what the right thing is to do -- in domains from the financial

正確的事情——從金融

to the gastronomic to the professional to the romantic.

到烹飪到職業到愛情。

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

exactly the right thing at all possible times,

在所有可能的時刻如何做正確的事情，

that would be a tremendous gift.

那可是一份非凡的智慧。

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

by a Dutch polymath named Daniel Bernoulli.

就為世人提供了這項智慧。

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，

and I also want to explain to you why it is

以及，我想向各位解釋

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。

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。

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。

But the simple English translation -- much less precise,

把它簡單翻譯成英文——雖然不夠精確，

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：

The expected value of any of our actions --

我們所有行為的預期值——

that is, the goodness that we can count on getting --

即是，我們所能期望得到的好處——

is the product of two simple things:

是以下兩個簡單事物的乘積：

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，

and the value of that gain to us.

和我們從中所獲得的益處的價值。

In a sense, what Bernoulli was saying is,

在某種意義上而言，Bernoulli所說的是，

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，

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。

Now, this simple equation, even for those of you

那麼，這個簡單的公式，即使對那些

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。

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

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，

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，

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，

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

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，

that multiplies to five, and that's more

兩者相乘得5，這比我收取的

than I'm charging you to play. So, the answer is, yes.

費用要多。所以，你會回答，好。

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。

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，

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。

People are horrible at estimating both of these things,

人們評估兩者的能力非常糟糕，

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。

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，

what the right thing is to do, and those are

會犯兩種錯誤，

errors in estimating the odds that they're going to succeed,

即錯誤地估計成功的機率，

and errors in estimating the value of their own success.

以及錯誤地估計成功的價值。

Now, let me talk about the first one first.

首先讓我談談第一個錯誤。

Calculating odds would seem to be something rather easy:

計算機率看起來是件很簡單的事情：

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。

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

or of flipping a heads.

拋出硬幣正面的可能性。

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，

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——

I should say, lose more -- gambling

我應該說，輸了更多的錢——在賭博上。

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。

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。

The way people figure odds

要談論人們計算機率的方式，

requires that we first talk a bit about pigs.

我們先得談談和豬有關的事宜。

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，

there are more dogs or pigs on leashes

在牛津的任何一天，

observed in any particular day in Oxford.

你認為被拴的狗多還是被拴的豬多。

And of course, you all know that the answer is dogs.

當然，你們都知道答案是狗。

And the way that you know that the answer is dogs is

你知道這個答案是狗

you quickly reviewed in memory the times

是靠你快速地回憶

you've seen dogs and pigs on leashes.

看到狗和豬被拴的次數。

It was very easy to remember seeing dogs,

我們很容易記起見到被拴的狗，

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

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，

then dogs on leashes are more probable.

那麼狗被拴的可能性更大。

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。

So, for example, here's a word puzzle.

舉例說，這裡有個填詞遊戲。

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

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？

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，

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，

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。

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，

with R in the third than the first place.

比第一字母是R的單詞要多得多。

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，

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。

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。

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。

It's like the dictionary;

很像詞典；

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。

So, this is an example of how this idea that

所以，這個例子說明一個道理，

the quickness with which things come to mind

即我們大腦回憶事物的速度，

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——

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。

For example, when Americans are asked to estimate the odds

譬如說，當讓美國人估計他們

that they will die in a variety of interesting ways --

奇奇怪怪的死因的機率時——

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

per 200 million U.S. citizens.

的死亡人數而計。

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

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。

Compare these to the actual numbers.

讓我們跟實際數據比較一下。

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，

two things are vastly over-estimated, namely tornadoes and fireworks.

兩者被大幅高估，即颶風和煙花；

Two things are vastly underestimated:

兩者被大幅低估：

dying by drowning and dying by asthma. Why?

溺水和哮喘。爲什麽？

When was the last time that you picked up a newspaper

你們還記得上次拿起一張報紙，

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？

It's not interesting because it's so common.

這沒什麽稀奇因為太普通了。

It's very easy for all of us to bring to mind instances

對我們來說，非常容易記起

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

tornadoes devastating cities, or some poor schmuck

諸如颶風摧毀城市，或是某個可憐的笨蛋

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。

Drownings and asthma deaths don't get much coverage.

對因溺水和哮喘而死的報導並不多。

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，

we vastly underestimate them.

我們極度低估了它們。

Indeed, this is kind of like the Sesame Street game

的確，這就有點像芝麻街遊戲

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

it's the swimming pool that doesn't belong, because the swimming pool

就對了，因為游泳池是

is the only thing on this slide that's actually very dangerous.

這張上唯一非常危險的東西。

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

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。

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

of people's ability to compute probabilities.

人們計算可能性的能力的例子。

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，

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

as a stupidity tax, because the odds of getting any payoff

愚蠢之稅，因為投資買彩票

by investing your money in a lottery ticket

而中獎的可能性

are approximately equivalent to flushing the money

跟把錢直接沖進馬桶差不多

directly down the toilet -- which, by the way,

而且，沖馬桶還

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。

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？

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：

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，

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——

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。

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。

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

with everybody who lost?

所作出的大量採訪呢？

Indeed, if we required that television stations run

的確，如果我們要求電視台

a 30-second interview with each loser

每次採訪大獎得主的時候，

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，

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

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，

"Me? I lost." "Me? I lost."

"我？我輸了。" "我？我輸了。"

Now, if you watch nine-and-a-half years of television --

那麼，如果你看了九年半的電視——

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，

and then at the end there's 30 seconds of, "and I won,"

然後最後的30秒"我贏了"，

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。

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。

There's 10 tickets in this lottery.

一共有10張彩票。

Nine of them have been sold to these individuals.

其中9張已經賣給其他不同的人了，

It costs you a dollar to buy the ticket and, if you win,

1元1張票，如果你贏了，

you get 20 bucks. Is this a good bet?

你得到20元。值得賭嗎？

Well, Bernoulli tells us it is.

嗯，Bernoulli告訴我們肯定的答案：

The expected value of this lottery is two dollars;

這個彩票的預期價值是2元，

this is a lottery in which you should invest your money.

你應該投資購買該彩票。

And most people say, "OK, I'll play."

大多數人會說，"好，我會買。"

Now, a slightly different version of this lottery:

現在，稍微改變一下彩票規則：

imagine that the nine tickets are all owned

假設9張票全部

by one fat guy named Leroy.

給一個叫Leroy的胖子買走了。

Leroy has nine tickets; there's one left.

Leroy有9張票；那就只剩下1張。

Do you want it? Most people won't play this lottery.

你還會買嗎？大多數人不想買了。

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，

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。

It's easy to see Leroy getting the check, right?

很容易看出Leroy會贏獎，對吧？

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。"

because you're not as likely to win as Leroy.

因為你跟Leroy得獎的機會不一樣大。

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

changes your decision to play,

改變了你是否要買的決定，

even though it does nothing whatsoever to the odds.

儘管你知道你贏的機率一點都沒變。

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，

compared to trying to estimate value:

但與評估價值相比較，簡直是小菜一碟：

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，

how much pleasure it will give us.

它會帶給我們多少快樂。

I want to talk now about errors in value.

我現在想談下價值的錯誤。

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？

Most of you have the intuition that it's not --

大多數人直覺它不值——

you wouldn't pay that for it.

你不會花那麼多錢買它。

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，

that you ask one, and only one question, which is:

只需要你問一個問題而已，即：

What else can I do with 25 dollars?

我還能用25元做什麽？

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，

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，

but somebody in the row in front of you has just opened

但你前排有個人剛剛打開了

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

is wafting over the seat, you think,

從座位上方飄了過來，這時你會想，

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。

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！

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。

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，

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。

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，

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？

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

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，

"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

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。

And this is a systematic error people make.

而這是人們犯的一個系統性錯誤。

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。

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，

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。

For example, this is, of course,

舉例來說，

one of the most delicious tricks in marketing,

一個最有效的營銷技巧是，

is to say something used to be higher,

告訴顧客商品的原價更高，

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。

When people are asked about these two different jobs:

當人們被問及兩份工作時：

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，

a job where you're getting a salary cut each year,

每年都會減薪，

and one in which you're getting a salary increase,

第二份工作是每年都會加薪，

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

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？

Because they had the sense that declining wages are worse

因為他們感覺逐年遞減的工資比

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

in the declining period. Here's another nice example.

後者多。這裡有另外一個例子。

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

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？

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：

$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，

so you decide to mull it over for a week.

於是你考慮了一個星期。

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——

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。

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

for something that was 700 last week.

買上個星期只有七百元的東西。

This tendency to compare to the past

人們喜歡與過去的事物比較的傾向

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，

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，

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。

Here's another example of how comparing to the past

這是另外一個跟過去比較是

can befuddle our decisions.

如何迷惑我們的決策的例子。

Imagine that you're going to the theater.

假設你要去劇院。

You're on your way to the theater.

你在去劇院的路上。

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。

You also have a 20-dollar bill.

你也有一張20元的鈔票。

When you arrive at the theater,

當你到達劇院時，

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。

Would you spend your remaining money on replacing it?

你會花剩下的錢再買一張嗎？

Most people answer, no.

大多數人的答案是，不會。

Now, let's just change one thing in this scenario.

那麼，讓我們把這個情境改變一點。

You're on your way to the theater,

你在去劇院的路上，

and in your wallet you have two 20-dollar bills.

在你的錢包裡有兩張20元的鈔票。

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。

Would you spend your remaining 20 dollars on a ticket?

你會花剩下的20元買電影票嗎？

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。

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？

Now, just in case you're not getting it,

萬一你還不太明白，