Currently reading David Adler's text on distributional weights in benefit-cost analysis (https://scholarship.law.duke.edu/faculty_scholarship/3110/), I cannot manage to fully grasp the definition of the anonymity axiom.
The isoelastic/Atkinson social welfare function (SWF) allows for an inequality aversion parameter; greater weight is put on changes affecting worse-off individuals. Adler states that this function satisfies the anonymity/impartiality axiom, defined here as "meaning indifference between any given utility vectora and all rearrangements of component numbers". I understand this, broadly, as meaning that the levels of utility, and not the persons enjoying those levels, are what counts.
I can't manage to reconcile the fact that the "anonymity/impartial SWFs focus only on the patern of well-being, and not on the identities of the people who end up at particular well-being levels" (page 267 of the text) with the use of an inequality aversion parameter, which, by definition, treats individuals differently. Would this not mean focusing "on the identities of the people who end up at particular well-being levels"?
What am I missing ?
Any links towards readings on this subject would be much appreciated as well.