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The justification for using Lorenz dominance as an inequality ranking condition has been based on the aggregate social welfare comparison and the Pigou–Dalton principle of transfers. Since both the aggregating aspect of the social welfare function and certain implications of the principle of transfers are debatable, ordering conditions stronger than Lorenz dominance are worth exploring. A particularly interesting direction to pursue is to follow the frequently invoked notion that inequality is the “gap” between the rich and the poor. This paper follows this notion to formally propose a unified utility-gap concept and characterizes several utility-gap based conditions as general stronger-than-Lorenz-dominance ranking criteria. Specifically, we propose utility-gap dominance which requires all pair-wise utility-gaps in one distribution to be uniformly smaller than those of the other distribution. We then explore a conceptually weaker dominance concept – quasi dominance – which imposes conditions only on the gap between each person’s utility and some reference utility point of the distribution. [ABSTRACT FROM AUTHOR]