1. 你有60％的时间会选择X，正确的机率有60％，另外有40％的时间选择O，而且正确的机率有40％。平均下来就是0.6×0.6 + 0.4×0.4 = 0.52。
2. Amos Tversky and Daniel Kahneman, “Judgment under Uncertainty: Heuristics and Biases,” Science 185, no. 4157 (1974): 1124–1131, https://people.hss.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf.
3. 参考Daniel Kahneman, Thinking, Fast and Slow (New York: Farrar, Strauss and Giroux, 2011); and Dan Ariely, Predictably Irrational (New York: HarperCollins, 2009).
4. Michael Lewis, Moneyball (New York: Norton, 2003).
5. 当然，虽说《魔球》是采用传统的统计学，但各球队现在正寻求以机器学习方法来执行这个功能，在过程中搜集到更多数据，这样的发展应该不让人意外。参考Takashi Sugimoto, “AI May Help Japan’s Baseball Champs Rewrite ‘Moneyball,’ ” Nikkei Asian Review, May 2, 2016, http://asia.nikkei.com/Business/Companies/AI-may-help-Japan-s-baseball-champs-rewrite-Moneyball.
6. Jon Kleinberg, Himabindu Lakkaraju, Jure Leskovec, Jens Ludwig, and Sendhil Mullainathan, “Human Decisions and Machine Predictions,” working paper 23180, National Bureau of Economic Research, 2017.
7. 研究也显示，算法可能会减少种族歧视的现象。
8. Mitchell Hoffman, Lisa B. Kahn, and Danielle Li, “Discretion in Hiring,” working paper 21709, National Bureau of Economic Research, November 2015, revised April 2016.
9. Donald Rumsfeld, news briefing, US Department of Defense, February 12, 2002, https://en.wikipedia.org/wiki/There_are_known_knowns.
10. Bertrand Rouet-Leduc et al., “Machine Learning Predicts Laboratory Earthquakes,” Cornell University, 2017, http://arxiv.org/abs/1702.05774.
11. Dedre Gentner and Albert L. Stevens, Mental Models (New York: Psychology Press, 1983); Dedre Gentner, “Structure Mapping: A Theoretical Model for Analogy,” Cognitive Science 7 (1983): 15–170.
12. 就算机器在这样的状况下做得更好，机率法则也代表，如果样本数少，一定还是有些不确定性。因此当数据稀少时，在已知的方法上，机器预测会不精准。机器可以让人理解预测有多不精准，就像我们在第八章的讨论，这就创造出人类能够扮演的一个角色，在预测不精准时判断如何行动。
13. Nassim Nicholas Taleb, The Black Swan (New York: Random House, 2007).
14. 在艾萨克．艾西莫夫（Isaac Asimov）的《基地》（Foundation）系列中，预测的能力强大到可以预见银河帝国（Galactic Empire）的毁灭，以及社会上日益增加的各种痛苦，而这正是故事的重心。不过就情节发展来说，重要的是，这些预测无法预见「突变体」（the mutant）的崛起。预测无法预见料想不到的事件。
15. Joel Waldfogel, “Copyright Protection, Technological Change, and the Quality of New Products: Evidence from Recorded Music since Napster,” Journal of Law and Economics 55, no. 4 (2012): 715–740.
16. Donald Rubin, “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,” Journal of Educational Psychology 66, no. 5 (1974): 688–701; Jerzy Neyman, “Sur les applications de la theorie des probabilities aux experiences agricoles: Essai des principes,” master’s thesis, 1923, excerpts reprinted in English, D. M. Dabrowska, and T. P. Speed, translators, Statistical Science 5 (1923): 463–472.
17. Garry Kasporov, Deep Thinking (New York: Perseus Books, 2017), 99–100.
18. Google Panda, Wikipedia, https://en.wikipedia.org/wiki/Google_Panda, accessed July 26, 2017. 其中以Google网络管理员的说法最为著名，“What’s It Like to Fight Webspam at Google·” YouTube, February 12, 2014, https://www.youtube.com/watch·v=rr-Cye_mFiQ.
19. 例如，2016年9月公告要彻底检修: Ashitha Nagesh, “Now You Can Finally Get Rid of All Those Instagram Spammers and Trolls,” Metro, September 13, 2016, http://metro.co.uk/2016/09/13/now-you-can-finally-get-rid-of-all-those-instagram-spammers-and-trolls-6125645/. 之后是2017年6月: Jonathan Vanian, “Instagram Turns to Artificial Intelligence to Fight Spam and Offensive Comments,” Fortune, June 29, 2017, http://fortune.com/2017/06/29/instagram-artificial-intelligence-offensive-comments/.判断策略行动者使用预测机器会发生的情况，是长久以来的问题。1976年，经济学家罗伯特．卢卡斯（Robert Lucas）曾就通货膨胀与其他经济指标的总体经济政策提出这个论点。如果在政策改变之后，众人最好也跟着改变行为，大家就会改变。卢卡斯强调，虽然在通货膨胀高时就业率通常也高，但如果中央银行改采提高通膨的政策，众人就会预期有通膨，通膨与就业的关系就会瓦解。因此，与其根据过去的数据推断政策，他主张政策的根据应该是了解人类行为的根本驱动因素，这就是所谓的「卢卡斯评论」（Lucas Critique）。参考Robert Lucas, “Econometric Policy Evaluation: A Critique,” Carnegie-Rochester Conference Series in Public Policy 1, no. 1 (1976): 19–46, https://ideas.repec.org/a/eee/crcspp/v1y1976ip19-46.html. 经济学家提姆．哈福特（Tim Harford）则用不同的方式说明：诺克斯堡（Fort Knox, 美国一处陆军基地）从来不曾被抢劫。那应该要花多少经费保护诺克斯堡？因为从来不曾被抢劫，安全防卫支出无法预测抢劫减少。预测机器大概就会建议不要把钱花在这里。既然安全防护措施无法减少抢劫，那又何必花钱？Tim Harford, The Undercover Economist Strikes Back: How to Run—or Ruin—an Economy (New York: Riverhead Books, 2014).
20. Dayong Wang et al., “Deep Learning for Identifying Metastatic Breast Cancer,” Camelyon Grand Challenge, June 18, 2016, https://arxiv.org/pdf/1606.05718.pdf.
21. Charles Babbage, On the Economy of Machinery and Manufactures (London: Charles Knight Pall Mall East, 1832), 162.
22. Daniel Paravisini and Antoinette Schoar, “The Incentive Effect of IT: Randomized Evidence from Credit Committees,” working paper 19303, National Bureau of Economic Research, August 2013.
23. 这种「第一关」（first pass）分工在许多预测机器的部署中可以看到。《华盛顿邮报》（Washington Post）有个内部AI，2016年刊登850篇报导，但每一篇刊登之前都由人类检查过。ROSS Intelligence也是采用相同流程，分析数千笔法律文件，并将其转为简短的备忘录。参考Miranda Katz, “Welcome to the Era of the AI Coworker,” Wired, November 15, 2017 https://www.wired.com/story/welcome-to-the-era-of-the-ai-coworker/.
