Parfit's final arguments in normative ethics

This paper starts by juxtaposing the normative ethics in the final part of Parfit's final book, On What Matters, vol. 3, with the normative ethics in his earlier books, Reasons and Persons and On What Matters, vol. 1. The paper then addresses three questions. The first is, where does the reflective-equilibrium methodology that Parfit endorsed in the first volume of On What Matters lead? The second is, is the Act-involving Act Consequentialism that Parfit considers in the final volume of On What Matters as plausible as Rossian deontology? The third is, how is the new argument that Parfit puts forward for Rule Consequentialism supposed to work?