Rawls wrote a bunch of stuff about fairness and justice, and I won't pretend to have read it all. But one idea he discussed is imagining oneself behind a "veil of ignorance" that conceals the particulars of one's attributes, circumstances, etc. In considering how society is structured, how resources are distributed, what the laws are etc, we should do so without attachment to our own individual utility.
So imagine a universe where we were all thinking, rational, disembodied souls before we were born, and as disembodied souls we could debate and together choose how the society we're born into would work -- but we don't individually get to choose who we will be born as. You don't get to know what your race, your gender, your family's income, class, region, etc. How would you want society to be structured? What would you want laws and norms to look like? etc.
My claim is roughly that the way to incentivize leaders to actually work for the wellbeing of their constituents is to artificially construct and impose such a veil of ignorance, so that leaders are pushed to improve the wellbeing of as many as possible.