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If one makes welfarist assumptions about the general good, and further assumes that SWFs can be fully characterized by the mean income and an inequality index, then it is possible to recover the social welfare function associated with each inequality index, up to an affine transform. I know how to do this, roughly, in principle. However I would like to derive an explicit SWF for each of a group of widely used inequality indexes, in order to check whether the SWFs so derived conform to some appealing axiomatic characterizations. My hope and belief is that well-behaved inequality indexes will correspond to well-behaved SWFs. However, I find that I do not understand the correspondence well enough to explicitly derive the functional form of the SWF from the functional form of the inequality index. Can anyone tell me if there is an established way to do this? I will accept a citation as an answer if it is explicit enough about how the calculation is done that I can replicate it for a different index.

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  • $\begingroup$ What do you mean by "recover the social welfare function"? Recover from what? $\endgroup$ Nov 8, 2023 at 20:17

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