Experiments in Distributive Justice and Their Limits

Mark Pennington argues political systems should be decentralized in order to facilitate experimental learning about distributive justice. Pointing out the problems with Pennington's Hayekian formulation, I reframe his argument as an extension of the Millian idea of 'experiments in living.' However, the experimental case for decentralization is limited in several ways. Even if decentralization improves our knowledge about justice, it impedes the actual implementation of all conceptions of justice other than libertarianism. I conclude by arguing for the compatibility of egalitarian redistribution with the epistemic virtues of markets pointed out by Hayek

Review of the New Communities Program: Toward Effective Implementation of Neighborhood Plans

Evaluates the progress of the New Communities Program, an initiative to revitalize sixteen Chicago neighborhoods, and recommends extending the MacArthur Foundation's financial support through another five-year grant

Sums of two s{s}-units via frey-hellegouarch curves

In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part, does not require lower bounds for linear forms in logarithms. Its main virtue is that it enables to carry out such a program explicitly, at least for certain small sets of primes S; we do so for S = {2, 3} and S = {3, 5, 7}.Comment: Missing solution in Prop. 5.4 added. To appear in Mathematics of Computatio

Extremal families of cubic Thue equations

We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form $F(x,y)=1$ with at least $5$ such solutions. Our approach combines elementary arguments, with lower bounds for linear forms in logarithms and lattice-basis reduction