A necessary and sufficient condition for linear aggregation of SSB utility functionals is presented. Harsanyi's social aggregation theorem for von NeumannâMorgenstern utility functions is shown to be a corollary to this result. Two generalizations of Fishburn and Gehrlein's conditional linear aggregation theorem for SSB utility functionals are also established.
The existence of an idea of a missing shade of blue contradicts Hume's first principle that simple ideas all derive from corresponding simple impressions. Hume dismisses the exception to his principle as unimportant. Why does he do so? His later account of distinctions of reason suggests a systematic way of dealing with simple ideas not derived from simple impressions. Why does he not return to the problem of the missing shade, having offered that account? Several suggestions as to Hume's solution (...) of the problem of the missing shade (not all appealing to distinctions of reason) are explored with an eye both to their adequacy as Humean solutions and their value as clues to his dismissal of the problem. Hypotheses concerning the latter perplexity are formulated and discussed as well. Senses in which the missing shade of blue is or may be a red herring are identified. In course, this author names Hume's missing shade marjorie grene. Historians of philosophy will want to adopt this nomenclature. (shrink)
The aim of this study was to test red - green dichromats' ability to discriminate between illuminant and surface-reflectance changes in natural scenes. Stimuli were simulations of natural scenes presented on a colour monitor with 10-bit resolution per gun. The natural scenes were obtained with a fast hyperspectral imaging system. Six different scenes (including rocks, foliage, and buildings) were tested. In each trial, two images were presented in sequence, each for 1 s, with no interval. The images differed in the (...) phase of daylight on the scene: first with correlated colour temperature 25 000 K, then 6 700 K. The spectral reflectance of a region in the second image was changed randomly, consistent with a local change in daylight. The observer's task was to decide whether a particular surface in the successive images was the same (pure illuminant change) or different (illuminant change with a surface-reflectance change). The performance of four deuteranopes and five protanopes varied considerably across the scenes tested, with mean colour constancy indices (± 1 SEM) of 0.48 (± 0.13) and 0.19 (± 0.10), respectively (1.0 representing ideal performance). Deuteranopes seemed less disadvantaged than protanopes, performing close to normal with some scenes. (shrink)
Colour constancy refers to the ability to extract information about surface colours independently of illumination conditions. A ripe strawberry, for example, appears the same red when viewed under a blue sky or a reddish sunset. Since Land's pioneering work, discussion has centred on the issue whether colour constancy is achieved primarily in the retina or visual cortex. Recently, the debate has shifted to a consideration of the constraints imposed by various psychophysical tasks and instructions. Humans can judge illuminant colour, reflected-light (...) colour, surface colour, and the relationship between surface colours within a scene. Such observations suggest that colour constancy may not be a unitary phenomenon, and that its different aspects may be mediated at different levels in the visual system. Several questions therefore arise: are the tasks of surface estimation and illuminant estimation complementary, insofar as good performance in one implies poor performance in the other? How does retinal adaptation alter performance? Is colour vision tuned to the statistical composition of natural surfaces and illuminants? What role does colour-opponent processing in retina and cortex play in colour constancy? These and related questions are explored here in order to better understand what we mean when we ask: "Why do strawberries look red?". (shrink)