A survey of summation.

Taken from 23 papers, these are summation experiments: the observer’s thresholds for a compound stimulus are compared with the thresholds for the components of the compound. [31, Sec. 1.11.2]. The index of summation, k, ranges from none (k = 0) to optimal (k = 1). This table shows that, whether using one or several senses, whether the task is high- or low-level, the summation is strong (k near 1) only if the two components are both perceived as aspects of the “same” thing. When cues are “different” things, summation is weak 0≤ k ≤0.58 with a mean 0.37; when cues are “same”, summation is strong 0.68≤ k ≤1 with a mean 0.89. This table is based on 23 papers, including all the perceptual summation efficiencies for adults that we found (or could calculate from published results) in a quick survey of the literature. It includes only summation of cues that are consistent and informative. It omits cue conflict studies, in which the cues provide conflicting information about the quality to be reported. It also omits the facilitation paradigm, in which one of the cues provides no information. At an n-component threshold that equates the energy of the components, if the summation index is k then the summation efficiency is251658240. Conservation of energy, i.e. the optimal algorithm, has k = 1. Independence of successes, i.e. probability summation, has k ≈ 0.57. In most cases the papers do not report whether their observers perceived the two components as the “same” object, so we have guessed, based on our experience and a close reading of what the papers do say. Another two papers turned up by our search could not be included in the Table because we were unable to classify their stimuli, with any confidence, as “same” or “different” [45], [65]. Obviously our guesses must yield to better assessments. Table S1 explains how k was estimated for each paper. Note that the predicted value for the summation index of roughly 0.6 for probability summation is for detection, whereas most of the experiments in Table 1 are identification.