The response ratio hypothesis for magnitude estimation

Assume that each presentation of a signal produces two independent random variable representations and that the ratio of responses on successive trials of a magnitude estimation experiment are proportional to the ratio of a representation from the present trial, which representation is then lost, to the remaining one from the previous trial. The mean response to a particular signal depends on the mean of the representation used, but in general exhibits drift over trials and sequential effects due to the preceeding trial; the mean response ratio does not exhibit drift, but it has a simple form only when there are no sequential effects; however, a modified mean ratio function has a simple form. A model suggested by D. V. Cross is a special case of this one. Simple timing and counting models for the representations fail to exhibit sequential effects, contrary to considerable data. However, data of the authors have suggested a version of the timing model in which the sample size of the representation varies by an order of magnitude depending on how close the signal is to the preceding one; this hypothesis accounts for the observed sequential effects and other aspects of the data.     

Transition structure versus commitment in sequential subjective probability revision

When Ss revise subjective probabilities, in the light of new evidence, a common finding is that they are conservative with respect to Bayes' theorem; revisions are too small. One kind of hypothesis to account for this is ‘model specific’, assuming a breakdown in an otherwise potentially Bayesian process. The other kind assumes that statistically irrelevant, task-specific information is processed. An example of the latter is the commitment hypothesis, assuming a commitment building up to the indications of early evidence, causing Ss to lag behind Bayes' theorem in their later judgements. Evidence is presented suggesting that Ss are not necessarily sensitive to mere sub-sets of a sequence, but that this form of suboptimality may result from overall sequence structure; specifically from a bias against long runs of like evidence. This would fit with findings from other areas of research, and would suggest that there is a general form of suboptimality operating which is relevant to all sequential processing tasks.     

The effects of concurrent responding and reinforcement on behavioral output

Four birds key pecked on concurrent variable-interval one-minute variable-interval four-minute schedules with a two-second changeover delay. Response rates to the variable-interval one-minute key were then reduced by signaling its reinforcer availability and later by providing its reinforcers independently of responding. Each manipulation increased response rates to the variable-interval four-minute key even though relative reinforcement rates were unchanged. In a final phase, eliminating the variable-interval one-minute key and its schedule produced the highest rates of all to the variable-interval four-minute key. These results show that both reinforcement and response rates to one schedule influence response rates to another schedule. These results join those of Guilkey, Shull, & Brownstein (1975) in failing to replicate Catania (1963). Moreover, they violate the predictions of the equation for simple action (de Villiers & Herrnstein, 1976). In terms of a median-rate measure (reciprocal of the median interresponse time), rates to the variable-interval four-minute key were high when responding was not reduced to the variable-interval one-minute key and were low when it was reduced. This rate difference suggests a process difference between concurrent-schedule procedures that maintain high concurrent response rates versus those that do not. This process difference jeopardizes attempts to integrate single- and concurrent-operant performances within a single formulation.     

Recent cohorts lead rejection of sex typing

In samples of the Detroit metropolitan population, four items indicating rejection of sex typing of children's household chores were negatively related to birth year of respondent in 1953, but positively related in 1971 and 1976: Older women were more likely to reject sex typing in 1953, but less likely to do so than younger women in 1971 and 1976. The regression was stronger for three items in 1976 than in 1971, while there was no change for the fourth. But associations between pairs of items in 1971 and 1976 were negatively related or unrelated to birth year. The explanation of these changes as an immediate and direct result of the women's movement is, therefore, discounted. The pattern of changes is congruent with assumptions in a model suggested by Carlsson and Karlsson (1979), which predicts oscillations in aggregate behavior with a period about a generation in length.This research was supported by NSF Grant SOC77-27365. Charles Brody Assisted with computations. Beverly Duncan made valuable suggestions. Howard Schuman generously provided early access to the 1976 data, collected for use in his own research.     

The demonstration of capacity limitation

The study of divided attention has produced many apparent demonstrations of “capacity limitation.” Possible ambiguities in such demonstrations are considered for three major types of experimental situation: simultaneous inputs with separate responses; choice; and classification. Two issues emerge. First, demonstrations always rest on assumptions about process set, i.e., the set of internal processes by which the task actually is performed. Alternative process sets are considered for situations of each type. Second, a demonstration of capacity limitation is made either by increasing the number of simultaneous processes, or by changing the bias between them. In either case effects unrelated to capacity limitation may influence the results. If several processes contribute to a single response, some performance decrement must accompany an increase in their number, simply through the increased overall chance for error. If the subject is biased toward one alternative in a choice or classification situation, the benefits enjoyed by this alternative may reflect not a preferential allocation of attentional capacity, but simply a willingness to decide in favor of this alternative with relatively little evidence.     

Two classes of models for magnitude estimation

One class of models assumes that presentation of a signal results in an internal representation as a random variable. Depending on whether the signal is close to or far from the preceding signal, the variance of the representation is smaller or larger. Responses are determined largely by this random variable; however, when the signal is close to the preceding one, the response is generated by modifying the representation multiplicatively by some function of the ratio of the previous response to its representation. Power and linear functions are explored. The form of the random variable is assumed to be that arising from either the timing or the counting model operating on a Poisson process. Detailed analyses are carried out successfully only for the timing model with neural sample sizes independent of intensity; however, the data require the sample to increase with intensity. The linear response function coupled with the constant sample size counting model appears somewhat viable, but detailed calculations are very difficult to carry out. The second class of models postulates a power function relation between magnitude estimates and signals intensity for which the exponent is a Gaussian distributed random variable and the unit is the product of two log normal random variables. Again we assume an attention band such that succesive stimuli that are widely separated in intensity lead to independent samples of the random variables while a variety of assumptions is explored for successive stimuli that are near each other in intensity. Although they each give rise to the qualitative features of the data, estimates of parameters are sufficiently inconsistent that we are led to reject all of the submodels studied.