Imprecise counting of observations in averaging tasks predicts primacy and recency effects

Primacy and recency effects -- wherein early and recent observations exert disproportionate influence on judgments -- have long been noted in cognitive tasks involving the sequential presentation of information. In studies where human subjects make decisions based on the average of a sequence of numbers, recency effects are typically modeled phenomenologically through exponential discounting, while primacy effects are neglected altogether. Here, we exhibit the prevalence of both effects in such tasks, and propose that they result from the observers imprecision in their running tally of how many pieces of information they have received. If their approximate counting follows a central tendency -- a typical Bayesian pattern -- then past information is overweighted near the beginning of the sequence, while new numbers are overweighted towards the end of the sequence. Thus both primacy and recency effects are simultaneously predicted by this single mechanism. The model moreover nests exponential discounting as a special case in which the observer has no information about the count. The behavioral data suggests that subjects indeed misestimate the count of observations, with biases similar to those observed in numerosity-estimation tasks. Finally, we present evidence that the central tendency of subjects shifts towards lower counts in tasks with shorter sequence lengths, consistent with a Bayesian estimation of the counts. These findings provide new insights into the cognitive processes underlying serial-position effects in averaging tasks, with broader implications for other cognitive domains.