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Visual Assumption and Perceptual Social Bias

https://doi.org/10.1080/09515089.2023.2228330

Abstract

Siegel recently distinguishes between seven possible ways in which our perceptual access to social information can be biased by flawed practice of either individuals or social structures, two of which, namely attention and cognitive penetration, imply that it is the content of perception, as opposed to that of judgments, that is biased. Both attention and cognitive penetration, however, rely on cognitive states imposing top-down influences on perceptual states. As such, perceptual bias resulting from them is to a large extent merely a derivation of cognitive bias. In this paper, I propose another way in which our perception can be biased, namely, as the result of faulty assumptions made by the visual system. Furthermore, I argue that in contrast to cognitive penetration and attentional direction, perceptual bias arising in this way is fundamentally perceptual and does not depend on inputs from one's cognitive system. This sort of perceptual bias, if it exists, would have important implications for how we conceptualize social bias and pose special challenges to traditional interventions designed to counteract bias.

Key takeaways
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  1. Perceptual social bias arises from faulty visual assumptions, independent of cognitive states.
  2. Siegel identifies seven mechanisms of visual bias; cognitive penetration and attentional direction rely on cognitive states.
  3. Empirical studies show that biases exist in weapon identification based on race, affecting perception.
  4. Cognitive accounts suggest participants misjudge tools as guns influenced by race-linked stereotypes.
  5. Visual assumptions, shaped by experience, can distort perception and contribute to social biases.
Visual Assumption and Perceptual Social Bias De Yang (University of Georgia) This is the penultimate draft of my paper published in Philosophical Psychology. Please cite as: Yang, D. (2023). Visual assumption and perceptual social bias. Philosophical Psychology, 1–26. https://doi.org/10.1080/09515089.2023.2228330 Abstract: Siegel recently distinguishes between seven possible ways in which our perceptual access to social information can be biased by flawed practice of either individuals or social structures, two of which, namely attention and cognitive penetration, imply that it is the content of perception, as opposed to that of judgments, that is biased. Both attention and cognitive penetration, however, rely on cognitive states imposing top-down influences on perceptual states. As such, perceptual bias resulting from them is to a large extent merely a derivation of cognitive bias. In this paper, I propose another way in which our perception can be biased, namely, as the result of faulty assumptions made by the visual system. Furthermore, I argue that in contrast to cognitive penetration and attentional direction, perceptual bias arising in this way is fundamentally perceptual and does not depend on inputs from one’s cognitive system. This sort of perceptual bias, if it exists, would have important implications for how we conceptualize social bias and pose special challenges to traditional interventions designed to counteract bias. 1. Introduction Our visual perception of the world is sometimes biased. This happens when there is a systematic discordance between our perception and the reality it is supposed to represent. Perceptual bias is prevalent in our daily life but is largely harmless. Yet, the vast amount of empirical research in the last two decades reveals there are instances of perceptual bias that bear social significance. The findings of this research include, but are not limited to, the following: a tool is more likely to be misrecognized as a gun when it is in the hand of a black man than when it is in the hand of a white man (Payne, Shimizu & Jacoby 2005); people perceive black men as bigger and more physically threatening than young white men (Wilson, Hugenberg & Rule, 2017); facial expressions of pain are less noticeable on black faces than on white faces (MendeSiedlecki, Qu-Lee, Backer & Van Bavel, 2019); faces are more likely to be misidentified as male when they are angry and as female when they are happy (Korb et al., 2022). I call these findings and the related real-life phenomena “perceptual social bias.” Although empirical evidence has unambiguously shown the prevalence of perceptual social bias in our daily life, it is still a matter of controversy as to how the biased perception happens. More specifically, empirical evidence is inadequate to decide, in the alleged cases of perceptual bias, whether it is one’s perceptual experience or some post-perceptual process that is biased. In a recent paper, Siegel (2020) identified seven possible ways in which our visual processing of social information can be biased, two of which imply that it is perceptual experience per se, as opposed to some post-perceptual processes related to perception, that is biased, namely, cognitive penetration and attentional direction. It is important to note, however, that both cognitive penetration and attentional direction rely on top-down feedback from the cognitive system, although in different ways. As such, even if there are cases of perceptual social bias resulting from cognitive penetration and attentional direction, they would still be dependent upon biased cognitive states and hence are merely derivations of cognitive bias. In this paper, however, I propose that there is yet another way in which perceptual social bias may arise, in addition to cognitive penetration and attentional direction. According to this proposal, perceptual social bias can be the result of faulty assumptions made by the visual system. I will argue that in contrast to cognitive penetration and attentional direction, the kind of bias resulting from this mechanism is fundamentally perceptual in the sense that it does not depend on inputs from one’s cognitive system, which would have important implications for how we counteract social bias. My plan for this paper is as follows. In the second section, I introduce Siegel’s suggestion that perceptual experience can be biased as the result of cognitive penetration and attentional direction and argue that they both require perception being modulated by cognitive states in a top-down manner. In section three, referring to the broadly construed carpentered-world explanation of the Müller-Lyer illusion, I explain how assumptions that govern the operations of the visual system can lead to systematically inaccurate visual representations of the world. In section four, drawing on relevant empirical research, I argue that the account introduced in section three may also explain perceptual social bias. I will end my paper by briefly discussing the implications of this mechanism and argue that it highlights an alternative way of conceptualizing social bias, in addition to the now popular conceptualization that focuses primarily on the distinction between explicit and implicit bias. 2. Perceptual Social Bias and Top-down Influence Traditionally, social bias was defined in terms of mistaken conscious attitudes and beliefs we have about a social group. For example, people often knowingly associate black individuals with being more hostile, men with being more aggressive, women with being more appeasing, etc. This is commonly referred to as explicit social bias. Since the 1990s, however, an increasing number of psychological studies have revealed that even when people do not admit consciously endorsing stereotypical associations, their implicit endorsement of these biases can be shown by their behaviors and decision-making. A self-professed egalitarian, for example, might unreflectively clutch her bag when her black neighbor passes by, but not when her white neighbor does the same. Similarly, an HR manager who vows to treat all job candidates equally may nonetheless show a preference for candidates with traditionally white names over traditionally ethnic-sounding names. This kind of bias is referred to as implicit social bias. Research on both explicit and implicit social bias is abundant in psychology and philosophy. Most of the research, however, focuses on the impact social biases have on highlevel functions such as thinking, decision-making, and action. It was only until the recent decade or so that researchers began to investigate the possibility that low-level functions like perception can also be biased. I briefly introduced some of the studies devoted to examining this possibility in section one. Those studies, however, are ambiguous between perceptual experience per se and some post-perceptual processes being biased. To appreciate the difference, consider the experiment of Payne and his colleagues (2005) on the weapon identification task, which is also the most extensively studied research paradigm in this field. The participants were briefly shown images of either a gun or a hand tool (wrench, plier, etc.) in the experiment. Then they were asked to report in less than a second whether that image contained a weapon or a tool. Before they started with the actual task, participants were primed with a face that was either white or black. It turned out that the priming had a significant effect on their reports: the participants were more likely to misidentify a hand tool as a gun when they were primed with a black face than a white face. Does the experimental result suggest, when misidentification happens, that the participants illusorily see guns where hand tools were present? Not necessarily. Because the experimental result is also compatible with the possibility that the participants simply misjudged or misinterpreted tools as weapons. This would still involve visual perception, but only insofar as it grounds their judgments or interpretations of the visual stimuli. If this is what happened in the experiment, the participants did not really “see” guns where tools were present, except in a loose or metaphorical sense. This is a theoretically less interesting possibility but compatible with the experimental results. At this point, we have two competing accounts regarding what was going on with the participants in Payne et al.’s experiment. Call the first interpretation the perceptual account and the second interpretation the cognitive account. The experimental results are compatible with both accounts. To adjudicate between the two accounts, Stokes and Payne (2010) conducted a follow-up experiment. The experiment adopted the same procedure as the original one, except that it allowed the participants to correct their reports after each trial with no time pressure. It turned out that the participants almost always gave the correct answer during the correction phase, even if their initial reports were false. This speaks strongly in favor of some version of the cognitive account. That is to say, the participants accurately represented the target object visually but somehow misrepresented it in their high-level judgment. After all, if they misperceived rather than simply misjudged the target object, it would be unclear on what ground they were able to correct their initial false reports. Note, however, that Stokes and Payne’s follow-up experiment provides only limited support for the cognitive account. Even if we put aside the common critique that the experimental settings lack ecological validity, there remains another problem. It is unclear to what extent the results derived from their particular experimental setting apply to other experimental settings. It is even unclear whether Stokes and Payne’s results can be replicated in similar but slightly different experimental settings. Correll and his colleagues (2015) employed an empirical setup that was similar to the one used by Stoke and Payne. But instead of using clear images, they used blurry ones. The results showed that the participants could not correct their reports even given unlimited time to respond. suggesting that they might have misperceived tools to be guns. Because otherwise, it is hard to explain why they could not correct their reports when there was no time pressure. 1 Given the wide variety of research findings, it is unlikely that there exists a single mechanism underlying the divergent phenomena of perceptual social bias. That is to say, the cognitive account may be the best explanation for some research findings, whereas the perceptual account may be the more plausible interpretation for yet others. But in this paper, I will focus on exploring the possibility of the perceptual account, which is less discussed in the literature. Given that some paradigmatic cases of social biases are themselves higher-level cognitive states, there is no mystery that judgments or other post-perceptual processes can be biased. The perceptual account, however, opens up a theoretically more interesting possibility and has far-reaching implications for how we should understand the role of perception in our mental life. Before I proceed, a caveat about the perceptual account needs to be made. In the discussion on visual perception, it is always risky to posit properties other than shape, size, color, etc. in one’s perceptual representation. While most philosophers and psychologists agree that low-level properties like shape, size, color, etc. can be represented in perceptual experience, there is little agreement about whether high-level properties like being a gun, being a person, etc. can be thus represented. Since the perceptual account implies that one sees (illusorily) a gun in the weapon identification task, one might be tempted to object to the account on the grounds that it implies a controversial claim about what our perceptual experience can represent. I think, however, that need not be the case. Although the perceptual account implies that the participant ‘sees’ a gun, it does not imply that she represents a gun as such. It is compatible with the perceptual account that she merely represents (inaccurately) the low-level properties (shape, size, color, etc.) of the object such that it looks like a weapon when in fact it is a tool. In this case, the participant’s perceptual representation is still restricted to low-level properties, and the above objection to the perceptual account is therefore unmotivated. In what follows in this paper, I will continue to speak of things like “perceivers represent guns in their visual experience” for the sake of simplicity. But in so doing, I do not claim that their visual experience represents guns as such. It is ultimately an empirical question as to whether the perceptual or cognitive account is true in a particular scenario or experimental setting. But philosophers can nonetheless contribute to the relevant research by speculating on possible ways in which perceptual social bias arises and reflecting on their implications for our understanding of the relevant phenomena. Based on the broad distinction between the perceptual account and the cognitive account, Siegel (2020) distinguishes further between different varieties of the two accounts. Siegel suggests seven possible ways in which perception can be biased, two of which imply it is the content of perceptual experience, as opposed to the content of judgment, that is biased, and hence presumably fall under the category of the perceptual account. One is through cognitive penetration, and the other is through attentional direction. If cognitive penetration is what happens to the subjects in the weapon identification task, then “the pliers look to the subjects exactly like a gun, due to the influence on the perceptual experience of a cognitive state activated by the black prime” (Siegel 2020, p. 103). Whereas if attentional direction is what happens, then “the pliers look somewhat like a gun because the state activated by the black prime directs the subject’s attention to features of the pliers that are congruent with being a gun (metallic), and away from features incongruent with being a gun (shape)” (ibid). According to this characterization, both cognitive penetration and attentional direction involve the activation of certain cognitive states, where cognitive states include beliefs, judgments, desires, etc. So how exactly are they different from each other? To answer this question, it will be helpful to consider the connection between cognition and perception. Almost everyone agrees that perception can influence cognition. My seeing it raining outside, for example, can dispose me to believe that it is raining. But is it equally obvious that the influence can happen in the opposite direction, namely, perception being influenced by cognition? That depends on the kind of influence we are talking about. Consider Macpherson (2017) 's example: You believe that you have an exam tomorrow. The belief causes you to be stressed, which in turn causes a migraine. Then the migraine causes you to experience flashing lights in your visual field. This is apparently an example of cognition influencing perception, and examples like this are ubiquitous in everyday life. But they are philosophically rather uninteresting because there is nothing puzzling about how this kind of influence takes place. Consider another example: Suppose you are looking at a painting and your attention is captured by a particular feature. As you turn your attention to this feature, you see more of its details. Presumably, in this case, your desire to see the painting in detail influences the content of your experience. This is an example of attentional direction. What we commonly refer to as attention covers a wide variety of distinct phenomena. For this reason, some philosophers and psychologists have even gone so far as to reject the usefulness of the very concept of attention (Anderson 2023; Hommel et al. 2019). But for the current discussion, it suffices to characterize attention as a process of selection, whereby a perceiver directs limited cognitive resources (sometimes unconsciously) towards an object(s) or feature(s) in the external environment. 2 This is exactly what happens in the example above and cases like that. The existence of cases in which this notion of attention direction alters the content of perception is relatively uncontroversial. But these cases do not count as cognitive penetration in the strict sense.3 Following Pylyshyn (1999), theorists engaged in the debate typically hold that a genuine case of cognitive penetration must satisfy two requirements, namely, semantic coherence and directness. Semantic coherence requires that the contents of the penetrating cognitive states stand in rational or content-preserving relation to those of the penetrated perceptual states. Whereas directness requires that the influence cognitive states exert on perceptual states is direct and is not mediated by some other states. The first example above clearly does not meet the requirement of semantic coherence: your belief of having an exam tomorrow is not semantically relevant to your seeing flashing lights. The second example does not satisfy the directness requirement. Though arguably, your desire to see the painting in more detail is semantically coherent with your actually seeing it in more detail, the influence is only indirect. That is, your desire enabled you to focus on the details of the painting through the accommodation of the lens in your eyes. To understand what cognitive penetration really amounts to, contrast this with an example that is conceivable but may not actually exist: your desire to see the painting more clearly exerts a direct influence on your visual perception, bringing the details of the painting into view even if your gaze direction remains the same. It is cases of this sort that proponents of cognitive penetration purport to identify. Unlike attentional direction, it is a matter of controversy whether instances of cognitive penetration really exist. But it is beyond the scope of this paper to deal with this issue, so I do not take sides on it. For the current purpose, it suffices for us to note from the discussion above that cognitive penetration and attentional direction are both top-down processes, processes in which cognitive or higher-level mental states influence perception. 4 In the case of cognitive penetration, cognitive states influence perceptual states directly. Whereas in the case of attentional direction, the influence of cognitive states on perceptual states is only indirect, that is, mediated by other mental or physical states. But despite the difference, top-down influence is implicated in both cognitive penetration and attentional direction. More empirical evidence is needed to determine whether cognitive penetration or attentional direction accounts for particular research findings regarding perceptual social bias. But if they do, the sort of perceptual social bias they account for would largely be derived from cognitive bias because both cognitive penetration and attentional direction require that the content of perceptual experience be influenced by biased high-level cognitive states in a topdown manner. In the next two sections, however, I will argue that there is yet another possible mechanism underlying perceptual social bias, which does not rely on top-down influence. 3. Visual Assumptions without Top-down Influence A recurring theme in vision science has been the postulation of perceptual tendencies or assumptions to explain the relationship between visual experience and the physical reality it represents. On the one hand, visual stimuli are ambiguous in the sense that, in principle, the 2D images projected on our retina correspond to an indefinite number of possible 3D arrangements of surface colors, shapes, illumination, etc. The same retinal image may correspond to a pig, only the rear half of a pig, a wax imitation peccary, a tapir, etc. But on the other hand, the resulting perceptual state is not ambiguous (if we exclude ambiguous figures); that is, we are typically quite confident about what we visually represent and are rarely confused. How is this possible? According to a popular view in vision science, this is the result of our visual systems making prior assumptions about the world we perceive. The most well-known example is the assumption of light-from-above. When estimating 3D shapes from shading, the human visual system resolves the ambiguity by assuming light usually shines from overhead. Figure 1 depicts a concave footprint illuminated from the bottom of the page. Yet, in the absence of visual cues Figure 1 Concave footprint illusion from Morgenstern et al. (2011) Figure 3 Carpentered world explanation for the Müller-Lyer illusion indicating the actual lighting source, the visual system defaults to the assumption of light-fromabove and thus interprets the figure as convex. Admittedly, this assumption functions merely as a heuristic for the functioning of the visual system and can be overridden by lighting cues that are even barely perceptible (Morgenstern, Murray & Harris, 2011). But still, light-from-above is the default assumption built into the human visual system. People with normal vision usually cannot help but view the image in this way unless stronger countervailing lighting cues are available. Figure 2 Müller-Lyer illusion Perceptual assumptions or heuristics like light-from-above are particularly useful in explaining optical illusions (Mamassian & Landy, 1998). But how does the human visual system acquire these assumptions? Though recently challenged, it is commonly believed that the assumption of light-from-above primarily reflects innately specified mechanisms, or “natural constraint” (Scholl, 2005). But there are also visual assumptions that are mainly learned through experience. An excellent example to illustrate this is the Müller-Lyer illusion. The Müller-Lyer illusion is an optical illusion consisting of two horizontal line segments that end with arrowheads pointing either inwards or outwards (figure 2), named after its discoverer, German sociologist Franz Carl Müller-Lyer in 1889. The two segments are of equal length. However, due to the presence of the arrowheads, people tend to perceive the segment with the arrowheads pointing inward to be longer than the other one. But despite its prevalent effect on human visual perception, it has long been known that everyone is not equally susceptible to its illusory effect. Collecting data from a sample consisting of Europeans, Africans, and the Philippines, Segall and his colleagues (1963) found that the Europeans were more susceptible to the Müller-Lyer illusion than the other groups of participants. To explain people’s different susceptibility to the illusion, Segall put forth the influential “carpentered world” hypothesis. Living in highly carpentered environments full of artifacts constructed from straight lines and right angles, Europeans have grown accustomed to seeing corners everywhere, as a result of which their visual systems develop a habit of interpreting the arrowheads in the Müller-Lyer shapes as far and near corners: arrows pointing outwards indicate nearer corners, and inward-pointing arrows indicate corners farther away. These corners are often reliable indicators of size differences in natural environments. But they become misleading when displayed on two-dimensional planes, resulting in the Müller-Lyer illusion. Figure 3 depicts a carpentered environment in which arrowheads function as corners. The red segment on the left looks considerably shorter than the one on the right. This is a perfectly accurate representation of the actual size of the two segments in natural three-dimensional environments. But once placed on a two-dimensional plane, the two segments would actually be of equal length even though they look different. This illusory experience happens because the perceivers’ repeated exposure to the kind of scenarios depicted in figure 3 has embedded certain assumptions or heuristics in their visual systems such that their brains override the retinal information which says both segments are equal in length. Note that Segall and his colleagues’ original study suffered from serious methodological flaws: since the sample consisted of subjects from three different ethnic groups, it left open the possibility that their ethnicity, rather than the ecological environment they inhabited, explained the difference in their Müller-Lyer susceptibility.5 But multiple studies in subsequent years, ruling out possible confounds, replicated the experimental results of Segall’s experiments (Deręgowski, 2013; Nijhawan, 1995; Pedersen & Wheeler, 1983). These studies thus provided solid evidence for the carpentered world hypothesis. To the extent that the Müller-Lyer illusion can at least partially be accounted for by the carpentered world hypothesis, two implications can be drawn for our current discussion. First, the carpentered world hypothesis implies that the visual assumptions making us susceptible to the illusion are, to some extent, learned from and shaped by prior visual experience rather than innately determined. According to the carpentered world hypothesis, visual percepts generated by the Müller-Lyer shape are determined empirically by the image-source relationships one has been exposed to over accumulated experience. The reason why people experience the MüllerLyer shape differently is that they have different perceptual histories. Those growing up in rectilinear environments were repeatedly exposed to Müller-Lyer shapes at relatively early stages in life. In their living environments, arrows pointing outwards indicate nearer corners, and inwards-pointing arrows indicate corners farther away. This, in conjunction with the more fundamental perspectival assumption that objects closer to the perceiver project larger images on her retina, has the effect that the length of the segment contained between two inward-pointing arrows is increased and that the length of the segment contained between two outward-pointing arrows is decreased. More recent attempts to account for the Müller-Lyer illusion in the spirit of the carpentered world hypothesis invoked the notion of visual statistical learning, which describes the extraction of statistical regularities from visual environments across time or space (Howe & Purves, 2005). According to this view, one of the key functions of our visual systems is to calculate the joint or conditional probabilities of shapes co-occurring during the viewing of complex visual configurations based on the visual experience of similar stimuli in the past. 6 7 In light of this account, what the visual system does when visually encountering a Müller-Lyer shape is to figure out, given the segments attached with inward and outward arrows, whether the two segments are more likely to be equal or different in length. Perceivers who grow up in a rectilinear carpentered environment are far more likely to see stimuli in which segments attached with arrows pointing outwards are shorter than those pointing inwards than stimuli in which the two segments are equal in length. This information is encoded in their visual systems, as a result of which they construct a visual representation that reflects this likelihood. Perceivers brought up in an environment that is not rectilinear, on the other hand, have seldom been exposed to this kind of visual cues. Their visual systems thus fail to learn to make inferences about the lengths of segments conditional on the presence of those arrows. Consequently, in their perception of the Müller-Lyer shape, the arrows pointing inwards or outwards, presumably resembling far and near corners in the carpentered world, have little interference with the images of the two segments projected on their retinas. This explains why they are less or even not at all susceptible to the illusion. The second implication of the carpentered world account of the Müller-Lyer illusion is the existence of a mechanism responsible for systematically inaccurate perceptual processing that is different from both attentional direction and cognitive penetration. Even if one is convinced and believes that the two segments in the Müller-Lyer illusion are equal in length, her visual experience would still represent them as different, meaning that her visual representation is independent of her cognitive states. But as I have explained in section 2, both attentional direction and cognitive penetration presuppose top-down influences from cognitive states. Hence, the mechanism responsible for the Müller-Lyer illusion, namely, visual assumptions learned from the perceptual world, must be different from both of them. But how could visual assumptions possibly be independent of higher-level cognitive states? The very notion of a visual assumption implies that vision involves inferences. As such, one might be tempted to think that visual assumptions must themselves be higher-level cognitive states, and hence for them to play a role in visual processing, top-down influence has to take place. However, this reasoning ignores the possibility that visual assumptions can be genuinely perceptual — that they are developed and encoded within the visual systems. First, vision is more than just the passive reception of information. Rather, the visual system actively participates in the processing of visual inputs and is “smart” enough to carry out a lot of inferential processes (Kanizsa 1985; Pylyshyn 1999). This is thus compatible with the view of our minds being modular (Fodor, 1983). As Munton points out: Much statistical learning is posited to take place within the visual system. Equally, non-visual information may influence the inputs and outputs to an early visual module without contravening the purported informational encapsulation of the visual system. (2019, p. 138) Informational encapsulation constrains the information visual modules can access: they can access only visual inputs, but not higher-level cognitive states. However, informational encapsulation says nothing about what perceptual modules can do with the visual inputs they receive (Firestone & Scholl 2016). As such, the visual system can make inferences about visual inputs based on visual assumptions that are innate or learned from experience even if the mind is modular in the stringent Fodorian sense.8 Second, the reason why visual assumptions can be developed and encoded within the visual system is that visual assumptions, unlike assumptions we make use of in syllogistic inference, need not have propositional content. In fact, many visual assumptions are simply not structured in such a way that can be properly characterized in terms of propositions. Instead, they are better characterized in terms of the probability distribution of possible representations accounting for visual inputs. 9 When presented with a stimulus, the image projected on the retina (i.e., visual input) gives rise to an indefinite number of possible representations (call each possible representation a visual hypothesis) to account for the stimulus. What the visual system does is calculate, based on the visual input, the likelihood of each visual hypothesis accurately representing reality and choose the one that maximizes the likelihood. In the case of the MüllerLyer illusion, a perceiver’s visual encounter with a Müller-Lyer shape automatically generates an indefinite number of visual hypotheses regarding the relative lengths of the two segments. The perceiver’s visual system then calculates the likelihood of these hypotheses. But for the sake of simplicity, suppose that the visual input gives rise to only two visual hypotheses, one representing the two lines of the shape as equal in length and the other representing the inwardpointing segment as longer than the outward-pointing segment. If no arrows were attached to the segments, the perceiver would see them as equal in length. This is because the images projected on the perceiver’s retinas are equal in length, and hence the probability of the former hypothesis being accurate is greater than its alternative. However, the presence of the arrows changes the probability distribution. As a result of visual statistical learning from past experience, the arrows attached to the segments add more weight to the hypothesis that the segments are different in length. Consequently, the perceiver’s visual system overrides the size of the retinal images, decides that the two segments are more likely to be different in length, and then represents the relative lengths of the two segments in this way in the visual experience. Indeed, this involves a good amount of inferential processes. But insofar as these inferences, based on the probability distribution of visual hypotheses, are statistical rather than semantic, there is nothing preventing them from happening within the visual system. Therefore, they need not be top-down in the sense that implies higher-level cognitive states exerting influence on lower-level perceptual states. 4. Visual Assumptions in Perceptual Social Bias The last section shows how visual assumptions learned from prior visual experience can modulate current visual perception by referring to the example of the Müller-Lyer illusion. In this section, I will argue that this mechanism may also be applied to explaining some types of perceptual social bias. If my argument is successful, another item would be added to Siegel’s list of the many ways in which one’s processing of perceptual information can be biased by the flawed practice of both individuals and social structures. The mechanism, as characterized in the last section, suggests that the more often perceivers are exposed to a certain kind of stimulus in the past, the more likely, when a specific visual input is given, they are to "see" that stimulus when the input is different but sufficiently similar to it. In the case of the Müller-Lyer illusion, their frequent exposure to corner cues in carpentered environments leads to the formation of an assumption that disposes their visual systems to overestimate the lengths of segments with inward arrows and to underestimate the length of segments with outward arrows. In consequence, when corner cues (i.e., the arrows) are available, the perceiver "sees" the two segments in a way that does not represent reality. Now we are ready to apply the analysis to perceptual social bias. In this section, I will take the study of weapon identification by Correll and his colleagues (2015) as my paradigmatic example, though mutatis mutandis, the analysis can be applied to other phenomena of perceptual social bias. But before I proceed, a caveat needs to be made concerning the ontological status of the concept of race. While the traditional naturalist conception of race, which treated race as reflecting biological foundations that separate humanity into discrete groups, has long been repudiated, there is still a debate concerning the ontological status of race among philosophers. Mallon (2006) famously distinguished between three main metaphysical positions about race in the relevant philosophical discussions. Racial population naturalism argues that although humanity cannot be separated into static and discrete groups as conceived of by traditional naturalism, races are still real in the sense that they are biologically grounded populations. In contrast, racial constructionism denies race has any biological foundations and instead holds that it is constructed through racialized social practice. Nonetheless, constructionism maintains the reality of race (though as a social, rather than biological reality), which puts it in opposition to the third metaphysical position about race, racial skepticism, which holds that race is not real and human races do not exist at all. Note that the debate on the ontological status of race is still ongoing and little consensus has been reached among philosophers.10 So in this paper, I will refrain from taking a stance on the debate and am not committed to any specific metaphysical position about race. Despite this, I will use terms such as "black" and "white" individuals for illustrative purposes only.11 But I remain neutral as to whether these terms designate biologically grounded social groups, racialized social groups, or something else. Recall that in their experiments, the participants were presented with images in which a man (either black or white) held an object in his hand, and their task was to identify whether the object was a gun or a tool by pressing buttons on keyboards. The image was blurry such that although the race of the man was easily recognizable, the object was not. It turned out that the participants were more likely to mistake tools for guns when they were in the hands of black men than when they were in the hands of white men. According to the explanation proposed above, this is what happened in the experiment: When presented with an image of a man (black or white) holding a tool, the visual input gives rise to an indefinite number of visual hypotheses (that object being a wrench, a hammer, a gun, etc.). The probabilities of each of them accurately representing reality are then calculated by the perceiver’s visual system. Due to the perceiver’s perceptual history of being more frequently exposed to black men with guns than white men with guns, more weight is given to the gun representation when the man in the image is black. As a result, the perceiver’s visual system decides, compared to when the face is white, that it is more likely that the object in the hand of the person is a gun in the presence of a black face. Therefore, other things being equal, the perceiver is more likely to misrepresent the object as a gun when the man is black than when he is white. This story is well in line with the accounts of perceptual social bias suggested by Munton (2019) and Neemeh (2020). I refer to this account as the simple probabilistic account of the learning of visual assumptions.12 However, an apparent problem arises for this simple account: it is improbable that the participants' encounters with stereotypical associations (e.g., black people with guns) in real life are frequent enough to embed assumptions in their visual systems, especially considering that most samples in the experiments consist of young college students (e.g., Correll, Wittenbrinks, Crawford & Sadler, 2015, study 2; Payne, Shimizu & Jacoby, 2005). They probably have little chance to interact with black people holding guns and may not even have seen guns at all in real life. Consequently, as Roberts says, "most of the students would have been unlikely to have encoded a statistical regularity between the two based on their perception of real-world objects" (2021, 4551). The above account does not seem adequate even in experiments where the sample consists of a broader population (e.g., Correll, Wittenbrinks, Crawford & Sadler, 2015, study 1). Admittedly, data reveal that black people account for a higher percentage of the offenders in violent crimes than other racial groups combined. For example, in 2019, 51.2% of all homicide offenders were black (JJDP n.d.). However, I doubt that the participants in those experiments have witnessed many violent crimes committed by black people with guns in real life. But if my doubt is valid, how is it possible for their visual systems to develop an assumption that associates black people with guns? One possibility is suggested by Roberts (2021), who claims that images might have played an essential role in the process of visual statistical learning. Roberts' primary focus is on how images contribute to the objectification of women in perception, but her suggestion can easily be extended to other forms of perceptual social bias, including people's perceptual tendency to associate black people with guns. Most ordinary people are unlikely to have witnessed a lot of violent crimes committed by black people with guns in real life. Nevertheless, we are frequently exposed to media coverage of violent crimes. In the coverage, black people are disproportionately depicted as either perpetrators or victims of violent crimes, both of which tend to link black people with guns. For example, in a recent report, researchers found that mugshots were used in coverage of 45% of cases involving black people accused of crimes, whereas the number is only 8% when it comes to cases involving white defendants (Equal Justice Initiative, 2021). This biased depiction of black people is also reflected in Hollywood movies. By analyzing a database of 160,000 acting credits from 26,000 major US movie releases, Zachary Crockett, a former Vox staff, found that "gang member" and "thug" roles were predominantly played by black actors — 62% of all actors who were credited as "gang members" and 66% who were credited as "thugs" are black (Crockett, 2016). These are just a few examples among many that show how the association between black people and guns is established through imagistic representations. Given that these images are prevalent in daily life and likely account for most ordinary people's perceptual encounters with black people carrying guns, it seems plausible that they are responsible for the development of visual assumptions that associate black people with guns in perception, as Roberts suggests. Roberts' suggestion overcomes the inadequacy of the simple probabilistic account of visual statistical learning by relocating the source of visual statistical learning from real-life experience to image perception. But in addition to Roberts’ suggestion, I argue that another revision, focusing on the process instead of the source of visual statistical learning, can also be made to the simple probabilistic account to accommodate the fact that people do not frequently encounter visual stimuli that associate black people with guns in real life. I now turn to this revision. Recall that according to the simple probabilistic account of visual statistical learning, one’s visual system calculates the probability of a visual hypothesis accurately representing reality on the basis of one’s perceptual history, namely, one’s visually encountering scenes in accordance with that hypothesis in the past. It assumes that one’s visual system is statistically rational in the sense that the likelihood of a visual hypothesis is proportional to the frequency of one’s exposure to image-source relations conforming to that hypothesis. As such, each visual encounter with people holding guns, whether black or white, would be equally weighted and encoded in a perceiver’s visual system. This assumption, however, has been called into question by some recent psychological and neurophysiological research. The weights assigned to visual encounters with stimuli can be influenced by various factors. Jones and his colleagues (2006) reported that primacy and recency effects impact perceptual processing: in some tasks, visual processing is biased toward earlier stimuli, while in other tasks, it is biased toward recent stimuli. Geisler and Kersten (2002) suggested that prior knowledge regarding the reliability of the information sources plays a role in adjusting the relative weights assigned to them. Hence, my perception of something in a normal situation is likely to be assigned more weight than something I see in a desert because the latter might just result from a mirage. Another factor I want to highlight that may influence the distribution of weights to visual encounters is the affective valence of the stimuli, due to its relevance to the current discussion. Drawing on two lines of empirical research, I argue that stimuli like a black man holding a gun are often processed more efficiently by our visual systems than, so to speak, a white man with a gun. As a result, our visual encounter with the former may be weighted more than the latter, and hence they do not contribute equally to the probability calculation of the visual system. The first line of research concerns people’s affective ratings of black people, especially black males. In a racialized society like the U.S., it is hardly surprising that negative affects often accompany ordinary people's perception of black men. Empirical findings from the last two decades also confirmed this. In Amodio and Hamilton (2012) 's study, participants were told by experimenters that they would have a discussion on social issues with either a white or a black partner. Information concerning the race of the discussion partner was tacitly conveyed to them by disclosing the partner's name. Although the discussion never actually happened, merely informing participants of the possible discussion was enough to manipulate their anxiety: participants who believed they would discuss with a black partner showed significantly greater anxiety than those with a white partner. In one of Shapiro et al. (2009)'s experiments, participants viewed an online slide show in which pairs of male faces appeared briefly on a screen in succession and were then asked to rate each in terms of how threatening the person came across. Due to sensory adaptation, when an angry white male face was paired with a white male face wearing a neutral expression, the neutral face was perceived as less threatening. This effect, however, did not take place when the two faces were black. In Trawalter et al. (2009)'s study, participants were briefly presented (30 ms) with the faces of black men. In the meanwhile, their pattern of attention was recorded using a dot-probe detection paradigm. The researchers found that their patterns of selective attention were very much like those when exposed to pictures of evolved threats such as spiders and snakes. The three studies are just a few of the vast literature on affective responses generated by the perception of black men. The research is varied. But it unanimously suggests that negative emotions often accompany people's perception of black men and black faces alone are enough to trigger feelings of fear in the perceivers. The second line of research concerns the well-known phenomenon that our visual systems process emotionally significant stimuli, especially threatening or fear-related stimuli, more efficiently than neutral stimuli. Whereas the former category includes stimuli such as spiders, pictures of mutilations, angry faces, or words like death and murder, the latter includes flowers, clownfish, neutral faces, or words like table, lamp, etc. Empirical research vindicating this phenomenon is enormous. Consider Soares and Esteves (2013) 's study. Participants were presented with displays for brief durations under conditions of high perceptual load (each of the displays contains 4-8 different objects). Their task was to detect specific objects from the displays. The results showed that the participants were faster at detecting fearful than neutral objects. Furthermore, the results showed that their detection was also more accurate when asked to identify the former compared to the latter. Also, consider studies on binocular rivalry. Binocular rivalry is a visual phenomenon in which two different images are presented simultaneously to each eye. Rather than perceiving a stable, single amalgam of the two stimuli, the perception of someone with normal binocular vision would alternate between them as they compete for perceptual dominance. This competition, however, becomes one-sided dominance when the two stimuli do not have the same affective valence. Alpers et al. (2005), for example, found that when presented with a neutral and a threatening image, the latter would usually predominate over the former in this rivalry, indicating that our visual systems give priority to the processing of fear-related stimuli. The above-mentioned are just a few of the studies on the efficient processing of emotionally valenced, especially negatively valenced visual information. There is still an ongoing debate concerning the underlying mechanism of this phenomenon. Some hold that affectively-valenced visual stimuli are processed more efficiently because they receive additional neural representation, while others suggest that it is the result of more attentional resources being allocated to emotionally charged visual stimuli. 13 But details of the debate need not bother us here. For the current purpose, it suffices for us to say that both accounts point in the same direction: affect-laden information, especially negatively valenced information, is treated by our visual systems differently than neutral stimuli. Consequently, it is encoded in our visual systems such that it is weighted more than neutral information. This corollary makes evolutionary sense because the ability to rapidly and accurately detect threatening stimuli confers enormous adaptive advantage. But this corollary, taken together with the first line of research on negative affects accompanying the perception of black men, leads to what Neemeh (2021) calls “bootstrap hell.” It opens up the possibility that, in calculating the probability of possible representations, if perceivers hold strong sentiments against black people, their past visual encounters with black men holding guns or images of this sort would be weighted more than those with white men even if they do not in fact encounter the former more frequently than the latter. 14 As a result of this unduly weighting, even a few visual encounters with black people carrying guns (either in real life or in images) would be sufficient for their visual system to develop a robust assumption associating black people with guns. As an anonymous reviewer has correctly pointed out, most of my considerations above are based on empirical studies with US-American participants. While this is true, I did it for legitimate reasons. This is because the paradigmatic example I have been using in this section to explain how perception can be shaped by biased visual assumptions, namely the weapon identification task, reflects a stereotypical association between black people and guns that is the most prominent in the US. It is unclear whether and to what extent this association is also held by people from different socio-cultural backgrounds. Despite this, my proposed account of perceptual bias is not limited to a specific group of people. Even if people with different sociocultural backgrounds do not have a strong tendency to associate black people with guns to the extent that their visual processing is influenced by it, it is not unreasonable to expect that they would have learned other forms of associations between a social group and some object or attribute from their environments, which leads to distorted visual processing. My proposed account may then be used to explain how this distortion occurs — the associations are learned through repeated exposure to stimuli conforming to them (maybe in conjunction with some other mechanisms adjusting the weights of the stimuli) and then developed into biased visual assumptions. Exploring cross-cultural differences, as well as similarities, in perceptual biases is both interesting and crucial for understanding their origins. But this topic has only recently begun to draw attention from researchers (Fiske 2017). Much more empirical work needs to be done before we can gain useful insights into how stereotypical associations differ across sociocultural contexts and how they influence perceptual processing from a philosophical perspective. 5. Concluding Remarks In the last two sections, I have advanced a possible explanation of how perception can be biased as the result of flawed visual assumptions. It adds another item to Siegel’s list of the many ways in which our access to social information can be biased. However, my project is largely speculative, and it ultimately depends on empirical research to decide whether the suggested mechanism is responsible for particular instances of perceptual social bias. Nonetheless, my proposed mechanism, if exists, would point to a kind of social bias that is fundamentally perceptual, which has important implications for how we conceptualize social bias. Unlike perceptual bias resulting from cognitive penetration and attentional direction, the kind of social bias resulting from faulty visual assumptions is fundamentally perceptual in the sense that it can directly modulate perceptual experience and can persist even in the absence of corresponding cognitive states. I call this kind of social bias exclusively perceptual bias. Note, however, that exclusively perceptual bias does not necessarily constitute a different kind of social bias, in addition to the familiar distinction between explicit and implicit bias. Exclusively perceptual bias is surely distinct from explicit bias to the extent that the latter is conceptualized as conscious attitudes or beliefs we hold toward a certain social group. As such, they are necessarily cognitive states and are hence must be different from exclusively perceptual bias. But on the other hand, the nature of implicit bias is a more controversial issue, probably due to the fact that it can only be probed through indirect measures. Traditionally, implicit bias has been conceptualized as simple associations between concepts or images. But in the last decade, this simple associationist view has been challenged, and a plethora of alternative ways to conceptualize implicit bias have been proposed: Gendler (2008) proposes to treat implicit bias as what she calls alief; Levy (2015) claims that implicit bias is patchy endorsements; Mandelbaum (2016) suggests that implicit bias is best understood as unconscious belief; Nanay (2021) conceptualizes implicit bias in terms of mental imagery. These proposals are incompatible with each other but are all backed by some empirical evidence. This fact leads Holroyd, Scaife, and Stafford (2017) to suggest that it is impossible to have a unified account of implicit bias, and it should rather be considered as a term that covers a heterogeneous set of mental or behavioral phenomena. If Holroyd and his colleagues’ suggestion is correct, then it is very likely that a subset of the phenomena researchers commonly classify as implicit bias actually coincides with what I call exclusively perceptual bias. So the significance of exclusively perceptual bias is not that it would constitute a distinct kind of social bias, as Neemeh (2020) seems to suggest. Rather, it is important because it points to the need to conceptualize social bias in terms of an alternative distinction, namely, that between perceptual and cognitive bias. This distinction has been long been neglected given that the traditional conceptualization of social bias relies almost exclusively on that between explicit and implicit bias. This neglect may have led researchers to ignore features that are unique to some forms of bias and results in their failure to come up with effective interventions to counteract them. If one has a false belief, the most effective way to change her belief would be to present her with evidence showing that her belief is false. But this method probably does not work to correct one’s inaccurate perception — no amount of evidence would change how one perceives an object. Similarly, training or interventions working effectively to counteract cognitive bias may not work equally well against bias that is fundamentally perceptual. But to come up with effective interventions to tackle perceptual bias, the necessary first step would be to recognize its perceptual nature. Notes: 1 A possible explanation for why the participants cannot correct their reports is that the images, due to their blurriness, are ambiguous between weapons and tools. As a result, the statistical regularity associating black faces with weapons biased their visual systems to interpret the images as weapons. This is the proposal I will develop further in sections three and four. 2 Thanks to an anonymous reviewer for bringing to my attention the wealth of empirical and philosophical research on attention. Two things need to be noted here. First, whereas it is common to characterize attention as a process of selection, Fazakas and Nanay (2021) have advance an alternative view suggesting that attention is actually a process of amplification rather than selection. But this need not undermine my characterization of attention because their characterization of attention is almost exclusively at the neural level, while mine is mostly at the subject level. Furthermore, even if their characterization is also reflected at the subject level, this alternative function of attention can also cause the alteration of perceptual contents, which is all I need at this point. Second, as a concept that comprises a variety of distinct phenomena, attentional phenomena can be divided in various, cross-cutting ways in terms of their subject-level functions and underlying neural mechanism. One important distinction relevant to the current discussion is between internal and external attention. Internal attention refers to how we focus inwardly to process and generate mental interpretations of this information, whereas external attention refers to the way we attend to relevant sensory information in our environment (Chun et al. 2011). Another important distinction is covert attention and overt attention, which are typically considered subtypes of external attention. Simply put, covert attention is defined as paying attention without moving the eyes and overt attention is defined as selectively processing one location over others by moving the eyes to point at that location (Itti & Koch 2000). My characterization of attention in the main text focuses exclusively on external attention because the current discussion is on outer perception. But it may cover both overt and covert attention since both subtypes of attention can result in the alteration of perceptual content. 3 Note that there are also philosophers suggesting that certain forms of attentional direction satisfy the requirement of directness and hence count as cases of cognitive penetration (see Macpherson, 2012; Stokes, 2018). Whether this suggestion is reasonable or not, however, is not the concern of this paper, because my aim in this paper is argue for a possible mechanism for perceptual social bias that is distinct from both attentional direction and cognitive penetration. As such, the plausibility of my proposal does not depend on a specific relationship between attention and cognitive penetration. 4 Even though they are not as extensively studied as top-down attention, there also exist attentional phenomena that are purely bottom-up, without being mediated by some higher cognitive state. The existence of bottom-up attention is common in everyday life and also wellestablished in cognitive psychology. It occurs when stimuli are salient because of their inherent properties relative to the background (Katsuki & Constantidinis 2014). For example, a perceiver’s attention is immediately drawn to a green dot when it is surrounded by all red dots. Examples like this are abundant and there may also be cases of perceptual social bias that can be accounted for by this kind of attention mechanism. But this does not undermine my argument for the existence of an additional mechanism of perceptual social bias. First, the kind of attention mechanism Siegel has in mind when she talks about attention being a possible explanation for perceptual bias is probably top-down. That is because bottom-up attention, being induced directly by external stimuli and not through the mediation of some internal states of the perceivers, does not sit well with Siegel’s characterization of the attention direction which states that “the state activated by the black prime directs the subject’s attention to features of the pliers that are congruent with being a gun (metallic), and away from features incongruent with being a gun (shape)” (2020, 103). Second, in the case of bottom-up attention, a question arises as to what makes the stimuli salient to a perceiver. One is that the salience is innate, just like in the above example: the perceiver’s visual systems are built in such a way that green and red create a strong visual contrast when put in adjacent to each other. The other possibility is that the salience of the stimuli relative to the background is learned from one’s perceptual history. If either possibility is true, then perceptual social biases caused by this bottom-up attention (if they exist at all) would be compatible with the additional mechanism I propose in section 3 and 4. 5 This is not a mere logical possibility, as Jahoda (1971) 's and Berry (1971) 's studies suggested that retinal pigmentation was actually correlated with people's susceptibility to the illusion, and retinal pigmentation was correlated with ethnicity. 6 This sort of view come in different forms. Gregory (1997), strictly following the carpentered world hypothesis, suggested that the arrows in the Müller-Lyer shape were perspective drawings of corners. Howe and Purves (2005) take what they called the wholly empirical approach and extended the Müller-Lyer shape to all objects in natural scenes, rather than just corners. Nour and Nour (2015) applied Bayesian statistics to analyze the visual system’s capacity to process visual information. 7 Characterized in terms of probability distributions, some of the things people commonly refer to as visual assumptions (i.e., the assumption of light-from-above) are not really visual assumptions in the strict sense. Rather, they should be considered as visual hypotheses, which are only components of visual assumptions. 8 Thanks to an anonymous reviewer for pointing this out. To clarify my point, I do not hereby assert the truth of the Fodorian modularity theory. Actually, as an anonymous reviewer has pointed out, the Fodorian view has been challenged and invalidated by massive empirical evidence and theoretical considerations. I agree that the theory has largely been rendered implausible, despite some recent attempts to defend it (Firestone & Scholl 2016). However, I do not take a stance on this debate in my paper. My claim is that even if the stringent Fodorian modularity theory were true, my view would still be valid because the visual system’s ability to make inferences need not depend on inputs from the cognitive system. Conversely, if the mind does not adhere to a modular framework (either Fodor’s framework or Carruthers’ less stringent modular framework), this would not undermine my view either. Because even if the visual system can be influenced by inputs from the cognitive system, it does not rule out the possibility that the visual system can also make inferences on its own. 9 This characterization of visual assumptions is directly implicated in the Bayesian approach to visual perception (Nour and Nour, 2015; Scholl, 2005). But it is also compatible with views that are not explicitly Bayesian (see Gregory, 1997; Howe & Purves, 2005). 10 Mallon suggests that the disagreements between the three positions are just illusory because they “share a broad base of agreement regarding the metaphysical facts surrounding racial or racialized phenomena that suggests their views are complementary parts of a complex view incorporating biological, social, and psychological facts” (2006, p.527). But see Hochman (2017) for an objection against Mallon’s suggestion. 11 I am grateful to an anonymous reviewer for pushing me to clarify these points. Also, it might seem that my use of these terms cannot really be neutral with respect to the three metaphysical positions about race because it cannot be compatible with racial skepticism, which denies the existence of race altogether. But note that often, racial skepticism is accompanied by an alternative social categorization to account for the apparent reality of race (e.g. Blum 2010). As such, it can still be meaningful to talk about black and white individuals even according to racial skepticism, though these terms are just proxies for some alternative social categories. 12 Note that Munton (2019) does not intend to propose a realistic explanation. Rather, her aim is to show that in a highly racialized society, even if our visual systems function ideally such that they perform perfect statistical learning, they might still result in biased perception and ground prejudiced beliefs. 13 Advocates of the first account suggest the existence of a visual pathway that is devoted specifically to the processing of affect-laden visual stimuli. Several lines of research indicate that the amygdala is involved in the encoding of affective stimuli but not in that of neutral stimuli (Amaral, Price, Pitkanen & Carmichael, 1992). Based on these lines of research, some then identified a subcortical neural pathway conveying visual information (LeDoux, 1986). Unlike the better-known ventral and dorsal pathways, this pathway is specialized in processing emotionally valenced, especially negatively valenced visual information. As a result of this additional visual pathway, the processing of affective stimuli, especially fear-related stimuli, is enhanced. However, the existence of such an additional visual pathway is contentious: some studies suggest that this pathway is not functional in primates (Pessoa & Ungerleider, 2004). So an alternative account proposes that threatening stimuli are processed more efficiently not because they are enhanced but rather because they are prioritized in visual processing. 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FAQs

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What experimental evidence supports the existence of perceptual social bias?add

Correll et al. (2015) found that participants misidentified tools as guns more frequently when held by black men, underscoring how racial biases can distort visual perception in weapon identification tasks.

How do cognitive penetration and attentional direction contribute to perceptual bias?add

Both cognitive penetration and attentional direction involve top-down influences from cognitive states that modulate perceptual experiences; Siegel identifies them as significant mechanisms affecting our visual processing of social information.

What role do visual assumptions play in the Müller-Lyer illusion?add

The Müller-Lyer illusion illustrates how visual assumptions about corner cues, developed from experience, lead to systematic misperceptions of length, as shown by Segall's carpentered world hypothesis.

How do media representations influence visual assumptions related to race?add

Frequent media depictions associating black individuals with violence contribute to biased visual assumptions, causing perceivers to disproportionately link black faces with weapons, as highlighted by Roberts' work on visual statistical learning.

What differentiates exclusively perceptual bias from cognitive bias?add

Exclusively perceptual bias operates independently of cognitive states, influencing direct perceptual experience, while cognitive biases are derived from conscious attitudes and beliefs about social groups.

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