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What is a standard term for utility functions of the type:
$$ u(x_1,\dots,x_m) = \max(\frac{x_1}{w_1},\dots,\frac{x_m}{w_m}) $$
where $x_i$ is the amount of commodity type $i$, and $w_i$ is a constant weight?
This is similar to Leontief utilities, only with max instead of min.
What term describes the type of goods with such a utility function? Initially I thought they were called "perfect substitutes", but now I see that this term is used for linear utility functions.
The Rawlsian welfare function, which takes the form of the min of all agent's utility, is often called the maximin function, because it maximizes minimum utility. In the spirit of that nomenclature, your function is a maximax utility function. And, apparently, this function does see some use. It is sometimes called the optimistic decision criteria, because a person evaluating projects based on their best outcome uses a similar evaluation function.
The maximax looks at the best that could happen under each action and then chooses the action with the largest value. They assume that they will get the most possible and then they take the action with the best best case scenario. The maximum of the maximums or the "best of the best". This is the lotto player; they see large payoffs and ignore the probabilities.
:)since the Rawlsian social welfare function is of the form $\min(u_1,\dots,u_m)$. $\endgroup$