Sen cycles and externalities

It has long been understood that externalities of some kind are responsible for Sen’s (1970) theorem on the impossibility of a Paretian liberal. However, Saari and Petron (2006) show that for any social preference cycle generated by combining the weak Pareto principle and individual decisiveness, every decisive individual must suffer at least one strong negative externality. We show that this fundamental result only holds when individual preferences are strict. Building on their contribution, we prove a general theorem for the case of weak preferences.