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  • Meet Lucy.

    譯者: Lilian Chiu 審譯者: Helen Chang

  • She was a math major in college,


  • and aced all her courses in probability and statistics.


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

    且在她所有的機率 及統計課中都出類拔萃。

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

    你認為下列何者比較有可能: 露西是肖像畫家,

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

    或者露西是肖像畫家, 同時也會玩撲克牌?

  • chose the equivalent of the second statement:

    在類似問題的研究中, 高達八成的受試者

  • that Lucy is a portrait artist who also plays poker.

    會選擇相對於 第二個陳述句的答案:

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

    露西是肖像畫家, 同時也會玩撲克牌。

  • but statistics and probability are useful in poker.

    畢竟,從我們對露西的所知, 看不出她喜愛藝術,

  • And yet, this is the wrong answer.


  • Look at the options again.


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


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

    我們怎麼知道第一個陳述句 比較有可能是真的?

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

    因為它是第二個陳述句的 「較不明確版」。

  • about what else she might or might not do.


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

    她可以會做/不會做 哪些其他的事。

  • based on the background information,


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

    想像她玩撲克牌比想像 她做藝術更容易許多,

  • However counterintuitive it seems to imagine Lucy as an artist,

    但只有在她兩件事都會做時, 第二個陳述句才會成立。

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

    不論想像露西身為藝術家 是個多麼反直覺的想像,

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

    第二個情況比第一個情況 又多加了一個條件,

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


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

    對任何可能的事件組合, A 事件發生的機率

  • the subset who are portrait artists might be relatively small.

    一定會比 A 和 B 事件 同時發生的機率高。

  • But it will necessarily be bigger

    如果我們隨機抽出 一百萬名主修數學的人,

  • than the subset who are portrait artists and play poker.

    當中的肖條畫藝術家子集合 可能相對會很小。

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


  • but not vice versa.

    會玩撲克牌的肖像畫 藝術家的子集合。

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

    屬於第二群的人, 一定也會屬於第一群——

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


  • This is a phenomenon known as the conjunction fallacy.


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

    所以,為什麼比較多條件的陳述句 有時看起來卻比較可信?

  • In this case, we look for what seems plausible

    這個現象就是所謂的 合取謬誤(交集偏誤)。

  • rather than what is statistically most probable.

    當我們被要求快速做決定時, 我們會傾向找截徑。

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

    在這個例子中,我們會去找 貌似可信的陳述句,

  • formed by the preceding information.

    而不是去找統計機率 最高的陳述句。

  • The additional detail about her playing poker


  • gives us a narrative that resonates with our intuitions


  • it makes it seem more plausible.


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

    反而提供了和我們的 直覺呼應的描述——

  • regardless of its actual probability.


  • This effect has been observed across multiple studies,

    我們會去選擇看似比較能 代表整體狀況的選項,

  • including ones with participants who understood statistics well


  • from students betting on sequences of dice rolls,

    在許多研究中都有 觀察到這種效應,

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

    包括找非常懂統計的人 來當受試者的研究在內——

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

    從讓學生針對一連串 擲骰子結果下注的研究,

  • Conspiracy theories and false news stories

    到外國政策專家預測外交危機 發生可能性的研究都有。

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

    合取謬誤並不只是在 假設情境中才會發生的問題。

  • the more resonant details are added to an outlandish story,


  • the more plausible it begins to seem.

    通常都是看似可信的 合取謬誤版本——

  • But ultimately, the likelihood a story is true

    幫一個古怪的故事 加上更多能呼應的細節,

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


Meet Lucy.

譯者: Lilian Chiu 審譯者: Helen Chang


影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

B1 中級 中文 TED-Ed 露西 機率 撲克牌 可信 謬誤

你能智取這種邏輯謬誤嗎?- Alex Gendler (Can you outsmart this logical fallacy? - Alex Gendler)

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    林宜悉 發佈於 2021 年 01 月 14 日