Is Justice a Fixed Point?

Abstract

Following the work of John Rawls, political theorists have fixated on the comparative stability of different equilibrium states of justice. This article identifies a crucial gap in this literature, namely, the lack of attention paid to nonequilibrating systems. Drawing on Kakutani's theorem, I present plausible cases in which society will fail to exhibit any equilibrium states of justice. An important implication for political theory is that, rather than focusing exclusively on stable equilibria, theorists should examine dynamic processes of justice, which need not exhibit equilibrating forces. To this end, a concept more useful than stability is that of robustness, or the ability of a system to maintain general desiderata in the face of an evolving conception of justice.

Fixed points and well-ordered societies

“… 10. Schaefer (2021: 4). Gerard Debreu, who won the 1983 Nobel Prize in Economics for his contributions to general equilibrium theory, once described Kakutani's theorem as “the most powerful tool for the proof of existence of an economic equilibrium”; Debreu (1982: 698) For use of the theorem in establishing the existence of a competitive (Walrasian) equilibrium, see McKenzie (1981).…”

“… 40. Thus at Schaefer (2021: 11), Schaefer credits Thrasher and Vallier with. “a major advance over prevailing static theories,” but immediately pronounces their approach “insufficiently radical.”…”