Pooling peripheral information: Averages versus extreme values

Suppose, as an idealization, that sensory intensity is coded in peripheral channels as identical Poisson pulse trains with intensity parameter a power function of signal intensity. Discrimination models based on either an average count computed over a fixed time or an average time computed for a fixed count per channel have difficulty in fitting the Weber function ($\text{ΔI}\text{I}$ versus I) if the free parameters are constrained to ranges determined from other experiments (magnitude estimation, reaction time). Here we study a different decision rule, namely, the most extreme observation in either the counting or timing mode. Our extremum-counting model, but not two timing ones, accounts very nicely for the Weber function. However, the ROC curves for these extremum models, which agree in shape with data of Green and Luce, yield estimates for the intensity parameter which are much larger than predicted by the power function growth used to calculate ΔI and about twice as large as those estimated from reaction time data collected in the same experiment.