Can you outsmart this logical fallacy

你能打敗這個(gè)邏輯謬誤嗎？

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Meet Lucy.?

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 or that Lucy is a portrait artist also plays poker?

認(rèn)識(shí)一下露西。

她在大學(xué)主修數(shù)學(xué)，并且在所有的概率與統(tǒng)計(jì)課程中獲得了高分。

你覺得哪個(gè)情況可能性更高：露西是一個(gè)肖像畫家，或露西不僅是一個(gè)肖像畫家，同時(shí)也是撲克玩家？

In studies of similar questions, up to 80% of participants chose the equivalent of the second statement that Lucy is a portrait artist who also plays poker.

After all, nothing we know about Lucy suggests an affinity?for art, but statistics and probability are useful in poker.

And yet, this is the wrong answer.

80%的參與者選擇了與第二個(gè)陳述等價(jià)的情況：即露西是一個(gè)肖像畫家，同時(shí)也是一個(gè)撲克玩家。

畢竟，我們所知的露西和藝術(shù)沒有什么聯(lián)系，但在撲克中，統(tǒng)計(jì)與概率卻很有用。

不過，這是一個(gè)錯(cuò)誤的猜測(cè)。

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.?

Saying that Lucy is a portrait artist doesn’t make any claims about what else she might or might not do.?

But even though it’s?far easier to imagine her playing poker than making art based on the background information, the second statement is only true if she does both of these things.

我們是如何知道第一個(gè)陳述更可能是真的呢？

因?yàn)橄啾鹊诙€(gè)陳述，它是細(xì)節(jié)較少的版本。

說露西是一個(gè)肖像畫家不代表她可能做，或可能不做其他事情。

基于背景信息，盡管想象露西玩撲克比想象她從事藝術(shù)工作簡(jiǎn)單得多，但只有在她同時(shí)做這兩件事時(shí)，第二個(gè)陳述才可為真。

However counterintuitive?it seems to imagine Lucy as an artist, the second scenario adds another condition on top of that, making it less likely.

For any possible set of events, the likelihood of A occurring 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, the subset who are portrait artists might be relatively small, but it will necessarily be bigger than the subset who are portrait artist and play poker.

Anyone who belongs to the second group will also?belong to the first, but not vice versa.?

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

不論想像露西是一個(gè)藝術(shù)家看起來有多違背直覺，第二個(gè)情景中額外增加的一個(gè)條件，使其可能性變低。

對(duì)于任何的事件集，事件A可能發(fā)生的概率總是比事件A和事件B同時(shí)發(fā)生的概率高。

如果我們隨機(jī)抽取100萬個(gè)數(shù)學(xué)專業(yè)的人，其中是肖像畫家的子集可能相對(duì)較少。但是這必定會(huì)大于同時(shí)擁有肖像畫家和撲克畫家雙重身份的子集。

任何屬于第二個(gè)子集的人，也同時(shí)屬于第一個(gè)子集。反之，卻并非如此。

條件越多，一個(gè)事件發(fā)生的可能性越低。

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.?

In this case, we look for what seems more plausible rather?than what is statistically most probable.

On its own, Lucy being an artist doesn’t match the expectations formed by the preceding?information.?

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, regardless of its actual probability.

所以，為什么包含更多條件的陳述有時(shí)更加令人信服？

這是一個(gè)稱為“合取謬誤”的現(xiàn)象。

當(dāng)我們被要求快速地做出選擇，我們通常偏向于選擇捷徑。

在這種情況下，我們會(huì)選擇看似更具可行性的選項(xiàng)，而非從統(tǒng)計(jì)意義上講最有可能的選項(xiàng)。

就其本身而言，露西是藝術(shù)家這一事件并不符合信息處理所生成的預(yù)期。

額外的一個(gè)關(guān)于她玩撲克的細(xì)節(jié)提供了與我們直覺相吻合的敘述—這細(xì)節(jié)使之看似更加可信，于是，無論選項(xiàng)的實(shí)際概率，我們選擇了看似更加具有整體代表性的選項(xiàng)。

This effect has been observed across multiple studies, including ones with participants who understood statistics well, from students betting on the sequences of dice rolls to foreign policy experts predicting the likelihood of a diplomatic crisis.?

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

Conspiracy theories and false news stories often rely on a version of the conjunction fallacy to seem credible--the more resonant?details are added to an outlandish?story, the more plausible it begins to seem.?

But ultimately, the likelihood that a story is true can never be greater than the probability that its least likely component is true.

在許多研究中，都觀察到了這一現(xiàn)象，包括那些熟知統(tǒng)計(jì)知識(shí)的研究參與者，從學(xué)生們對(duì)骰子之處順序的賭注，到外交政策專家對(duì)外交危機(jī)可能性的預(yù)測(cè)。

合取謬誤不是一個(gè)僅存在于假設(shè)情況下的問題。

陰謀論和虛假新聞通常仗著一個(gè)合取謬誤的版本，使之看似可信—在一個(gè)奇特故事中加入越是與我們直覺相互呼應(yīng)的細(xì)節(jié)，會(huì)使這個(gè)故事看起來更加真實(shí)。

但最終，一個(gè)故事為真的可能性永遠(yuǎn)不會(huì)超過事實(shí)真相最小的可能性。

Much of our society relies on majority vote and consensus, so it’s natural to think that the more consensus, the better.?

But how much trust should we place in unanimous decisions??

Check out this video on the paradox of unanimity.

我們社會(huì)的大部分人都依賴于多數(shù)投票和共識(shí)，所以人們很自然地認(rèn)為共識(shí)越多越好。

但是，我們應(yīng)該對(duì)一致決定給予多大的信任呢？

看看這個(gè)關(guān)于一致悖論的視頻。

特別感謝@?221A_Baker_St 投稿整理的本期文檔