andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1615 knowledge-graph by maker-knowledge-mining
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Introduction: A tall thin young man came to my office today to talk about one of my current pet topics: stories and social science. I brought up Tom Wolfe and his goal of compressing an entire city into a single novel, and how this reminded me of the psychologists Kahneman and Tversky’s concept of “the law of small numbers,” the idea that we expect any small sample to replicate all the properties of the larger population that it represents. Strictly speaking, the law of small numbers is impossible—any small sample necessarily has its own unique features—but this is even more true if we consider network properties. The average American knows about 700 people (depending on how you define “know”) and this defines a social network over the population. Now suppose you look at a few hundred people and all their connections. This mini-network will almost necessarily look much much sparser than the national network, as we’re removing the connections to the people not in the sample. Now consider how
sentIndex sentText sentNum sentScore
1 A tall thin young man came to my office today to talk about one of my current pet topics: stories and social science. [sent-1, score-0.446]
2 Strictly speaking, the law of small numbers is impossible—any small sample necessarily has its own unique features—but this is even more true if we consider network properties. [sent-3, score-1.29]
3 The average American knows about 700 people (depending on how you define “know”) and this defines a social network over the population. [sent-4, score-0.48]
4 Now suppose you look at a few hundred people and all their connections. [sent-5, score-0.091]
5 This mini-network will almost necessarily look much much sparser than the national network, as we’re removing the connections to the people not in the sample. [sent-6, score-0.665]
6 For novelistic reasons he can only have a handful of major characters and a few dozen or so minor characters. [sent-8, score-0.447]
7 If he gives them a realistic level of interconnections, the resulting network will not be a reasonable small-scale replica of society at large—it will be too sparsely connected. [sent-9, score-0.889]
8 To make his story-network realistic in a larger sense, he has to overload his characters with connections (“coincidences”) beyond what would actually arise in a group this small. [sent-10, score-1.075]
9 Thus, it’s not fair to slam Wolfe for having too many connections or coincidences in his books—these are a necessary artifice that allows him to achieve a realistic density of connections in a small group of characters. [sent-11, score-1.796]
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