Frequency, probability, and prediction: easy solutions to cognitive illusions?

Many errors in probabilistic judgment have been attributed to people's inability to think in statistical terms when faced with information about a single case. Prior theoretical analyses and empirical results imply that the errors associated with case-specific reasoning may be reduced when people make frequentistic predictions about a set of cases. In studies of three previously identified cognitive biases, we find that frequency-based predictions are different from-but no better than-case-specific judgments of probability. First, in studies of the "planning fallacy, " we compare the accuracy of aggregate frequency and case-specific probability judgments in predictions of students' real-life projects. When aggregate and single-case predictions are collected from different respondents, there is little difference between the two: Both are overly optimistic and show little predictive validity. However, in within-subject comparisons, the aggregate judgments are significantly more conservative than the single-case predictions, though still optimistically biased. Results from studies of overconfidence in general knowledge and base rate neglect in categorical prediction underline a general conclusion. Frequentistic predictions made for sets of events are no more statistically sophisticated, nor more accurate, than predictions made for individual events using subjective probability.     

Do action systems resist visual illusions?

Arguments about the relative independence of visual modules in the primate brain are not new. Recently, though, these debates have resurfaced in the form of arguments about the extent to which visuomotor reaching and grasping systems are insensitive to visual illusions that dramatically bias visual perception. The first wave of studies of illusory effects on perception and action have supported the idea of independence of motor systems, but recent findings have been more critical. In this article, I review several of these studies, most of which (but not all) can be reconciled with the two-visual-systems model.     

When does action resist visual illusions?

Over the past decade, many studies of non-pathological individuals have reported functional dissociations between perceptual judgments and motor responses. These results suggested an interpretation of the ventral and dorsal streams in the primate visual system as independent modules for visual awareness and the visual guidance of actions. However, recent comparisons of perception and grasping responses in size-contrast displays have been widely reported to show that apparent dissociations are actually experimental artifacts. An overview of the literature suggests that the issue of visuomotor dissociations in healthy individuals is far from settled. Some results suggest that immunity from visual illusions might be found when task requirements emphasize observer-relative reference frames. These results suggest that the functional specialization of the two visual subsystems might be less rigid than originally posited.     

Three elemental illusions determine theZöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Zöllner figure at the intersecting angles between 36° and 83° (i.e., a reversal of the Zöllner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced Une (test line) is single. When an illusory line is usedas the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45°. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Zöllner figure.     

Do positive illusions contribute to human well-being?

Psychologists such as Shelly E. Taylor have championed the idea that certain false beliefs, referred to as positive illusions, fulfill a significant role in contributing to human well-being. The goal of this article is to critically review the empirical evidence for this claim. The main concern, then, is whether the empirical evidence is conclusive in regard to the value of positive illusions for agents. The conclusion to be developed is that the latest psychological research is inconclusive in regard to the value positive illusions. This is due not only to evidence that draws into question the value of positive illusions for agents, but also due to methodological and conceptual problems with the positive illusion literature. Consequently, it could be the case that false beliefs contribute to agent well-being in specific situations, but it is difficult to claim that certain false beliefs are required for agent well-being.     

Still motion? Motion illusions and luminance contrast

The influence of different luminance contrasts and equiluminance on illusory motion in four inducing patterns was studied: enigma, rotating snakes, pinna, and rotating-tilted-lines. At high luminance contrast the Pinna and the rotating-tilted-lines illusions are significantly stronger than at low luminance contrast, whereas the Enigma and Rotating Snakes illusions are stronger at low luminance contrast. At equiluminance along the L-M axis the strength of all illusions is greatly reduced. Data suggest that luminance contrast constitutes one important factor for their occurrence.     

Three elemental illusions determine the Zöllner illusion

We have discovered an apparent contraction illusion of acute angles in a special form of the Z?llner figure at the intersecting angles between 36 degrees and 83 degrees (i.e., a reversal of the Z?llner illusion). The necessary condition for this illusion is that inducing lines are long enough and the induced line (test line) is single. When an illusory line is used as the induced line, the magnitude of contraction increases. Short inducing lines give no illusion or a slight expansion of acute angles at the intersecting angle of 45 degrees. We have ascertained that the source of this expansion is the narrow region in the vicinity of the induced line, whereas the source of the contraction is much broader regions. Furthermore, we have discovered another expansion mechanism, which is generated by the symmetrical configuration of the standard Z?llner figure.     

Modeling geometric–optical illusions: A variational approach

Visual distortions of perceived lengths, angles, or forms, are generally known as “geometric–optical illusions” (goi). In the present paper we focus on a class of gois where the distortion of a straight line segment (the “target” stimulus) is induced by an array of non-intersecting curvilinear elements (“context” stimulus). Assuming local target–context interactions in a vector field representation of the context, we propose to model the perceptual distortion of the target as the solution to a minimization problem in the calculus of variations. We discuss properties of the solutions and reproduction of the respective form of the perceptual distortion for several types of contexts. Moreover, we draw a connection between the interactionist model of gois and Riemannian geometry: the context stimulus is understood as perturbing the geometry of the visual field from which the illusory distortion naturally arises. The approach is illustrated by data from a psychophysical experiment with nine subjects and six different contexts.     

The regression to right angles tendency,lateral inhibition,and the transversals in the Zöllner and Poggendorff illusions

A new version of the Zöllner illusion is demonstrated. Two different ways in which the regression to right angles tendency might operate are distinguished and considered in relation to the illusion. Experiments are reported which show that the one consistent with lateral inhibition between orientation detectors gives the better explanation of the illusion. The implications of this for the Poggendorff illusion are considered.     

Virtual and drawing structures for the Müller-Lyer illusions

This research assessed the relative contribution of 3-D virtual structure that generated the stimulus drawings (scene-based and picture-based theories) and 2-D structure of the drawings (object-based theories). Virtual structures were right-angle convex and concave corners in front of and behind the picture plane, respectively. Virtual corner size was manipulated directly (Experiment 1) and indirectly by manipulating drawing station point distance (Experiments 2 and 3), corner depth (Experiment 4), and corner distance from the picture plane (Experiments 5 and 6). Experiments 2 and 4 held the size of the projected corner edge (interior target line) constant, causing virtual corner size to vary, whereas Experiments 3, 4, 5, and 6 held size of the virtual corners constant, causing size of the projected corner edge or interior target line to vary. Subjects reproduced the length of the projected corner edge (interior target line). The illusions (difference between reproduced size of the projected corner edge and T-junction control) were generally well fit by the weighted sum of virtual corner size and size of the projected corner edge, but the projected distance between boundary line terminations (intertip distance) appeared as an additional contributing factor in Experiments 5 and 6. The implications of this methodological approach are discussed for theories of the illusions.     

Length illusions in conventional and single-wing Müller-Lyer stimuli

Warren and Bashford (1977) reported that eliminating one of the wing components from the conventional (i.e., two-wing) Müller-Lyer figures had no appreciable effect on the magnitude of the acute-angle (contraction) illusion but substantially reduced the magnitude of the obtuse-angle (expansion) illusion. In addition, they found that whereas the contractionary effects of the acute-angle components tended to be confined to the region of the shaft adjacent to the angles, the expansionary effects of the obtuse-angle components were more uniformly distributed across the shaft. Since these findings challenge many theories of the Müller-Lyer illusion, the purpose of the present investigation was to evaluate further Warren and Bashford's work with four experiments. Experiments 1 and 2 assessed length illusion magnitudes by requiring subjects to adjust either the length of a plain comparison line to match the length of the Müller-Lyer test figures (Experiment 1) or the length of comparison Müller-Lyer figures to match the length of plain test lines (Experiment 2). Experiments 3 and 4 used a bisection task to assess whether the illusory effects of the angle components are confined mainly to regions of the shaft adjacent to the angles. Consistent with most theories of the Müller-Lyer illusion, eliminating one of the wing components reduced both forms of the Müller-Lyer length illusion to a similar extent. In addition, the acute- and obtuse-angle forms yielded similar patterns of bisection errors, with substantial errors for regions of the shaft adjacent to the angles and negligible errors for regions of the shaft distant from the angles.     

Are thresholds reduced by illusions? An attempt at replication

Three experiments are reported, which are attempts to replicate the finding of Ross and Gregory (1964) that difference thresholds for weights can be lowered by means of the size-weight illusion. Three different procedures were used, the first one (experiment I) being designed to show whether or not changes in a subject's judgement criterion could account for apparent changes in sensitivity. The second method (Experiment II) was a replication of Ross and Gregory's first procedure, in which the standard weight was judged before the comparison. In Experiments I and II a larger illusion was induced than in the original studies, but in Experiment III both the weights and container sizes were practically identical to those used by Ross and Gregory. The procedure was also the same as their most successful procedure (number 3) in which standard and comparison were judged simultaneously. The findings were uniformly negative: there was no evidence of criterion shift when the size-weight illusion was induced nor did we find the lowering of threshold previously reported.     

Ebbinghaus illusions: Size contrast or contour interaction phenomena?

Forty-eight graduate and undergraduate students between 17 and 30 years of age judged the size of the central circle in Ebbinghaus figures presented under either simultaneous or successive viewing conditions. Successive presentation eliminated the illusion produced by the normally overestimated figure and diminished that produced by the underestimated figure. Under simultaneous viewing conditions, increasing the number of surrounding circles reduced the magnitude of the reversed illusion produced by the normally overestimated figure but had no effect on the illusion produced by the underestimated figure. Under successive viewing conditions, increasing the number of surrounding circles had no effect on the magnitude of illusion produced by the normally overestimated figure but increased the illusion produced by the underestimated figure. These data were interpreted as inconsistent with a size contrast explanation of the Ebbinghaus illusions and suggested that these illusions may be produced by a contour interaction process.     

Visual and visually mediated haptic illusions with Titchener’s ⊥

For a replication and expansion of a previous experiment of mine, 14 newly recruited participants provided haptic and verbal estimates of the lengths of the two lines that make up Titchener’s ⊥. The stimulus was presented at two different orientations (frontoparallel vs. horizontal) and rotated in steps of 45 deg around 2π. Haptically, the divided line of the ⊥ was generally underestimated, especially at a horizontal orientation. Verbal judgments also differed according to presentation condition and to which line was the target, with the overestimation of the undivided line ranging between 6.2 % and 15.3 %. The results are discussed with reference to the two-visual-systems theory of perception and action, neuroscientific accounts, and also recent historical developments (the use of handheld touchscreens, in particular), because the previously reported “haptic induction effect” (the scaling of haptic responses to the divided line of the ⊥, depending on the length of the undivided one) did not replicate.     

Age-related susceptibility to the Müller-Lyer and the horizontal-vertical illusions

Participants between the ages of 3 and 20 years adjusted the Müller-Lyer illusion and the inverted-T form of the Horizontal-Vertical illusion. Perceptual error was quantified using signal detection and nonparametric measures of sensitivity and responsivity. Significant changes in sensitivity and responsivity were found for each illusion across participants' ages. No effect of sex of participant was found. Sensitivity and responsivity were largely asymptotic between the ages of 13 to 15 years for the Müller-Lyer illusion and between the ages of 11 to 15 years for the Horizontal-Vertical illusion.