “acquaintanceship,” which in turn has gotten blurred together with the even more ephemeral notion of “one-way acquaintanceship” (i.e., “I’ve heard of you, but you don’t know me from Adam”). Although some people on MySpace have a million “friends,” as soon as we apply even the loosest definition of friendship, such as each person knowing the other on a first-name basis, the number immediately drops to the range of a few hundred to a few thousand. Interestingly, this range has remained surprisingly constant since the first studies were conducted in the late 1980s (McCormick et al. 2008; Bernard et al. 1989, 1991; Zheng et al. 2006).
9. There are a number of subtleties to the issue of chain lengths in small-world experiments that have led to a certain amount of confusion regarding what can and cannot be concluded from the evidence. For details about the experiment itself, see Dodds, Muhamad, and Watts (2003), and for a clarifying discussion of the evidence, as well as a detailed analysis of chain lengths, see Goel, Muhamad, and Watts (2009).
10. See Watts and Strogatz (1998); Kleinberg (2000a; 2000b); Watts, Dodds, and Newman (2002); Watts (2003, ch. 5); Dodds, Muhamad, and Watts (2003); and Adamic and Adar (2005) for details on the searchability of social networks.
11. Influencers go by many names. Often they are called opinion leaders or influentials but they are also called e-fluentials, mavens, hubs, connectors, alpha mums, or even passionistas. Not all of these labels are intended to mean exactly the same thing, but they all refer to the same basic idea that a small number of special individuals have an important effect on the opinions, beliefs, and consumption habits of a large number of “ordinary” individuals (see Katz and Lazarsfeld 1955, Merton 1968b, Weimann 1994, Keller and Berry 2003, Rand 2004, Burson-Marsteller 2001, Rosen 2000, and Gladwell 2000 for a range of influentials-related labels). Ed Keller and Michael Berry claim that “One in ten Americans tells the other nine how to vote, where to eat, and what to buy.” They conclude, in fact, that “Few important trends reach the mainstream without passing through the Influentials in the early stages, and the Influentials can stop a would-be trend in its tracks” (Keller and Berry 2003, pp. 21–22); and the market-research firm Burson-Marsteller concurs, claiming that “The far-reaching effect of this powerful group of men and women can make or break a brand, marshal or dissolve support for business and consumer issues, and provide insight into events as they unfold.” All one needs to do, it seems, is to find these individuals and influence them. As a result, “Influencers have become the ‘holy grail’ for today’s marketers” (Rand 2004).
12. For the original quote, see Gladwell (2000, pp. 19–21).
13. See Keller and Berry (2003, p. 15).
14. See, for example, Christakis and Fowler (2009), Salganik et al. (2006), and Stephen (2009).
15. In fact, even then you can’t be sure. If A and B are friends, they are likely to have similar tastes, or watch similar shows on TV and so be exposed to similar information; thus what looks like influence may really just be homophily. So if every time a friend of A’s adopts something that A adopts, we attribute that to A’s influence, we are probably overestimating how influential A is. See Aral (2009), Anagostopoulos et al. (2008), Bakshy et al. (2009), Cohen-Cole and Fletcher (2008b, 2008a) Shuliti and Thomas (2010), and Lyons (2010) for more details on the issue of similarity versus influence.
16. See Katz and Lazarsfeld (1955) for a discussion of the difficulty of measuring influence, along with a more general introduction to personal influence and opinion leaders. See Weimann (1994) for a discussion of proxy measures of influence.
17. See Watts (2003) and Christakis and Fowler (2009) for discussions of contagion in social networks.
18. The connection between influentials and contagion is most explicit in Gladwell’s analogy of “social epidemics,” but a similar connection is implied throughout the literature on influentials. Everett Rogers (1995, p. 281) claims that “The behavior of opinion leaders is important in determining the rate of adoption of an innovation in a system. In fact, the S-shape of the diffusion curve occurs because once opinion leaders adopt and tell others about the innovation, the number of adopters per unit time takes off.” Keller and Berry make a similar point when they claim that influentials are “like the central processing units of the nation. Because they know many people and are in contact with many people in the course of a week, they have a powerful multiplier effect, spreading the word quickly across a broad network when they find something they want others to know about” (Keller and Berry 2003, p. 29).
19. For details of the models, see Watts and Dodds (2007).
20. The original Bass model is described by Bass (1969).
21. See Gladwell (2000, p. 19).
22. A number of people interpreted this result as a claim that “influentials don’t exist,” but that’s actually not what we said. To begin with, as I’ve discussed, there are so many different kinds of influentials that it would be impossible to rule them all out even if that was what we intended to do. But we didn’t intend to do that. In fact, the whole point of our models was to assume the existence of influentials and see how much they mattered relative to ordinary individuals. Another misconception regarding our paper was that we had claimed that “influentials don’t matter,” but that’s not what we said either. Rather, we found only that influentials are unlikely to play the role described by the law of the few. Whether or not influentials, defined somehow, can be reliably identified and exploited in some manner remains an open question.
23. See Adar and Adamic (2005); Sun, Rosenn, Marlow, and Lento (2009); Bakshy, Karrer, and Adamic (2009); and Aral et al. (2009) for details.
24. For details of the Twitter study see Bakshy et al (2010).
25. For the anecdote about Kim Kardashian’s $10,000 Tweets, see Sorkin (2009, b).
CHAPTER 5: HISTORY, THE FICKLE TEACHER
1. A number of sociologists have even argued explicitly that history ought to be a scientific discipline with its own laws and methods for extracting them (Kiser and Hechter 1998). Historians, meanwhile, have been more circumspect regarding the scientific status of their discipline but have nonetheless been tempted to draw analogies between their own practices and those of natural scientists (Gaddis 2002).
2. See Scott (1998) for a discussion of what he calls metis (the Greek word for “skill”), meaning the collection of formal decision procedures, informal rules of thumb, and trained instinct that characterized the performance of experienced professionals.
3. For more on creeping determinism and hindsight bias, see the classic article by Baruch Fischhoff (1982). Philosophers and psychologists disagree over how strong our psychological bias to think deterministically really is. As Roese and Olson (1996) point out, people frequently do engage in counterfactual thinking—imagining, for example, how things might have worked out “if only” some antecedent event had not taken place—suggesting that commonsense views of causality are more conditional than absolute. A more correct way to state the problem, therefore, is that we systematically overweight the likelihood of what happened relative to the counterfactual outcomes. For the purpose of my argument, however, it is sufficient that we do the latter.
4. See Dawes (2002, Chapter 7) for the full story of Flight 2605 and analysis.
5. See Dawes (2002) and Harding et al. (2002) for more on school shootings.
6. See Gladwell (2000, p. 33)
7. See Tomlinson and Cockram (2003) for details on the SARS outbreaks in the Prince of Wales Hospital and the Amoy Gardens apartment complex. Various theoretical models (Small et al. 2004; Bassetti et al. 2005; Masuda et al. 2004) have subsequently b
een proposed to explain the SARS epidemic in terms of superspreaders.
8. See Berlin (1997, p. 449).
9. Gaddis (2002), in fact, makes more or less this argument.
10. For the full argument, see Danto (1965).
11. For the full story of Cisco, see Rosenzweig (2007).
12. See Gaddis (2002).
13. See Lombrozo (2007) for details of the study. It should be noted that when told in simple terms the relative probabilities of the different explanations, participants did in fact choose the more complex explanation at a much higher rate. Such explicit information, however, is rarely available in real-world scenarios.
14. See Tversky and Kahneman (1983) for details.
15. For evidence of confidence afforded by stories, see Lombrozo (2006, 2007) and Dawes (2002, p. 114). Dawes (1999), in fact, makes the stronger argument that human “cognitive capacity shuts down in the absence of a story.”
16. For example, a preference for simplicity in explanations is deeply embedded in the philosophy of science. The famous Ockham’s razor—named for the fourteenth-century English logician William of Ockham—posits that “plurality ought never be posited without necessity,” meaning essentially that a complex theory ought never to be adopted where a simpler one would suffice. Most working scientists regard Ockham’s razor with something close to reverence—Albert Einstein, for example, once claimed that a theory “ought to be as simple as possible, and no simpler”—and the history of science would seem to justify this reverence, filled as it is with examples of complex and unwieldy ideas being swept away by simpler, more elegant formulations. What is perhaps less appreciated about the history of science is that it is also filled with examples of initially simple and elegant formulations becoming increasingly more complex and inelegant as they struggle to bear the burden of empirical evidence. Arguably, in fact, it is the capacity of the scientific method to pursue explanatory power, even at the cost of theoretical elegance and parsimony, where its real strength lies.
17. For Berlin’s full analysis of the differences between science and history, and the impossibility of remaking the latter in the image of the former, see Berlin (1960).
18. See Gaddis (2002) for a warning about the perils of generalizing, and also some examples of doing just that.
19. George Santayana (1905).
CHAPTER 6: THE DREAM OF PREDICTION
1. See Rosenbloom (2009).
2. See Tetlock (2005) for details.
3. See Schnaars (1989, pp. 9–33) for his analysis and lots of entertaining examples. See also Sherden (1998) for additional evidence of the lousy forecasting record of futurologists. See also Kuran (1991) and Lohmann (1994) for discussions of the unpredictability of political revolutions; specifically the 1989 collapse of the East Germany. And see Gabel (2009) for a retrospective look at the Congressional Budget Office’s Medicare cost predictions.
4. See Parish (2006) for a litany of intended blockbusters that tanked at the U.S. box office (although some, like Waterworld, later became profitable through foreign box office revenues and video and DVD sales). See Seabrook (2000) and Carter (2006) for some entertaining stories about some disastrous miscalculations and near-misses inside the media industry. See Lawless (2005) for some interesting background on the publisher Bloomsbury’s decision to acquire Harry Potter (for £2,500). General information about production in cultural industries is given in Caves (2000) and Bielby and Bielby (1994).
5. In early 2010, the market capitalization of Google was around $160B, but it has fluctuated as high as $220B. See Makridakis, Hogarth, and Gaba (2009a) and Taleb (2007) for lengthier descriptions of these and other missed predictions. See Lowenstein (2000) for the full story of Long-Term Capital Management.
6. Newton’s quote is taken from Janiak (2004, p. 41).
7. The Laplace quote is taken from http://en.wikipedia.org/wiki/Laplace’s-demon.
8. Lumping all processes into two coarse categories is a vast oversimplification of reality, as the “complexity” of a process is not a sufficiently well understood property to be assigned anything like a single number. It’s also a somewhat arbitrary one, as there’s no clear definition of when a process is complex enough to be called complex. In an elegant essay, Warren Weaver, then vice president of the Rockefeller Foundation, differentiated between what he called disorganized and organized complexity (Weaver 1958), where the former correspond to systems of very large numbers of independent entities, like molecules in a gas. Weaver’s point was that disorganized complexity can be handled with the same kinds of tools that apply to simple systems, albeit in a statistical rather than deterministic way. By organized complexity, however, he means systems that are neither simple nor subject to the helpful averaging properties of disorganized systems. In my dichotomous classification scheme, in other words, I have effectively lumped together simple systems with disorganized systems. As different as they are, however, they are similar from the perspective of making predictions; thus conflation does not affect my argument.
9. See Orrell (2007) for a slightly different take on prediction in simple versus complex systems. See Gleick (1987), Watts (2003), and Mitchell (2009) for more general discussions of complex systems.
10. When I say we can predict only the probability of something happening, I am speaking somewhat loosely. The more correct way to talk about prediction for complex systems is that we ought to be able to predict properties of the distribution of outcomes, where this distribution characterizes the probability that a specified class of events will occur. So, for example, we might predict the probability that it will rain on a given day, or that the home team will win, or that a movie will generate more than a certain level of revenue. Equivalently, we might ask questions about the number of points by which we expect the home team to win, or the expected revenue of a particular class of movies to earn, or even the variance that we expect to observe around the average. Regardless, all these predictions are about “average properties” in the sense that they can be expressed as an expectation of some statistic over many draws from the distribution of outcomes.
11. For a die roll, it’s even worse: The best possible performance is to be right one time out of six, or less than 17 percent. In real life, therefore, where the range of possible outcomes can be much greater than a die roll—think, for example, of trying to predict the next bestseller—a track record of predicting the right outcome 20 percent of the time might very well be as good as possible. It’s just that being “right” 20 percent of the time also means being “wrong” 80 percent of the time; that just doesn’t sound very good.
12. See http://www.cimms.ou.edu/~doswell/probability/Probability.html. Orrell (2007) also presents an informative discussion of weather prediction; however, he is mostly concerned with longer-range forecasts, which are considerably less reliable.
13. Specifically, “frequentists” insist that statements about probabilities refer to the relative fraction of particular outcomes being realized, and therefore apply only to events, like flipping a coin, that can in principle be repeated ad infinitum. Conversely, the “evidential” view is that a probability should be interpreted only as the odds one ought to accept for a particular gamble, regardless of whether it is repeated or not.
14. See de Mesquita (2009) for details.
15. As Taleb explains, the term “black swan” derives from the European settlement of Australia: Until the settlers witnessed black swans in what is now Western Australia, conventional wisdom held that all swans must be white.
16. For details of the entire sequence of events surrounding the Bastille, see Sewell (1996, pp. 871–78). It is worth noting, moreover, that other historians of the French Revolution draw the boundaries rather differently from Sewell.
17. Taleb makes a similar point—namely that to have predicted the invention of what we now call the Internet, one would have to have known an awful lot about the applications to which the Internet was put after it had been invented. As Taleb puts it, “t
o understand the future to the point of being able to predict it, you need to incorporate elements from this future itself. If you know about the discovery you are about to make, then you have almost made it” (Taleb 2007, p. 172).
CHAPTER 7: THE BEST-LAID PLANS
1. Interestingly, a recent story in Time magazine (Kadlec 2010) contends that a new breed of poker players is relying on statistical analysis of millions of games played online to win at major tournaments.
2. See Ayres (2008) for details. See also Baker (2009) and Mauboussin (2009) for more examples of supercrunching.
3. For more details on prediction markets, see Arrow et al. (2008), Wolfers and Zitzewitz (2004), Tziralis and Tatsiopoulos (2006), and Sunstein (2005). See also Surowiecki (2004) for a more general overview of the wisdom of crowds.
4. See Rothschild and Wolfers (2008) for details of the Intrade manipulation story.
5. In a recent blog post, Ian Ayres (author of Supercrunchers) calls the relative performance of prediction markets “one of the great unresolved questions of predictive analytics” (http://freakonomics.blogs.nytimes.com/2009/12/23/prediction-markets-vs-super-crunching-which-can-better-predict-how-justice-kennedy-will-vote/).
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