The Libertarian paradox: some further observations

It is shown that the weak Pareto principle consists of two parts: Pareto Neutrality and Weak Pareto Unanimity. It is the Pareto Neutrality which is responsible for the Paradox of the Paretian Libertarian. The libertarianism condition can also be factorized into two parts: the Libertarian Invariance and the Libertarian Non-Imposition. It is the Libertarian Invariance which is responsible or the Paradox of the Paretian Libertarian. Under conditions of Unrestricted Domain, Pareto Neutrality and Libertarian Invariance, if we require a social preference to be acyclic, then(1) neither can individuals' personal rights be respected, nor can they be reversed;(2) neither can unanimous group rights be respected, nor can they be reversed. Consequently, the Paradox of the Paretian Libertarian is due to the inconsistent use of information contained in the weak Pareto principle and the libertarianism condition.I would like to thank Nick Baigent, Prasanta Pattanaik, John Riley, Amartya Sen and Kotaro Suzumura for their comments. I would also like to thank two anonymous referees for their suggestions and comments on earlier drafts of the paper which led to a great improvement of the present version.