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Small correction: Statistics and sociology, not economics, where Gini's affiliations
Gini didn't introduced majorization, which is the primary overlap. As I recall that's due to the economist Lorenz and the mathematician Muirhead (though, as is often the case, there are likely antecedents & it's all a bit fuzzy). I don't recall the details all that closely.
Thanks for the clarification, didn't realize Lorentz has been an economist, interestingly that paper went to the American statistical association
A classical analogue is that if you have a set of iron balls in a vacuum with temperatures {T_1, ..., T_n}, and strategically allow them to momentarily touch to exchange heat, you can get them to temperatures {S_1, ..., S_n} if and only if the former set majorises the latter.
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