SPN follows from the strong neutrality (SN) condition of Section 4.5, on identifying \(\langle R_{i}\rangle\) with \(\langle R_{i}^*\rangle\). Parks (1976), and independently Kemp and Ng (1976), showed that there are “single profile” versions of Arrow’s theorem using SPN instead of I. These theorems were supposed to block the Bergson-Samuelson approach. In fact, condition SPN is just as easily set aside as SN, and for the same reason: both exclude non-welfare information that is relevant to the comparison of social states from an ethical standpoint. Samuelson (1977) ridiculed SPN using an example about redistributing chocolate. It is similar in structure to the example of Peter and Paul, in  Section 4.5.