Can you outsmart this logical fallacy? - Alex Gendler

譯者: Lilian Chiu 審譯者: Helen Chang

Meet Lucy.

見見露西。

She was a math major in college,

她在大學時主修數學，

and aced all her courses in probability and statistics.

且在她所有的機率 及統計課中都出類拔萃。

Which do you think is more likely: that Lucy is a portrait artist,

你認為下列何者比較有可能： 露西是肖像畫家，

or that Lucy is a portrait artist who also plays poker?

或者露西是肖像畫家， 同時也會玩撲克牌？

In studies of similar questions, up to 80 percent of participants

在類似問題的研究中， 高達八成的受試者

chose the equivalent of the second statement:

會選擇相對於 第二個陳述句的答案：

that Lucy is a portrait artist who also plays poker.

露西是肖像畫家， 同時也會玩撲克牌。

After all, nothing we know about Lucy suggests an affinity for art,

畢竟，從我們對露西的所知， 看不出她喜愛藝術，

but statistics and probability are useful in poker.

但統計和機率在撲克牌中很有用。

And yet, this is the wrong answer.

但，這個答案是錯的。

Look at the options again.

再看一次那些選項。

How do we know the first statement is more likely to be true?

我們怎麼知道第一個陳述句 比較有可能是真的？

Because it’s a less specific version of the second statement.

因為它是第二個陳述句的 「較不明確版」。

Saying that Lucy is a portrait artist doesn’t make any claims

說露西是肖像畫藝術家並沒有提到

about what else she might or might not do.

她可以會做／不會做 哪些其他的事。

But even though it’s far easier to imagine her playing poker than making art

雖然，根據背景資訊，

想像她玩撲克牌比想像 她做藝術更容易許多，

based on the background information,

the second statement is only true if she does both of these things.

但只有在她兩件事都會做時， 第二個陳述句才會成立。

However counterintuitive it seems to imagine Lucy as an artist,

不論想像露西身為藝術家 是個多麼反直覺的想像，

the second scenario adds another condition on top of that, making it less likely.

第二個情況比第一個情況 又多加了一個條件，

讓可能性更低。

For any possible set of events, the likelihood of A occurring

對任何可能的事件組合， A 事件發生的機率

will always be greater than the likelihood of A and B both occurring.

一定會比 A 和 B 事件 同時發生的機率高。

If we took a random sample of a million people who majored in math,

如果我們隨機抽出 一百萬名主修數學的人，

the subset who are portrait artists might be relatively small.

當中的肖條畫藝術家子集合 可能相對會很小。

But it will necessarily be bigger

但它一定會大於

than the subset who are portrait artists and play poker.

會玩撲克牌的肖像畫 藝術家的子集合。

Anyone who belongs to the second group will also belong to the first–

屬於第二群的人， 一定也會屬於第一群——

but not vice versa.

但反過來就不一定了。

The more conditions there are, the less likely an event becomes.

條件越多，事件發生的機率就越低。

So why do statements with more conditions sometimes seem more believable?

所以，為什麼比較多條件的陳述句 有時看起來卻比較可信？

This is a phenomenon known as the conjunction fallacy.

這個現象就是所謂的 合取謬誤（交集偏誤）。

When we’re asked to make quick decisions, we tend to look for shortcuts.

當我們被要求快速做決定時， 我們會傾向找截徑。

In this case, we look for what seems plausible

在這個例子中，我們會去找 貌似可信的陳述句，

rather than what is statistically most probable.

而不是去找統計機率 最高的陳述句。

On its own, Lucy being an artist doesn’t match the expectations

露西身為藝術家這件事情本身，

並不符合前述資訊所形成的預期。

formed by the preceding information.

The additional detail about her playing poker

關於她會玩撲克牌的額外細節資訊

gives us a narrative that resonates with our intuitions—

反而提供了和我們的 直覺呼應的描述——

it makes it seem more plausible.

讓它變得似乎更可信。

And we choose the option that seems more representative of the overall picture,

我們會去選擇看似比較能 代表整體狀況的選項，

regardless of its actual probability.

不論它實際的機率多高。

This effect has been observed across multiple studies,

在許多研究中都有 觀察到這種效應，

including ones with participants who understood statistics well–

包括找非常懂統計的人 來當受試者的研究在內——

from students betting on sequences of dice rolls,

從讓學生針對一連串 擲骰子結果下注的研究，

to foreign policy experts predicting the likelihood of a diplomatic crisis.

到外國政策專家預測外交危機 發生可能性的研究都有。

The conjunction fallacy isn’t just a problem in hypothetical situations.

合取謬誤並不只是在 假設情境中才會發生的問題。

Conspiracy theories and false news stories

陰謀理論和假新聞報導

often rely on a version of the conjunction fallacy to seem credible–

通常都是看似可信的 合取謬誤版本——

the more resonant details are added to an outlandish story,

幫一個古怪的故事 加上更多能呼應的細節，

the more plausible it begins to seem.

它就會顯得更像真的。

But ultimately, the likelihood a story is true

但，最終，這個故事為真的機率

can never be greater than the probability that its least likely component is true.

絕對不會高於故事中 最難置信的部分為真的機率。