Why is bias and variance of multimodal temporal numerosity judgement consistent with Maximum Likelihood Estimation?

Abstract In Temporal Numerosity Judgment (TNJ) observers naturally underestimate the number of pulses presented in a rapid pulse sequence. We investigated if bimodal presentation affects performance and whether this effect is in agreement with Maximum Likelihood Estimation (MLE). MLE predicts that the bimodal underestimation should lie in between the unimodal underestimations and the bimodal variance should be smaller than the unimodal variances. We tested congruent and incongruent audiovisual pulse sequences (1 10 flashes or beeps with equal, +1, or -1 distractors; ISI's 20 or 60 ms) and instructed participants to either report the number of flashes, beeps or both. Our results show that the audiovisual underestimation is smaller than each unimodal underestimation when counting beeps or both, but not when counting flashes. When counting both, the audiovisual variance is equal to the lowest unimodal variance, but when counting beeps or flashes the variance is larger than each of the unimodal variances. This suggests that multimodal TNJ is inconsistent with the predictions of MLE models, regardless whether integration is partial or complete.