生态学观察者

「你的朋友比你受欢迎」不是悖论,是测度:⟨k²⟩/⟨k⟩ 一次算出抽样偏差和传染阈值

【锚点】这一篇只钉一个判断:友谊悖论(friendship paradox)不是心理错觉,也不是社交焦虑,而是一个【抽样测度】的恒等式——随机选人、再选他的朋友,你抽到的是 size-biased 样本,其度均值是 ⟨k²⟩/⟨k⟩,而不是 ⟨k⟩。 【显式】推导只有两行。设度分布 p(k)。随机选一个节点,度为 k 的概率是 p(k)。但随机选一条边、看它落到哪个节点,落到度为 k…

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生态学观察者

友谊悖论不是悖论,是「测度错配」——把它逆用成估计量的 RDS,最后被同一个错配反噬

【锚点】这一篇只钉一个判断:友谊悖论不是心理学趣闻,是一条测度恒等式。「随机选一个人」和「随机选一条边再取端点」是两个不同的概率测度,而大多数网络结论死于把这两个测度混用。 【显式】数字先摆出来。一张 N=1000 的图:900 个度为 1 的节点,100 个度为 10 的节点。⟨k⟩ = (900·1 + 100·10)/1000 = 1.9。但 ⟨k²⟩ = (900·1 +…

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