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What's the correct mathematical name for the partial ordering on vectors based on what is sometimes called "Pareto Dominance"?

Does Pareto Dominance have an alternative name in fields other than economics?

For two vectors of the same dimension, one Pareto Dominates the other if all its elements are greater than the corresponding element in the other vector.

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up vote 1 down vote accepted

Depending on if you allow "greater" to mean "greater or equal" or to mean "strictly greater" we have two answers coming from Order Theory, respectively:

Those two, along with the lexicographic order (which I searched to find this answer), are the three best-known choices among the possible orders on the Cartesian product of two totally ordered sets, as is stated in

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