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I think it's interesting that you mention "relevant factors." When we looked at the work of Perelman we were left with the problem of determining just what the relevant factors were. Perelman gave us a formal rule of justice -- to treat equal cases equally -- but no way of determining which cases were equal. Not a small problem!

Rawls doesn't have a scientific or logical 'proof' that some factors are relevant and some are not. Instead, he appeals to a shared American tradition to make that determination.

So, in a way, history provides the answer for a given culture. In other words, our widely shared beliefs, which have developed over time, provide the answer. They tell us what is relevant and Rawls tries to embody them in his Original Position.