Efficiency in redundancy

Abstract

In engineering, redundancy is the duplication of vital systems for use in the event of failure. In studies of human cognition, redundancy often refers to the duplication of the signal. Scores of studies have shown the salutary effects of a combined auditory and visual signal over single modality, the advantage of processing complete faces over facial features, and more recently the advantage of two observers over one. But what if the signal (or the number of observers) is fixed and cannot be altered or augmented? Can people improve the efficiency of information processing by recruiting an additional, redundant system? Here we demonstrate that recruiting a second redundant system can, under reasonable assumptions about human capacity, result in improved performance. Recruiting a second redundant system may come with a higher energy cost, but may be worthwhile in high-stakes situations where processing information accurately is crucial.

Keywords: Cognitive system; Decision making; Information processing.

Figure 1

(A) Depiction of a human processing an incoming signal using one information processing system. (B) Depiction of a human processing an incoming signal using an additional second, redundant information processing system. Recruiting such a second system may come with costs such as a higher resource demand. (C) When making ecologically plausible assumptions about human capacity, the recruitment of a second, redundant information processing system can result in improved performance as measured by reward rate across different levels of assumed information processing speed. The x-axis represents the speed of processing from low to high, as measured by drift rate v (see section “The diffusion decision model”). The y-axis represents the reward rate advantage of two processing systems over one processing system. Red bars indicate positive values suggesting a two systems advantage, whereas blue bars would have indicated an advantage for one system. This figure represents the outcome for a subsample of the parameter combinations. More complete results are reported in the text below.

Figure 2

The 2DDM offers a corrective mechanism that can overcome erroneous decisions. In this example, Response 1 is the correct choice, however, the 1DDM incorrectly ends up at the boundary corresponding to Response 2 (top-panel). In the 2DDM (bottom-panel), one process erroneously crossing the wrong boundary does not necessarily result in an incorrect choice since a response is only triggered once both processes agree.

Figure 3

Unlimited capacity ($l=1$). Reward rate for different threshold settings. Each panel displays the results for a different drift rate setting. The dotted lines indicate the maximum reward rate. The shading gradient indicates the proportion of trials simulated from the 2DDM that took longer than five seconds and have been excluded from the analysis. For most panels and most threshold settings, this proportion is negligible.

Figure 4

Unlimited capacity ($l=1$). Mean RT for correct and incorrect responses, as well as accuracy, indicated by the size of the dots. Each panel displays the results for a different drift rate setting.

Figure 5

Each panel displays the difference in the maximum reward rate across threshold settings in the 2DDM and 1DDM, for a different setting of l. Positive values, represented by red bars, correspond to cases in which the 2DDM resulted in a higher maximum reward rate, negative values, represented by blue bars, show cases in which the 1DDM resulted in a higher reward rate.

Figure 6

Exemplary results for for a system with one (“1DDM”), two (“2DDM”), three (“3DDM”), and four accumulators (“4DDM”), for both the fixed capacity case and the unlimited capacity case. Upper row: Reward rate as a function of threshold a for one drift rate setting (i.e., $v=1.5$). Bottom row: corresponding timeout proportions (i.e., trials that took longer than five seconds and have thus been excluded from the reward rate calculations that are displayed in the upper row), for each setting of threshold a.