Can you outsmart this logical fallacy? - Alex Gendler

翻译人员: Jiasi Hao 校对人员: Wei Zhang

Meet Lucy.

认识一下露西。

She was a math major in college,

她在大学主修数学，

and aced all her courses in probability and statistics.

并且在所有的概率与统计课程中 获得了高分。

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

你觉得哪一个情况可能性更高： 露西是一个肖像画家，

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

或露西不仅是一个肖像画家， 同时也是扑克玩家？

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

在一个提出相似问题的研究中， 高达 80% 的参与者

chose the equivalent of the second statement:

选择了与第二个陈述等价的情况：

that Lucy is a portrait artist who also plays poker.

即露西是一个肖像画家， 而且也是一个扑克玩家。

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

毕竟，我们所知的露西 和艺术没有什么联系，

but statistics and probability are useful in poker.

但在扑克中， 概率与统计却很有用。

And yet, this is the wrong answer.

不过，这是一个错误的猜测。

Look at the options again.

再次看一下两个选择的陈述。

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

我们是如何知道第一个陈述 更可能是真的呢？

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

因为相比第二个陈述， 它是细节较少的版本。

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

说露西是一个肖像画家

不代表她可能做，或可能不做 其它事情。

about what else she might or might not do.

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

基于背景信息， 尽管想象露西玩扑克

比想象她从事艺术工作简单得多，

based on the background information,

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

但只有在她同时做这两件事时 第二个陈述才可为真。

However counterintuitive it seems to imagine Lucy as an artist,

不论想象露西是一个艺术家 看起来有多违背直觉，

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

第二个情景中额外增加的一个条件 使其可能性变低。

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

对于任何可能的事件集， 事件 A 可能发生的概率

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

总是比事件 A 和事件 B 同时发生的概率高。

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

如果我们随机抽取 100 万个数学专业的人，

the subset who are portrait artists might be relatively small.

其中是肖像画家的子集 可能相对较小。

But it will necessarily be bigger

但是这必定会大于

than the subset who are portrait artists and play poker.

同时拥有肖像画家和扑克玩家 双重身份的子集。

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

任何属于第二个子集的人， 也同时属于第一个子集。

but not vice versa.

反之，却并非如此。

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

条件越多， 一个事件发生的可能性越低。

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

所以，为什么包含更多条件的陈述 有时更加令人信服？

This is a phenomenon known as the conjunction fallacy.

这是一个称为 “合取谬误”的现象。

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

当我们被要求快速地做出选择， 我们通常偏向于选择捷径。

In this case, we look for what seems plausible

在这种情况下， 我们会选择看似更具可行性的选项，

rather than what is statistically most probable.

而非从统计意义上讲 最有可能的选项。

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

就其本身而言， 露西是艺术家这一事件

并不符合信息处理所生成的预期。

formed by the preceding information.

The additional detail about her playing poker

额外的一个关于她玩扑克的细节

gives us a narrative that resonates with our intuitions—

提供了与我们直觉相吻合的叙述——

it makes it seem more plausible.

这细节使之看似更加可信。

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

于是，不论选项的实际概率，

我们选择了看似 更加具有整体代表性的选项。

regardless of its actual probability.

This effect has been observed across multiple studies,

在许多研究中， 都观察到了这一现象，

including ones with participants who understood statistics well–

包括那些熟知统计知识的 研究参与者——

from students betting on sequences of dice rolls,

从学生们对骰子掷出顺序的赌注，

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

到外交政策专家 对外交危机可能性的预测。

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

合取谬误不是一个 仅存在于假设情况下的问题。

Conspiracy theories and false news stories

阴谋论和虚假新闻

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

通常仗着一个合取谬误的版本， 使之看似看信——

the more resonant details are added to an outlandish story,

在一个奇特故事中加入 越是与我们直觉相互呼应的细节，

the more plausible it begins to seem.

会使这个故事看起来更加真实。

But ultimately, the likelihood a story is true

但最终，一个故事为真的可能性

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

永远不会超过 事实真相最小的可能性。