Measuring disagreement in groups facing limited choice problems

A measure of the amount of disagreement, D, in a group facing a problem with limited solution choices is proposed. D is simple to calculate, meaningfully derived and provides a standard scale from 0 to 1 for the disagreement of any size group facing a number of solution choices. It also provides a related measure, d, which allows the measurement of the disagreement of each individual in the group. D essentially compares the number of differences found between pairs of individuals in the group with the number of differences theoretically possible. Extension of the measure to the case where the solution choices are represented by ranked, interval and ratio scale data shows that D is equal to twice the variance of the solution scores, although in this case the maximum value of D may be greater than 1. The properties of this measure are explored and found to be similar to what is expected of a measure of disagreement. An example application is given, illustrating how disagreement at both the individual and group levels can be meaningfully and usefully represented by d and D. The measure was used in an experiment where computer-mediated groups of five subjects, interacting only through a computer network, had to provide group solutions to multi-choice questions with four choice options.