Humans differentially weight different stimuli in averaging tasks, which has been interpreted as reflecting encoding bias. We examine the alternative hypothesis that stimuli are encoded with noise and then optimally decoded. Under a model of efficient coding, the amount of noise should vary across stimuli and depend on statistics of the stimuli. We investigate these predictions through a task in which the participants are asked to compare the averages of two series of numbers, each sampled from a prior distribution that varies across blocks of trials. The participants encode numbers with a bias and a noise that both depend on the number. Infrequently occurring numbers are encoded with more noise. We show how an efficient-coding, Bayesian-decoding model accounts for these patterns and best captures the participants’ behaviour. Finally, our results suggest that Wei and Stocker’s “law of human perception”, which relates the bias and variability of sensory estimates, also applies to number cognition.

人类在平均任务中对不同的刺激进行不同的加权，这被解释为反映了编码偏差。我们检查了另一种假设，即刺激用噪声编码，然后进行最佳解码。在有效编码模型下，噪声量应随刺激而变化，并取决于刺激的统计数据。我们通过一项任务来调查这些预测，在该任务中，参与者被要求比较两个系列数字的平均值，每个数字都是从在试验块中变化的先验分布中采样的。参与者对数字进行编码，偏差和噪声都取决于数字。不经常出现的数字被编码为更多的噪声。我们展示了高效编码、贝叶斯解码模型如何解释这些模式并最好地捕捉参与者的行为。最后，