This study intends to provide a new insight into the concentration and dominance indices as the concerns grow about the increasing concentration in the markets around the world. Most of the studies attempting to measure concentration or dominance in a market employ the popular concentration/dominance indices like Herfindahl-Hirschmann, Hannah-Kay, Rosenbluth-Hall-Tidemann and Concentration ratio. On the other hand, measures of qualitative variation are closely related to entropy, diversity and concentration/dominance measures. In this study, two normalized dominance measures that can be derived from the work of Wilcox on qualitative variation are proposed. The limiting distributions of these normalized dominance measures are formulated. By some simulations, asymptotic behaviors of these indices are analyzed under some assumptions about the market structure. In the end, by an application on the Turkish car sales in 2019, it is determined that the values of dominance indices vary in a considerably large range. Thus one of the dominance indices is determined to have the advantage of having less error in estimation, less sensitivity to smaller market shares, and less sampling variability.