Recent theoretical approaches to the problem of psychophysical di scrimination have produced what may be classified as • statistical d ecision ' or • data accumulation ' models. While the former have received much atten ti on their application to judgment and choice meets with some difficulties. Among the latter, the two types which have received most attention are a • runs' and a • recruitment' model, but neither seems able to account for all of the relevant data. It is suggeste d instead that an • accumulator' m odel, in which sampled events may vary in magnitude as well as probability, ca n be developed t o give 0. good account of much of the available data on psychophysical discrimination. Two experiments are reported, in which the subject presses one of two keys as soon a s he has decided whether the longer of two sim ulta neous ly presented lines is on the left or right. Results are found to be inconsistent with 0. runs or recruitment process, but t o accord well with predictions from the accumulator model. Other evidence consistent with such a mechanism is briefly reviewed.

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Indices of human performance are less clear-cut than analogous measures in the physical sciences for several reasons. Variables which can alter performance include the noise upon which sensory signals are imposed, the bias shown by an observer towards one or another alternative, the use of an optional-stopping strategy for examining sensory input, and the accumulation of statistical information over time concerning the source of the input. The development of a theoretical appreciation of these variables is traced and, on this basis, a measure of the noise, which sets a limit to discriminative capacity, is suggested. The proposed index is simply the standard deviation of the best fitting normal ogive, calculated for the psychometric function obtained in a forced-choice discrimination task by the method of constant stimuli, the discriminanda being presented for 100 ms, in random order, and followed by appropriate backward masking. The index is thus closely related to traditional psychophysical measures, but is distinguished by the detailed specification of conditions under which it should be obtained. Analysis of data from previous experiments gives some indication of the order of magnitude that might be expected from a carefully controlled determination of the measure. In addition, three experiments were carried out to evaluate this suggestion, and to test its underlying rationale. In the first two, observers were required to discriminate, by pressing one of two keys, between two lines of markedly different length, exposed in random order for ten different durations. In the third, stimulus exposure was held constant, while ten different stimulus differences were presented in random order. Results from the first two experiments yielded estimates of minimum inspection time close to 100 ms, and were inconsistent with the view that observers can abandon an optional-stopping procedure of processing sensory information in favour of responding by a deadline. Measures of noise calculated in the third experiment were of the order expected on the proposed rationale, while response latencies were again inconsistent with the notion of deadline responding. Further analysis of the results of the three experiments suggests that measures of inspection time and noise, together with a third index related to the degree of caution exercised by an observer, appear to be stable and consistent descriptors of performance. The wider implications of the successful use of this kind of perceptual index of performance are discussed with reference to the measurement of visual acuity, as a means for detecting effects of environmental stress, and as a conceptual framework for the understanding of individual differences.

Little research has been carried out on human performance in optimization problems, such as the Traveling Salesman problem (TSP). Studies by Polivanova (1974, Voprosy Psikhologii, 4, 41-51) and by MacGregor and Ormerod (1996, Perception & Psychophysics, 58, 527-539) suggest that: (1) the complexity of solutions to visually presented TSPs depends on the number of points on the convex hull; and (2) the perception of optimal structure is an innate tendency of the visual system, not subject to individual differences. Results are reported from two experiments. In the first, measures of the total length and completion speed of pathways, and a measure of path uncertainty were compared with optimal solutions produced by an elastic net algorithm and by several heuristic methods. Performance was also compared under instructions to draw the shortest or the most attractive pathway. In the second, various measures of performance were compared with scores on Raven's advanced progressive matrices (APM). The number of points on the convex hull did not determine the relative optimality of solutions, although both this factor and the total number of points influenced solution speed and path uncertainty. Subjects' solutions showed appreciable individual differences, which had a strong correlation with APM scores. The relation between perceptual organization and the process of solving visually presented TSPs is briefly discussed, as is the potential of optimization for providing a conceptual framework for the study of intelligence.

We investigated the properties of the distribution of human solution times for Traveling Salesperson Problems (TSPs) with increasing numbers of nodes. New experimental data are presented that measure solution times for carefully chosen representative problems with 10, 20,. .. 120 nodes. We compared the solution times predicted by the convex hull procedure proposed by MacGregor and Ormerod (1996), the hierarchical approach of Graham, Joshi, and Pizlo (2000), and by five algorithms drawn from the artificial intelligence and operations research literature. The most likely polynomial model for describing the relationship between mean solution time and the size of a TSP is linear or near-linear over the range of problem sizes tested, supporting the earlier finding of Graham et al. (2000). We argue the properties of the solution time distributions place strong constraints on the development of detailed models of human performance for TSPs, and provide some evaluation of previously proposed models in light of our findings.

Various sequential sampling models of discrimination were quantitatively tested in a task requiring binary classification of the means of distributions of line segments. Experiment 1 tested accumulator and random walk models, which were shown to be unable to account for either the speed-accuracy trade-off or the moments of the response time distributions. Results were confirmed by Experiment 2 in which distributions were fitted. Data were well described by a model that assumed magnitude-dependent information loss during the sampling period.

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