Can you outsmart this logical fallacy

你能打败这个逻辑谬误吗？

来源视频

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?

认识一下露西。

她在大学主修数学，并且在所有的概率与统计课程中获得了高分。

你觉得哪个情况可能性更高：露西是一个肖像画家，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% 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%的参与者选择了与第二个陈述等价的情况：即露西是一个肖像画家，同时也是一个扑克玩家。

毕竟，我们所知的露西和艺术没有什么联系，但在扑克中，统计与概率却很有用。

不过，这是一个错误的猜测。

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.

我们是如何知道第一个陈述更可能是真的呢？

因为相比第二个陈述，它是细节较少的版本。

说露西是一个肖像画家不代表她可能做，或可能不做其他事情。

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，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, 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.

不论想像露西是一个艺术家看起来有多违背直觉，第二个情景中额外增加的一个条件，使其可能性变低。

对于任何的事件集，事件A可能发生的概率总是比事件A和事件B同时发生的概率高。

如果我们随机抽取100万个数学专业的人，其中是肖像画家的子集可能相对较少。但是这必定会大于同时拥有肖像画家和扑克画家双重身份的子集。

任何属于第二个子集的人，也同时属于第一个子集。反之，却并非如此。

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? 

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，为什么包含更多条件的陈述有时更加令人信服？

这是一个称为“合取谬误”的现象。

当我们被要求快速地做出选择，我们通常偏向于选择捷径。

在这种情况下，我们会选择看似更具可行性的选项，而非从统计意义上讲最有可能的选项。

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。

额外的一个关于她玩扑克的细节提供了与我们直觉相吻合的叙述—这细节使之看似更加可信，于是，无论选项的实际概率，我们选择了看似更加具有整体代表性的选项。

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.

在许多研究中，都观察到了这一现象，包括那些熟知统计知识的研究参与者，从学生们对骰子之处顺序的赌注，到外交政策专家对外交危机可能性的预测。

合取谬误不是一个仅存在于假设情况下的问题。

阴谋论和虚假新闻通常仗着一个合取谬误的版本，使之看似可信—在一个奇特故事中加入越是与我们直觉相互呼应的细节，会使这个故事看起来更加真实。

但最终，一个故事为真的可能性永远不会超过事实真相最小的可能性。

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.

我们社会的大部分人都依赖于多数投票和共识，所以人们很自然地认为共识越多越好。

但是，我们应该对一致决定给予多大的信任呢？

看看这个关于一致悖论的视频。

特别感谢@ 221A_Baker_St 投稿整理的本期文档