Suboptimality in perceptual decision making

Abstract

Human perceptual decisions are often described as optimal. Critics of this view have argued that claims of optimality are overly flexible and lack explanatory power. Meanwhile, advocates for optimality have countered that such criticisms single out a few selected papers. To elucidate the issue of optimality in perceptual decision making, we review the extensive literature on suboptimal performance in perceptual tasks. We discuss eight different classes of suboptimal perceptual decisions, including improper placement, maintenance, and adjustment of perceptual criteria; inadequate tradeoff between speed and accuracy; inappropriate confidence ratings; misweightings in cue combination; and findings related to various perceptual illusions and biases. In addition, we discuss conceptual shortcomings of a focus on optimality, such as definitional difficulties and the limited value of optimality claims in and of themselves. We therefore advocate that the field drop its emphasis on whether observed behavior is optimal and instead concentrate on building and testing detailed observer models that explain behavior across a wide range of tasks. To facilitate this transition, we compile the proposed hypotheses regarding the origins of suboptimal perceptual decisions reviewed here. We argue that verifying, rejecting, and expanding these explanations for suboptimal behavior - rather than assessing optimality per se - should be among the major goals of the science of perceptual decision making.

Keywords: Bayesian decision theory; cue combination; modeling; optimality; perceptual decision making; suboptimality; uncertainty; vision.

Figure 1

Graphical depiction of Bayesian inference. An observer is deciding between two possible stimuli – s₁ (e.g., leftward motion) and s₂ (e.g., rightward motion) – which produce Gaussian measurement distributions of internal responses. The observer’s internal response varies from trial to trial, depicted by the three yellow circles for three example trials. On a given trial, the likelihood function is the height of each of the two measurement densities at the value of the observed internal response (lines drawn from each yellow circle) – i.e., the likelihood of that internal response given each stimulus. For illustration, a different experimenter-provided prior and cost function is assumed on each trial. The action a_i corresponds to choosing stimulus s_i. We obtain the expected cost of each action by multiplying the likelihood, prior, and cost corresponding to each stimulus, and then summing the costs associated with the two possible stimuli. The optimal decision rule is to choose the action with the lower cost (equivalent to choosing the bar with less negative values). In trial 1, the prior and cost function are unbiased, so the optimal decision depends only on the likelihood function. In trial 2, the prior is biased toward s₂, making a₂ the optimal choice even though s₁ is slightly more likely. In trial 3, the cost function favors a₁, but the much higher likelihood of s₂ makes a₂ the optimal choice.

Figure 2

Depiction of the measurement distributions (colored curves) and optimal criteria (equivalent to the decision rules) in 2-choice tasks. The upper panel depicts the case when the two stimuli produce the same internal variability (σ₁ = σ₂). The gray vertical line represents the location of the optimal criterion. The lower panel shows the location of the optimal criterion when the variability of the two measurement distributions differs (σ₁ < σ₂, in which case the optimal criterion results in a higher proportion of s₁ responses).

Figure 3

Depiction of a failure to maintain a stable criterion. The optimal criterion is shown in Figure 2 but observers often fail to maintain that criterion over the course of the experiment, resulting in a criterion that effectively varies over trials. Colored curves show measurement distributions.

Figure 4

Depiction of optimal adjustment of choice criteria. In addition to the s₁ and s₂ measurement distributions (in thin red and blue lines), the figure shows the corresponding posterior probabilities as a function of x assuming uniform prior (in thick red and blue lines). The vertical criteria depict optimal criterion locations on x (thin gray lines) and correspond to the horizontal thresholds (thick yellow lines). Optimal criterion and threshold for equal prior probabilities and payoffs are shown in dashed lines. If unequal prior probability or unequal payoff is provided such that s₁ ought to be chosen three times as often as s₂, then the threshold would optimally be shifted to 0.75, corresponding to a shift in the criterion such that the horizontal threshold and vertical criterion intersect on the s₂ posterior probability function. The y-axis is probability density for the measurement distributions, and probability for the posterior probability functions (the y-axis ticks refer to the posterior probability).

Figure 5

A. Depiction of one possible accuracy/RT curve. Percent correct responses increases monotonically as a function of RT and asymptotes at 90%. B. The total reward/RT curve for the accuracy/RT curve from panel A with the following additional assumptions: (i) observers complete as many trials as possible within a 30-minute window, (ii) completing a trial takes 1.5 seconds on top of the RT (due to stimulus presentation and between-trial breaks), and (iii) each correct answer results in 1 point, while incorrect answers result in 0 points. The optimal RT – the one which maximizes the total reward – is depicted with dashed lines.

Figure 6

Depiction of how an observer should give confidence ratings. Similar to Figure 4, both the measurement distributions and posterior probabilities as a function of x assuming uniform prior are depicted. The confidence thresholds (depicted as yellow lines) correspond to criteria defined on x (depicted as thick gray lines). The horizontal thresholds and vertical criteria intersect on the posterior probability functions. The y-axis is probability density for the measurement distributions, and probability for the posterior probability functions (the y-axis ticks refer to the posterior probability).

Figure 7

Depiction of the relationship between 1-stimulus and 2-stimulus tasks. Each axis corresponds to a 1-stimulus task (e.g., Figure 2). The three sets of concentric circles represent 2D circular Gaussian distributions corresponding to presenting two stimuli in a row (e.g., s₂,s₁ means that s₂ was presented first and s₁ was presented second). If the discriminability between s₁ and s₂ is d′ (1-stimulus task; gray lines in triangle), then the Pythagorean theorem gives us the expected discriminability between s₁,s₂ and s₂,s₁ (2-stimulus task; blue line in triangle).

Figure 8

Optimal cue combination. Two cues that give independent information about the value of a sensory feature (red and blue curves) are combined to form a single estimate of the feature value (yellow curve). The combined cue distribution is narrower than both individual cue distributions, and its mean is closer to the mean of the distribution of the more informative cue.

Figure 9

Examples of illusions and biases. A) Cardinal repulsion. A nearly vertical (or horizontal) line looks more tilted away from the cardinal axis than it is. B) Adelson’s checkerboard brightness illusion. Square B appears to be brighter than square A, even though the two squares have the same luminance. Figure courtesy of Michael Bach (http://www.michaelbach.de/ot/lum-adelsonCheckShadow/index.html). C) Tilt aftereffect. After viewing a tilted adapting grating (left), observers perceive a vertical test grating (right) to be tilted away from the adaptor. D) Effects of spatial attention on contrast appearance (Carrasco, Ling, and Read 2004). An attended grating appears to have higher contrast than the same grating when it is unattended. E) Effects of action affordances on perceptual judgments (Witt 2011). Observers judge an object to be closer (far white circle compared to near white circle) relative to the distance between two landmark objects (red circles) when they are holding a tool that allows them to reach that object than when they have no tool.