Double- and single-bisection methods for subjective probability assessment in a location-scale family

A common problem is to determine by an elicitation process the parameters of a subjective distribution in a location-scale family. One method is to elicit assessments of the median and one other quartile, equate the assessed median to the location parameter, and estimate the scale from the difference. In a second method, all three quartiles are elicited and then the scale is estimated from the interquartile range. With either method, the location and scale estimates are not made independently. These methods are here studied by introducing probability models for the elicitation process itself. It is shown that the second (full-quartiles) method has important advantages not held by the first.