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How to make good guessesTim Harford-Share Print Clip Gift Article Comments  
‘Would you say that someone reading the FT is more likely to have a PhD or to have no college degree at all?’
What’s the likelihood that the British economy will fall into recession this year? Well, I’ve no idea — but I have a new way to guess.
Before I reveal what this is, here’s a totally different question. Imagine that you see someone reading the Financial Times. Would you say that this individual, clearly a person of discernment, is more likely to have a PhD or to have no college degree at all?
The obvious response is that the FT reader has a PhD. Surely people with PhDs better exemplify the FT reader than people with no degree at all, at least on average — they tend to read more and to be more prosperous.
illustration by Harry Haysom of an FT reader©Harry Haysom
But the obvious response is too hasty. First, we should ask how many people have PhDs and how many people have no college degree at all? In the UK, more than 75 per cent of adults have no degree but the chance that a randomly chosen person has a PhD is probably less than 1 per cent.
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It only takes a small proportion of non-graduates to read the FT before they’ll outnumber the PhD readers. This fact should loom large in our guess, but it does not.
Logically, one should combine the two pieces of information, the fact that PhDs are rare with the fact that FT readers tend to be well educated. There is a mathematical rule for doing this perfectly (it’s called Bayes’ rule) but numerous psychological experiments suggest that it never occurs to most of us to try. It’s not that we combine the two pieces of information imperfectly; it’s that we ignore one of them completely.
The number that gets ignored (in this example, the rarity of PhDs) is called the “base rate”, and the fallacy I’ve described, base rate neglect, has been known to psychologists since the 1950s.
Why does it happen? The fathers of behavioural economics, Daniel Kahneman and Amos Tversky, argued that people judge such questions by their representativeness: the FT reader seems more representative of PhDs than of non-graduates. Tversky’s student, Maya Bar-Hillel, hypothesised that people seize on the most relevant piece of information: the sighting of the FT seems relevant, the base rate does not. Social psychologists Richard Nisbett and Eugene Borgida have suggested that the base rate seems “pallid and abstract”, and is discarded in favour of the vivid image of a person reading the pink ’un. But whether the explanation is representativeness, relevance, vividness or something else, we often ignore base rates, and we shouldn’t.
At a recent Financial Times event, psychologist and forecasting expert Philip Tetlock explained that good forecasters pay close attention to base rates. Whether one is forecasting whether a marriage will last, or a dictator will be toppled, or a company will go bankrupt, Tetlock argues that it’s a good idea to start with the base rate. How many marriages last? How many dictators are toppled? How many companies go bankrupt? Of course, one may have excellent reasons to depart from the base rate as a forecast but the base rate should be the beginning of the journey.
On this basis, my guess is that there is a 10 per cent chance that the UK will begin a recession in 2016. How so? Simple: in the past 70 years there have been seven recessions, so the base rate is 10 per cent.
Base rates are not just a forecasting aid. They’re vital in clearly understanding and communicating all manner of risks. We routinely hear claims of the form that eating two rashers of bacon a day raises the risk of bowel cancer by 18 per cent. But without a base rate (how common is bowel cancer?) this information is not very useful. As it happens, in the UK, bowel cancer affects six out of 100 people; a bacon-rich diet would cause one additional case of bowel cancer per 100 people.
Thinking about base rates is particularly important when we’re considering screening programmes or other diagnostic tests, including DNA tests for criminal cases.
Imagine a blood test for a dangerous disease that is 75 per cent accurate: if an infected person takes the test, it will detect the infection 75 per cent of the time but it will also give a false positive 25 per cent of the time for an uninfected person. Now, let’s say that a random person takes the test and seems to be infected. What is the chance that he really does have the disease? The intuitive answer is 75 per cent. But the correct answer is: we don’t know, because we don’t know the base rate.
Once we know the base rate we can express the problem intuitively and solve it. Let’s say 100 people are tested and four of them are actually infected. Then three will have a (correct) positive test, but of the 96 uninfected people, 24 (25 per cent) will have a false positive test. Most of the positive test results, then, are false.
It’s easy to leap to conclusions about probability, but we should all form the habit of taking a step back instead. We should try to find out the base rate, or at least to guess what it might be. Without it, we’re building our analysis on empty foundations.
Tim Harford is the author of ‘The Undercover Economist Strikes Back’. Twitter: @TimHarford
Illustration by Harry Haysom
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这位专栏作家确是一位好写手，请看相关的另一篇：“客观”只是一种错觉-http://www.ftchinese.com/story/001067028?full=y
英国《金融时报》专栏作家 蒂姆•哈福德
“你开车的时候有没有注意到，”喜剧演员乔治•卡林(George Carlin)评论道，“任何开得比你慢的人都是笨蛋，任何开得比你快的人都是疯子？”
的确如此。但如果你想一想卡林的俏皮话，你就会发现，还可能是什么其他结果吗？你根据行车条件决定了合适的行车速度，因此从定义上说，在你看来其他任何人的驾驶速度都是不合适的。
如果我以每小时70公里的速度开车超过了一辆以每小时60公里的速度行驶的汽车，可能我应该这么想，“嗯，对于这条路上的合理车速，平均的看法是每小时65公里。”然而，几乎没人会真的这么想。为什么呢？
斯坦福大学(Stanford University)心理学家、新书《房间里最聪明的人》( The Wisest One in the Room)的合著者之一李•罗斯(Lee Ross)，将这个问题描述成“天真的现实主义”。他指的是一种诱人的观念：我们看到的是世界真正的模样，既没有偏见，也没有谬误。这是一种非常强大的错觉，以至于一旦我们遇到了观点与我们相左的人，我们会本能地认为对方受到了误导，而不是意识到或许我们自己才是能够从中学到点什么的人。
真相是，我们都有偏见，这些偏见决定了我们所看到的景象。一个较早的例子是1954年的一项研究，内容是有关人们如何看达特茅斯学院(Dartmouth College)和普林斯顿大学(Princeton University)之间的一场大学橄榄球赛。研究者艾伯特•哈斯托夫(Albert Hastorf)和哈德利•坎特里尔(Hadley Cantril)向达特茅斯学院和普林斯顿大学的学生展示了一段比赛录像，发现他们对比赛的认知相差极大，让人难以相信他们看到的实际上是同一段录像。比如，普林斯顿的学生记下的达特茅斯学院的橄榄球队员的犯规次数是达特茅斯学院学生的两倍。
后来，一个包括耶鲁大学(Yale University)的丹•卡亨(Dan Kahan)在内的小组进行了一项调查，调查人员向学生们展示了一段游行的视频片段，并且编造了一些有关这次游行的说法。一些学生被告知，这是一次在堕胎诊所前进行的反堕胎抗议游行；其他人则被告知，这是一次在征兵办公室外、针对美国军队（当时）的“不问，不说”政策的抗议游行。
尽管看的是完全一样的片段，实验对象对抗议者的激进程度得出了截然不同的结论。持自由主义观点的学生并不担心他们眼中捍卫同性恋权利的抗议者的行为，但他们担心那些反堕胎抗议者的行为；持保守主义观点的学生的看法则与之相反。尽管事实上，研究人员提出的并不是抗议活动总体上能否被接受的问题，而是有关抗议活动的一些细节的问题：抗议者是否向旁观者大叫？抗议者是否堵住了建筑物的出入口？
我们只会看到自己想看的东西。我们还倾向于把那些和我们的想法和行动不一致的“笨蛋”和“疯子”往最坏了想。叶米利•普罗宁(Emily Pronin)等人进行的一项研究要求人们填写一份有关各种政治问题的调查问卷。然后研究人员重新分发这些问卷，这样每一位参与者都会看到另外一个人的回答。之后研究人员会要求参与者描述他们回答这些问题的思路，并猜测另一个人的思路是怎样的。
受调查者通常会说，他们受到了一些理性上的原因的影响，比如“关注事实”，那些和他们意见一致的人也是出于同样的动机。他们认为，那些和他们意见不一致的人是在寻求“同辈的认可”，或者是出于“政治正确”的考虑。我关注事实，而你却为了同辈的认可而屈从。我衡量利弊，而你却被游说分子玩弄于股掌之上。
即使我们对那些与我们意见不一致的人持宽容的看法，我们的同理心也只到这里为止。比如，我们或许会允许某人因为他们的文化背景持不同的观点——但我们往往会认为，他们或许能够认识到自己观点的错误，而不是我们会认识到自己的观点的错误。
可怜英国广播公司(BBC)还试图对英国全民公投决定是否退欧这样的政治话题进行客观中立的报道。疑欧派会认为这些报道倾向于布鲁塞尔，而亲欧派则会抱相反的看法。双方都会认为腐败、欺诈或者愚蠢在作怪。当然，这总是有可能的，但也有可能这些激情澎湃的支持者在看到客观性的时候根本不认为那是客观。
然而事情还能是什么其他样子吗？如果任何媒体批评一种你个人欣赏的政治立场，那么就有一个矛盾要解决了。要解释这一分歧，一个简单的方法是得出结论：要么是媒体有偏见，要么是你有偏见。你可以猜一猜人们在本能之下会做出什么选择。难怪对美国媒体偏见的严谨的研究表明，大多数报纸、电台或者电视台不会试图说服他们的读者、听众和观众；相反，它们会迎合受众的偏见。
要对抗“天真的现实主义”很难，因为“我们客观地看待世界”这个错觉非常强大。至少，我自己还未曾太过担心这一点。幸运的是，我自己的观点是基于对事实的仔细分析，我的政治观点反映的是对事实的冷静评估，而不是出于自利、集体思维或者文化偏见。当然，会有人比我的立场更左，他们是笨蛋。比我右的人呢？疯子。
作者著有《卧底经济学家反击战》(The Undercover Economist Strikes Back)
译者/石斛