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Equality, efficiency, and the priority of the worse-off

Egalitarian theories of justice hold that equality should be promoted. Typically, perfect equality will not be achievable, and it will be necessary to determine which of various unequal distributions is the most equal. All plausible conceptions of equality hold that, where perfect equality does not obtain, (1) any benefit (no matter how small) to a worst-off person that leaves him/her still a worst-off person has priority (with respect to equality promotion) over any benefit (no matter how large) to a best-off person, and (2) any benefit to a worse-off person (even if not a worst-off person) has priority over a benefit of the same size to a better off person (even if not a best-off person). Beyond that there is much disagreement.