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 who 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。 你觉得哪一个情况可能性更高: 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 percent 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.
在一个提出相似问题的研究中, 高达 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, 而且也是一个扑克玩家。 毕竟,我们所知的露西 和艺术没有什么联系, 但在扑克中, 概率与统计却很有用。 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. However counterintuitive it seems to imagine Lucy as an artist, the second scenario adds another condition on top of that, making it less likely.
再次看一下两个选择的陈述。 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 其它事情。 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。 不论想象露西是一个艺术家 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。
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 artists 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.
对于任何可能的事件集, 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 可能相对较小。 但是这必定会大于 同时拥有肖像画家和扑克玩家 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 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. This effect has been observed across multiple studies, including ones with participants who understood statistics well– from students betting on sequences of dice rolls, to foreign policy experts predicting the likelihood of a diplomatic crisis.
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,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。 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—— 从学生们对骰子掷出顺序的赌注, 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. 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 a story is true can never be greater than the probability that its least likely component is true.
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, 使之看似看信—— 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。