Social diversification, injustices, and Pareto optimality with non-binary preferences

We prove the existence of a Pareto optimal state of a finite society that has socially differentiated persons, each with non-binary personal preferences that quasi-order a finite set of alternatives. Everybody engages in a volitional act of choice by maximization of non-binary preferences. As a consequence of interpersonal interaction among social creatures, the social interaction outcome defined as belonging to a nonempty social maximal set exists, and thus is Pareto optimal. Injustices inflicted by one group of persons upon a socially distinct one, arising from social diversification, are, however, consistent with such a collective outcome. (95 words)