"nothing more than social choices" (p. 106). Topics implicated along the way include game theory, the compensation principle in welfare economics, extended sympathy, Leibniz's principle of the identity of indiscernibles, logrolling, and similarity of social judgments through single-peaked preferences, Kant's categorical imperative, or the decision process. Terminology The book defines a few terms and logical symbols used thereafter and their applied empirical interpretation (pp. 11–19, 23). Key among these is the "vote" ('set of orderings') of the society (more generally "collectivity") composed of individuals (“voters” here) in the following form: Voters, a finite set with at least two members, indexed as i = 1, 2, ... n. Commodities, the objects of choice (things that voters might want, goods and services), both private and public (municipal services, statecraft, etc.). A social state is a specification (formally, an element of a vector) of a distribution among voters of commodities, labor, and resources used in their productions. The set of social states, the set of all 'social states', indexed as x, y, z, . ., with at least three members. A (weak) ordering, a ranking by a voter of all 'social states' from more to less preferred, including possible ties. The set of 'orderings', the set of all n orderings, one ordering per voter. The ordering of each voter ranks social states, including the distribution of commodities (possibly based on equity, by whatever metric, or any other consideration), not merely direct consumption by that voter. So, the ordering is an "individual value," not merely, as in earlier analysis, a purely private "taste." Arrow notes that the distinction is not sharp. Resource allocation is specified in the production of each social state in the ordering. The comprehensive nature of commodities, the set of social states, and the set of orderings was noted by early reviewers. The two properties that define any ordering of the set of objects in question (all social states here) are: connectedness (completeness): All the objects in the set are included in the ranking (no "undecideds" nor "abstentions") and transitivity: If, for any objects x, y, and z in the set, x is ranked at least as high as y and y is ranked at least as high as z, then x is ranked at least as high as z. The earlier definition of an ordering implies that any given ordering entails one of three responses on the "ballot" as between