2007年9月18日 我是怎么出错的

I intend to break a record with this column, and publish what must surely be the FT’s longest ever correction. It’s not that I enjoy self-flagellation in public. But the manner of my error offers a lesson about economics as well as journalism¹.

首次说一下我的错误。在最近的《亲爱的经济学家》专栏中，我描述了经济学家哈罗德?霍特林(Harold Hotelling)的研究。但在文章中，我把人们广泛引用的一个例子归到霍特林头上，而霍特林本人可能从未引用过。

First, the error. In the “Dear Economist” column, I recently described the research of Harold Hotelling. But I attributed to Hotelling an anecdote² that is widely used but was probably never used by Hotelling himself.

布里斯托大学(Bristol University)地理学教授罗恩?约翰斯顿(Ron Johnston)好心地指出了我的错误。“我想，你绝非第一个犯这样错误的人。你在使用两个或者两个以上冰激凌小贩在海滩上确定摊位的例子时，错误地提到霍特林1929年发表的那篇经典论文。实际上不是这样的：他举的更为平实的例子是，两个‘商铺的地点……假设沿一条长度为1的直线均匀分布，这条直线可能是一个小镇上的主干道，也可能是一条跨大洲铁路’。”

Ron Johnston, a geography professor at the University of Bristol, was kind enough to point out my mistake. “You are, I fear, by no means the first person to incorrectly cite Hotelling’s classic 1929 paper as using the example of two or more ice-cream sellers locating on a beach. [It] did not: his much more prosaic³ example was of two ‘places of business’ serving ‘buyers ... supposed uniformly distributed along a line of length 1, which may be Main Street in a town or a transcontinental railroad’.”

那么，我为什么疏忽了呢？我非常清楚霍特林的模型，但由于我是在旅行途中写的那篇文章，因此无法查阅1929年的《经济学杂志》(Economic Journal)。我当时在想，这件冰激凌逸闻到底是不是关于霍特林的，于是就上互联网查了查关于他的模型的记述，然后就发现人们反复将这件逸闻与他联系在一起。（正如约翰斯顿指出的那样，我绝不是第一个犯这个错误的人。）由于相对无关紧要，我就完成了这个专栏，然后将我的疑问抛之脑后。

So why did I slip up? I know Hotelling’s model fairly well, but I wrote my answer while travelling and unable to access the Economic Journal of 1929. Wondering whether the ice-cream anecdote really was Hotelling’s, I checked accounts of his model on the internet and found the anecdote attributed to him again and again. (As Johnston correctly pointed⁴ out, I am by no means the first to make the mistake.) The stakes in this case being rather low, I drafted my column and then forgot about my doubts.

我是经济学家所谓的“信息羊群行为”的受害者。想象一下，一群完全理性但有些懒惰的经济学教授在互联网上张贴关于霍特林模型的记述。每位教授都不确信这个冰激凌故事是否是真的，因此每个人都在猜测，而不是花点时间去趟图书馆。

I was a victim of what economists⁵ call “informational herding”. Imagine a series of perfectly⁷ rational but somewhat lazy economics professors posting accounts of the Hotelling model on the internet. Each professor is unsure of whether the ice-cream story is true or not so each makes his best guess rather than taking the time to make that trip to the library.

如果头两位教授是错的，并把这件冰激凌逸闻写进他们的课程笔记里，他们就开创了一个先例，而人们如果忽视这个先例，就显得不理性了。第三位教授或许会回想起，霍特林并没有提到冰激凌，但当他看见他同事写的东西时，就会理性地怀疑自己的记忆。由于他不确定，并且认为两个脑袋肯定胜过一个脑袋，同时他也不愿意去图书馆走一趟，那么，他就也会将这件逸闻写进自己的文章中。

If the first two professors are wrong, and include the ice-cream anecdote in their course notes, they set a precedent⁸ that it is irrational⁹ to ignore. The third professor may recall that Hotelling did not mention ice cream, but rationally doubts his memory when he sees what his colleagues have written. Since he is unsure and reckons that two heads are better than one – and also prefers not to trek¹⁰ to the library – he also includes the anecdote.

尽管存在种种错误和懒惰，但每个人的行为都是理性的。第三位教授认为，他两位同事的正确几率加起来要高于他独自一人的正确几率。这种想法是对的。但奇怪的是，现在很多教授可能都会这样做：尽管怀疑这件逸闻是假的，但却最终服从于前人们的集体智慧。

Despite the errors and the laziness, everybody involved has behaved rationally. The third professor is correct to believe that his two colleagues are more likely to be right together than he is to be right alone. But the curious thing is that any number of professors may now follow suit, suspecting that the anecdote is bogus but deferring¹¹ to the collective wisdom of their predecessors¹².

这种逻辑同样也适用于一间大办公室里的人们对火警的反应。看到其他人都没有动，每个人可能都会压抑自己的疑问，并呆在原地不动。一旦人们开始大批离开，所有人可能就会涌向同一个出口。

The same reasoning could apply to people responding to a fire alarm in a large office. Seeing that nobody else is moving, each person is likely to suppress their doubts and stay put. Once the exodus¹³ does begin, everyone may pour towards the same exit.

或者，我们也可以想想《哈里?波特》(Harry¹⁴ Potter)等系列丛书获得成功的例子。上百万人购买这些书，因为其他上百万人已经买了。人们假设其他人都不会错，但理性羊群理论认为，只有最初一些读者做出了有根据的决定。其他人都在依赖前人的决定。

Or consider the success of books such as the Harry Potter series. Millions of people buy such books because millions of other people have bought them. The assumption is that all these other readers can’t be wrong; but the theory of rational herds¹⁵ suggests that only the first few of those readers made an informed decision. Everybody else was relying on the early adopters.

但理性羊群可以很快改变它们的主意。所有人都知道，最先行动的羊实际上决定了整个羊群的行为，因为没有哪个后来者有足够的信心背离它们的决定。这意味着，如果一位评论员做了自己的功课，并觉得有足够的信心发表不同看法，未来所有的教授、读者或者办公室职员将都会觉得同样有信心追随这一先例。只消一位英国《金融时报》专栏作家便可以纠正一个长期存在的传说——如果他做了适当的功课的话。对不起。

Yet rational herds can quickly change their minds. Everybody knows that the early movers effectively decided¹⁶ the behaviour of the entire herd⁶, because nobody who came later felt confident enough to depart from their decision. That means that if a single commentator¹⁷ did his homework and felt confident enough to dissent¹⁸, all future professors, book-buyers or office workers would feel similarly confident in following that lead. Just one FT columnist¹⁹ could correct a long-standing myth – if he did his homework properly. Sorry.