Abstract: With the inequality increasingly prominent, the indicator to measure inequity is more and more important. Because of significant cost to collect data in inequality measure, it is very interesting to ask how to reduce the amount of data acquisition to compare the degree of inequality. The literatures on inequality keep silent on this problem. Since the indicator to measure inequity has a direct association with the Schur-convex function, based on the Schur-convex function and under the conditions of a few known variable values, this paper gives the sufficient conditions of the relationship of majorization between two variable vectors though determining the upper and lower bounds of majorization. Using this condition, we can compare the degree of inequality. And the application of Shannon entropy in inequality measure is given.

Key words: Shannon Entropy, Schur-convex function, Majorization, Inequality metrics, Sufficient Condition