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.