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We all make decisions every day; we want to know
我們每天都作出決定;我們想知道如何做
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what the right thing is to do -- in domains from the financial
正確的事情——從金融
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to the gastronomic to the professional to the romantic.
到烹飪到職業到愛情。
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And surely, if somebody could really tell us how to do
當然,如果有人能夠真的能告訴我們
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exactly the right thing at all possible times,
在所有可能的時刻如何做正確的事情,
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that would be a tremendous gift.
那可是一份非凡的智慧。
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It turns out that, in fact, the world was given this gift in 1738
事實上,早在1738年,荷蘭博學家Daniel Bernoulli
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by a Dutch polymath named Daniel Bernoulli.
就為世人提供了這項智慧。
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And what I want to talk to you about today is what that gift is,
我今天想講的是這項智慧是什麽,
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and I also want to explain to you why it is
以及,我想向各位解釋
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that it hasn't made a damn bit of difference.
爲什麽這項智慧根本就沒有影響我們的生活。
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Now, this is Bernoulli's gift. This is a direct quote.
這就是Bernoulli提供的智慧。這是他的原文。
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And if it looks like Greek to you, it's because, well, it's Greek.
如果這看上去像希臘文,因為,它就是希臘文。
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But the simple English translation -- much less precise,
把它簡單翻譯成英文——雖然不夠精確,
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but it captures the gist of what Bernoulli had to say -- was this:
但它抓住了Bernoulli所表達的要點:
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The expected value of any of our actions --
我們所有行為的預期值——
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that is, the goodness that we can count on getting --
即是,我們所能期望得到的好處——
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is the product of two simple things:
是以下兩個簡單事物的乘積:
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the odds that this action will allow us to gain something,
這就是,該行為能使我們獲益的機率,
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and the value of that gain to us.
和我們從中所獲得的益處的價值。
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In a sense, what Bernoulli was saying is,
在某種意義上而言,Bernoulli所說的是,
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if we can estimate and multiply these two things,
如果我們能夠評估這兩者並把它們相乘,
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we will always know precisely how we should behave.
我們就會精確的知道自己應該怎麼做。
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Now, this simple equation, even for those of you
那麼,這個簡單的公式,即使對那些
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who don't like equations, is something that you're quite used to.
不喜歡公式的人而言,也是很平常簡單的。
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Here's an example: if I were to tell you, let's play
舉個例子:如果我告訴你,讓我們來玩
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a little coin toss game, and I'm going to flip a coin,
一個拋硬幣的遊戲,我會拋一個硬幣,
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and if it comes up heads, I'm going to pay you 10 dollars,
如果是正面朝上,我會給你10元,
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but you have to pay four dollars for the privilege of playing with me,
但你得花4元來得到這個與我玩的機會,
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most of you would say, sure, I'll take that bet. Because you know
你們大多數人會說,好,我參加。因為你們知道
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that the odds of you winning are one half, the gain if you do is 10 dollars,
你們贏的機會是一半,如果贏的話會得到10元,
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that multiplies to five, and that's more
兩者相乘得5,這比我收取的
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than I'm charging you to play. So, the answer is, yes.
費用要多。所以,你會回答,好。
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This is what statisticians technically call a damn fine bet.
這就是統計師們技術上所稱的很棒的賭局。
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Now, the idea is simple when we're applying it to coin tosses,
那麼,當我們把這個原理應用到拋硬幣上時,是很簡單的,
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but in fact, it's not very simple in everyday life.
但實際上,在應用到日常生活中卻並不那麼簡單。
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People are horrible at estimating both of these things,
人們評估兩者的能力非常糟糕,
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and that's what I want to talk to you about today.
而這就是我今天想要談論的話題。
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There are two kinds of errors people make when trying to decide
人們在為自己的行為作決策時,
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what the right thing is to do, and those are
會犯兩種錯誤,
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errors in estimating the odds that they're going to succeed,
即錯誤地估計成功的機率,
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and errors in estimating the value of their own success.
以及錯誤地估計成功的價值。
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Now, let me talk about the first one first.
首先讓我談談第一個錯誤。
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Calculating odds would seem to be something rather easy:
計算機率看起來是件很簡單的事情:
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there are six sides to a die, two sides to a coin, 52 cards in a deck.
一個骰子有六面,一個硬幣有兩面,一副撲克牌有52張。
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You all know what the likelihood is of pulling the ace of spades
你們都知道摸到黑桃A或者
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or of flipping a heads.
拋出硬幣正面的可能性。
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But as it turns out, this is not a very easy idea to apply
但結果是,這個道理如果應用於日常生活的時候,
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in everyday life. That's why Americans spend more --
就不那麼容易了。這也是爲什麽美國人花了更多的錢——
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I should say, lose more -- gambling
我應該說,輸了更多的錢——在賭博上。
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than on all other forms of entertainment combined.
這些錢比所有其他娛樂形式費用的總和還要多。
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The reason is, this isn't how people do odds.
原因就是,人們並不用這種方式來計算機率。
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The way people figure odds
要談論人們計算機率的方式,
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requires that we first talk a bit about pigs.
我們先得談談和豬有關的事宜。
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Now, the question I'm going to put to you is whether you think
我現在要問你們的問題是,
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there are more dogs or pigs on leashes
在牛津的任何一天,
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observed in any particular day in Oxford.
你認為被拴的狗多還是被拴的豬多。
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And of course, you all know that the answer is dogs.
當然,你們都知道答案是狗。
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And the way that you know that the answer is dogs is
你知道這個答案是狗
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you quickly reviewed in memory the times
是靠你快速地回憶
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you've seen dogs and pigs on leashes.
看到狗和豬被拴的次數。
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It was very easy to remember seeing dogs,
我們很容易記起見到被拴的狗,
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not so easy to remember pigs. And each one of you assumed
但不那麼容易記起被拴的豬。而且你們每個人會假設
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that if dogs on leashes came more quickly to your mind,
如果狗被拴的情景更快地出現在你的腦海中的話,
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then dogs on leashes are more probable.
那麼狗被拴的可能性更大。
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That's not a bad rule of thumb, except when it is.
這個憑感覺的方法還不錯,但也有例外。
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So, for example, here's a word puzzle.
舉例說,這裡有個填詞遊戲。
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Are there more four-letter English words
在四個字母的英文單詞裡,第三個字母是R的單詞
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with R in the third place or R in the first place?
與第一個字母是R的單詞哪個比較多?
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Well, you check memory very briefly, make a quick scan,
嗯,你們會很快搜索下記憶,作一個快速掃描,
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and it's awfully easy to say to yourself, Ring, Rang, Rung,
對你來說記起這些單詞太容易了,Ring,Rang,Rung,
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and very hard to say to yourself, Pare, Park: they come more slowly.
而記起Pare,Park就很難:它們在腦海中出現得更慢。
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But in fact, there are many more words in the English language
而實際上,在英文裡,第三字母是R的單詞,
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with R in the third than the first place.
比第一字母是R的單詞要多得多。
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The reason words with R in the third place come slowly to your mind
你回憶起第三字母是R的單詞比較慢的原因,
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isn't because they're improbable, unlikely or infrequent.
不是因為它們不存在,不大可能出現或使用頻率少。
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It's because the mind recalls words by their first letter.
而是因為我們的大腦是用第一個字母來回憶單詞。
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You kind of shout out the sound, S -- and the word comes.
我們好像是用大腦在讀這個單詞的音,S——然後單詞就出來了。
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It's like the dictionary;
很像詞典;
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it's hard to look things up by the third letter.
我們很難用第三個字母來查找單詞。
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So, this is an example of how this idea that
所以,這個例子說明一個道理,
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the quickness with which things come to mind
即我們大腦回憶事物的速度,
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can give you a sense of their probability --
會影響你對該事物出現的可能性的感覺——
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how this idea could lead you astray. It's not just puzzles, though.
而這個道理可能會讓你出現誤差。這並不僅限於填詞遊戲。
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For example, when Americans are asked to estimate the odds
譬如說,當讓美國人估計他們
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that they will die in a variety of interesting ways --
奇奇怪怪的死因的機率時——
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these are estimates of number of deaths per year
這些估計數據是以每年每兩億美國人
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per 200 million U.S. citizens.
的死亡人數而計。
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And these are just ordinary people like yourselves who are asked
他們只是一些是跟你我一樣的普通人。問他們
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to guess how many people die from tornado, fireworks, asthma, drowning, etc.
猜測一下會有多少人死於颶風,煙花,哮喘,溺水等等。
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Compare these to the actual numbers.
讓我們跟實際數據比較一下。
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Now, you see a very interesting pattern here, which is first of all,
你們可以看到一個非常有趣的現象,首先,
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two things are vastly over-estimated, namely tornadoes and fireworks.
兩者被大幅高估,即颶風和煙花;
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Two things are vastly underestimated:
兩者被大幅低估:
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dying by drowning and dying by asthma. Why?
溺水和哮喘。爲什麽?
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When was the last time that you picked up a newspaper
你們還記得上次拿起一張報紙,
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and the headline was, "Boy dies of Asthma?"
上面的的大標題是“男孩死於哮喘”是什麽時候嗎?
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It's not interesting because it's so common.
這沒什麽稀奇因為太普通了。
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It's very easy for all of us to bring to mind instances
對我們來說,非常容易記起
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of news stories or newsreels where we've seen
我們曾看到報紙和電視上的新聞報導
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tornadoes devastating cities, or some poor schmuck
諸如颶風摧毀城市,或是某個可憐的笨蛋
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who's blown his hands off with a firework on the Fourth of July.
在國慶節被煙花炸掉雙手。
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Drownings and asthma deaths don't get much coverage.
對因溺水和哮喘而死的報導並不多。
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They don't come quickly to mind, and as a result,
我們並不會很快記起這類事件,而結果就是,
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we vastly underestimate them.
我們極度低估了它們。
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Indeed, this is kind of like the Sesame Street game
的確,這就有點像芝麻街遊戲
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of "Which thing doesn't belong?" And you're right to say
"哪樣東西與眾不同?" 你說游泳池不同
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it's the swimming pool that doesn't belong, because the swimming pool
就對了,因為游泳池是
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is the only thing on this slide that's actually very dangerous.
這張上唯一非常危險的東西。
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The way that more of you are likely to die than the combination
也就是說,你們死於游泳池的可能性
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of all three of the others that you see on the slide.
比這張圖片上其他三種加起來還要高。
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The lottery is an excellent example, of course -- an excellent test-case
彩票是一個很棒的例子,一個測試
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of people's ability to compute probabilities.
人們計算可能性的能力的例子。
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And economists -- forgive me, for those of you who play the lottery --
先對那些買彩票的朋友說聲抱歉,
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but economists, at least among themselves, refer to the lottery
但經濟學家們,至少在他們之間,把彩票稱為
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as a stupidity tax, because the odds of getting any payoff
愚蠢之稅,因為投資買彩票
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by investing your money in a lottery ticket
而中獎的可能性
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are approximately equivalent to flushing the money
跟把錢直接沖進馬桶差不多
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directly down the toilet -- which, by the way,
而且,沖馬桶還
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doesn't require that you actually go to the store and buy anything.
不需要你親自去彩票店跑一趟。
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Why in the world would anybody ever play the lottery?
究竟世上爲什麽會有人想買彩票呢?
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Well, there are many answers, but one answer surely is,
嗯,有許多答案,但其中肯定包括這個答案:
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we see a lot of winners. Right? When this couple wins the lottery,
我們看到許多中大獎的人。對吧?當這對夫妻贏了大獎,
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or Ed McMahon shows up at your door with this giant check --
或Ed McMahon帶著一張巨大的支票來到你家門口時——
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how the hell do you cash things that size, I don't know.
我可不知道你怎麼用那麼巨大的支票去換錢。
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We see this on TV; we read about it in the paper.
我們在電視上看到這些,在報紙上讀到這些。
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When was the last time that you saw extensive interviews
你們什麽時候見過對每個輸錢的人
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with everybody who lost?
所作出的大量採訪呢?
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Indeed, if we required that television stations run
的確,如果我們要求電視台
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a 30-second interview with each loser
每次採訪大獎得主的時候,
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every time they interview a winner, the 100 million losers
必須播放對每個輸家一段30秒的採訪,
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in the last lottery would require nine-and-a-half years
那麼上次開獎後你得全神貫注地花上9年半的時間
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of your undivided attention just to watch them say,
來看那1億輸家採訪,你會看到他們說,
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"Me? I lost." "Me? I lost."
"我?我輸了。" "我?我輸了。"
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Now, if you watch nine-and-a-half years of television --
那麼,如果你看了九年半的電視——
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no sleep, no potty breaks -- and you saw loss after loss after loss,
不睡不拉——你就會往復循環地看到輸輸輸,
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and then at the end there's 30 seconds of, "and I won,"
然後最後的30秒"我贏了",
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the likelihood that you would play the lottery is very small.
這樣你去買彩票的可能性就很小了。
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Look, I can prove this to you: here's a little lottery.
來,我可以證明給你:這兒有個小彩票。
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There's 10 tickets in this lottery.
一共有10張彩票。
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Nine of them have been sold to these individuals.
其中9張已經賣給其他不同的人了,
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It costs you a dollar to buy the ticket and, if you win,
1元1張票,如果你贏了,
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you get 20 bucks. Is this a good bet?
你得到20元。值得賭嗎?
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Well, Bernoulli tells us it is.
嗯,Bernoulli告訴我們肯定的答案:
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The expected value of this lottery is two dollars;
這個彩票的預期價值是2元,
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this is a lottery in which you should invest your money.
你應該投資購買該彩票。
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And most people say, "OK, I'll play."
大多數人會說,"好,我會買。"
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Now, a slightly different version of this lottery:
現在,稍微改變一下彩票規則:
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imagine that the nine tickets are all owned
假設9張票全部
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by one fat guy named Leroy.
給一個叫Leroy的胖子買走了。
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Leroy has nine tickets; there's one left.
Leroy有9張票;那就只剩下1張。
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Do you want it? Most people won't play this lottery.
你還會買嗎?大多數人不想買了。
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Now, you can see the odds of winning haven't changed,
你可以看到贏的機率並沒有改變,
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but it's now fantastically easy to imagine who's going to win.
但現在非常容易想像出誰會是贏家。
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It's easy to see Leroy getting the check, right?
很容易看出Leroy會贏獎,對吧?
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You can't say to yourself, "I'm as likely to win as anybody,"
你不會對自己說,"我跟其他人得獎的機會一樣大。"
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because you're not as likely to win as Leroy.
因為你跟Leroy得獎的機會不一樣大。
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The fact that all those tickets are owned by one guy
所有其他彩票被一個人買走的事實
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changes your decision to play,
改變了你是否要買的決定,
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even though it does nothing whatsoever to the odds.
儘管你知道你贏的機率一點都沒變。
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Now, estimating odds, as difficult as it may seem, is a piece of cake
那麼,評估可能性的難度,雖然看起來很難,
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compared to trying to estimate value:
但與評估價值相比較,簡直是小菜一碟:
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trying to say what something is worth, how much we'll enjoy it,
評估價值就是試圖找出某樣東西的價值,我們對它的享受程度,
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how much pleasure it will give us.
它會帶給我們多少快樂。
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I want to talk now about errors in value.
我現在想談下價值的錯誤。
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How much is this Big Mac worth? Is it worth 25 dollars?
這個巨無霸漢堡包值多少錢?值25元嗎?
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Most of you have the intuition that it's not --
大多數人直覺它不值——
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you wouldn't pay that for it.
你不會花那麼多錢買它。
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But in fact, to decide whether a Big Mac is worth 25 dollars requires
而實際上,決定一個巨無霸漢堡是否值25元,
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that you ask one, and only one question, which is:
只需要你問一個問題而已,即:
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What else can I do with 25 dollars?
我還能用25元做什麽?
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If you've ever gotten on one of those long-haul flights to Australia
如果你曾坐過那種去澳大利亞的長途航班,
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and realized that they're not going to serve you any food,
而且得知他們不會提供任何食物,
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but somebody in the row in front of you has just opened
但你前排有個人剛剛打開了
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the McDonald's bag, and the smell of golden arches
麥當勞的紙袋,那金黃色圓麵包的香味
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is wafting over the seat, you think,
從座位上方飄了過來,這時你會想,
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I can't do anything else with this 25 dollars for 16 hours.
我在這16個小時用這25元什麽也不能做。
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I can't even set it on fire -- they took my cigarette lighter!
我甚至不能點燃它——他們把我的打火機收走了!
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Suddenly, 25 dollars for a Big Mac might be a good deal.
突然,25元買個巨無霸漢堡可能是筆好交易。
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On the other hand, if you're visiting an underdeveloped country,
相反的情況,如果你去參觀一個發展中國家,
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and 25 dollars buys you a gourmet meal, it's exorbitant for a Big Mac.
25元就可以讓你大快朵頤,而買巨無霸漢堡就太貴了。
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Why were you all sure that the answer to the question was no,
爲什麽在我還沒告訴你們所處的情境時,
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before I'd even told you anything about the context?
你們都確定對這個問題的答案是"不"呢?
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Because most of you compared the price of this Big Mac
因為你們大多數人將這個巨無霸漢堡的價格
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to the price you're used to paying. Rather than asking,
與你們過去常付的價格比較。而不是問,
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"What else can I do with my money," comparing this investment
"我還能用這錢幹什麼",即將這項投資與
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to other possible investments, you compared to the past.
其他可能的投資比較,你們是與過去的情境比較。
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And this is a systematic error people make.
而這是人們犯的一個系統性錯誤。
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What you knew is, you paid three dollars in the past; 25 is outrageous.
你所知道的是,你在過去是花3元;如果花25元就太過分了。
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This is an error, and I can prove it to you by showing
這是一個錯誤,我可以證明給大家看,
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the kinds of irrationalities to which it leads.
我會展示給大家看它可以導致什麼樣的非理性。
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For example, this is, of course,
舉例來說,
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one of the most delicious tricks in marketing,
一個最有效的營銷技巧是,
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is to say something used to be higher,
告訴顧客商品的原價更高,
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and suddenly it seems like a very good deal.
這樣的話,現價一下子就看起來很划算了。
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When people are asked about these two different jobs:
當人們被問及兩份工作時:
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a job where you make 60K, then 50K, then 40K,
第一份工作你的年薪先是6萬元,然後5萬元,然後4萬元,
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a job where you're getting a salary cut each year,
每年都會減薪,
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and one in which you're getting a salary increase,
第二份工作是每年都會加薪,
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people like the second job better than the first, despite the fact
人們更喜歡第二份工作,儘管事實上
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they're all told they make much less money. Why?
他們都被告知會賺得更少。爲什麽會這樣?
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Because they had the sense that declining wages are worse
因為他們感覺逐年遞減的工資比
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than rising wages, even when the total amount of wages is higher
遞增的工資要差,儘管總數算起來前者要比
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in the declining period. Here's another nice example.
後者多。這裡有另外一個例子。
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Here's a $2,000 Hawaiian vacation package; it's now on sale for 1,600.
這是一套價值二千元的夏威夷假日套票,現在促銷價是一千六百元
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Assuming you wanted to go to Hawaii, would you buy this package?
假設你想去夏威夷,你願意買這個套票嗎?
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Most people say they would. Here's a slightly different story:
大多數人會同意購買。那麼把條件稍微改變一下:
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$2,000 Hawaiian vacation package is now on sale for 700 dollars,
2000元的夏威夷假日套票現在只售700元,
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so you decide to mull it over for a week.
於是你考慮了一個星期。
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By the time you get to the ticket agency, the best fares are gone --
等你來到售票代理的時,最好的價格過期了——
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the package now costs 1,500. Would you buy it? Most people say, no.
現在的價格是一千五百元。你還會買嗎?大多數人會說,不會。
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Why? Because it used to cost 700, and there's no way I'm paying 1,500
爲什麽?因為它過去的價格是七百元,而我絕不會花一千五百元
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for something that was 700 last week.
買上個星期只有七百元的東西。
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This tendency to compare to the past
人們喜歡與過去的事物比較的傾向
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is causing people to pass up the better deal. In other words,
導致人們錯過了更好的交易。換句話說,
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a good deal that used to be a great deal is not nearly as good
一個划算的交易,會因為它之前更划算而導致現在顯得不那麼划算,
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as an awful deal that was once a horrible deal.
同樣,一個糟糕的交易,會因為之前更糟糕而導致現在顯得不那麼糟糕。
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Here's another example of how comparing to the past
這是另外一個跟過去比較是
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can befuddle our decisions.
如何迷惑我們的決策的例子。
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Imagine that you're going to the theater.
假設你要去劇院。
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You're on your way to the theater.
你在去劇院的路上。
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In your wallet you have a ticket, for which you paid 20 dollars.
你錢包里放著你花了20元買的一張票。
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You also have a 20-dollar bill.
你也有一張20元的鈔票。
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When you arrive at the theater,
當你到達劇院時,
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you discover that somewhere along the way you've lost the ticket.
你發現不知怎樣電影票在路上丟了。
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Would you spend your remaining money on replacing it?
你會花剩下的錢再買一張嗎?
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Most people answer, no.
大多數人的答案是,不會。
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Now, let's just change one thing in this scenario.
那麼,讓我們把這個情境改變一點。
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You're on your way to the theater,
你在去劇院的路上,
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and in your wallet you have two 20-dollar bills.
在你的錢包裡有兩張20元的鈔票。
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When you arrive you discover you've lost one of them.
當你到達劇院時你發現丟了一張。
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Would you spend your remaining 20 dollars on a ticket?
你會花剩下的20元買電影票嗎?
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Well, of course, I went to the theater to see the play.
嗯,當然了:我是去劇院看電影的。
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What does the loss of 20 dollars along the way have to do?
在路上丟了20元跟這個有什麽關係?
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Now, just in case you're not getting it,
萬一你還不太明白,
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