Numerical Analysis of Consensus Measures within Groups

Measuring the consensus for a group of ordinal-type responses is of practical importance in decision making. Many consensus measures appear in the literature, but they sometimes provide inconsistent results. Therefore, it is crucial to compare these consensus measures, and analyze their relationships. In this study, we targeted five consensus measures: [Formula: see text] (from entropy), [Formula: see text] (from absolute deviation), [Formula: see text] (from variance), [Formula: see text] (from skewness), and [Formula: see text] (from conditional probability). We generated 316,251 probability distributions, and analyzed the relationships among their consensus values. Our results showed that [Formula: see text] and [Formula: see text] tended to provide consistent results, and the ordering [Formula: see text] held at a high probability. Although [Formula: see text] had a positive correlation with [Formula: see text] and [Formula: see text] , it had a much lower tolerance for even a small proportion of extreme opposite opinions than [Formula: see text] and [Formula: see text] did.