 I have glossed over an important detail of Young’s characterization of scoring rules. Note that the reinforcement property refers to the behavior of a voting method on different populations of voters. To make this precise, the formal definition of a voting method must allow for  domains that include profiles (i.e., sequences of ballots) of different lengths. To do this, it is convenient to assume that the domain of a voting method is an anonymized profile: Given a set of ballots \(\mathcal{B}\), an anonymous profile is a function \(\pi:\mathcal{B}\rightarrow\mathbb{N}\). Let \(\Pi\) be the set of all anonymous profiles. A variable domain voting method assigns a non-empty set of voters to each anonymous profile—i.e., it is a function \(V:\Pi\rightarrow \wp(X)-\emptyset\)). Of course, this builds in the property of Anonymity into the definition of a voting method. For this reason, Young (1975) does not need to state Anonymity as a characterizing property of scoring rules. 