A geometric approach for computing a measure of consensus for groups

Akiyama et al. in [1] present a new important method to determine the index of disagreement, Φ, and measure consensus, Ψ, for a group of individuals responding to a Likert scale question. Their new measure exploits the conditional distribution of the variance for a given mean. The index allows for the comparison of consensus values of different questions for the same group or the same question for different groups, even though the questions may have different means. However, in [1] the complicated details make the new index very difficult to compute. This paper presents a simpler and more straight forward method to determine the Akiyama et al. measure of consensus, Ψ, by using computational geometry and numerical concepts. This geometric method is much easier to understand and computes the same values that Akiyama et al. get using their method. Moreover, this new algorithmic method is much easier to generalize to values of n larger than n = 5, since there are many studies that use Likert scales with more than five answer choices. The algorithms presented in this paper can easily be applied using any software package with just a few steps for calculations. The authors have developed a simple spreadsheet for computing Φ and Ψ that allows the users to enter the mean and variance to get the index of disagreement and measure of consensus values. 962 Mushtaq Abdal Rahem and Marjorie Darrah