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In this work, we modify the affine wealth model of wealth distributions toexamine the effects of nonconstant redistribution on the very wealthy. Previousstudies of this model, restricted to flat redistribution schemes, havedemonstrated the presence of a phase transition to a partially wealth-condensedstate, or "partial oligarchy," at the critical value of an order parameter.These studies have also indicated the presence of an exponential tail in wealthdistribution precisely at criticality. Away from criticality, the tail wasobserved to be Gaussian. In this work, we generalize the flat redistributionwithin the affine wealth model to allow for an essentially arbitraryredistribution policy. We show that the exponential tail observed nearcriticality in prior work is, in fact, a special case of a much broader classof critical, slower-than-Gaussian decays that depend sensitively on thecorresponding asymptotic behavior of the progressive redistribution model used.We thereby demonstrate that the functional form of the tail of the wealthdistribution in a near-critical society is not universal in nature but ratherentirely determined by the specifics of public policy decisions. This issignificant because most major economies today are observed to benear-critical.

The Nonuniversality of Wealth Distribution Tails Near Wealth Condensation Criticality