any pair of social states (x, y): better than, as good as, or worse than (in preference ranking). (Here "as good as" is an "equally-ranked," not a "don't know," relation.) An ordering of a voter is denoted by R. That ordering of voter i is denoted with a subscript as . If voter i changes orderings, primes distinguish the first and second, say compared to ' . The same notation can apply for two different hypothetical orderings of the same voter. The interest of the book is in amalgamating sets of orderings. This is accomplished through a 'constitution'. A constitution (or social welfare function) is a voting rule mapping each (of at least one) set of orderings onto a social ordering, a corresponding ordering of the set of social states that applies to each voter. A social ordering of a constitution is denoted R. (Context or a subscript distinguishes a voter ordering R from the same symbol for a social ordering.) For any two social states x and y of a given social ordering R: x P y is "social preference" of x over y (x is selected over y by the rule). x I y is "social indifference" between x and y (both are ranked the same by the rule). x R y is either "social preference" of x over y or "social indifference" between x and y (x is ranked least as good as y by the rule). A social ordering applies to each ordering in the set of orderings (hence the "social" part and the associated amalgamation). This is so regardless of (dis)similarity between the social ordering and any or all the orderings in the set. But Arrow places the constitution in the context of ordinalist welfare economics, which attempts to aggregate different tastes in a coherent, plausible way. Arrow (pp. 15, 26–28) shows how to go from the social ordering R for a given set of orderings to a particular 'social choice' by specifying: the environment, S: the subset of social states that is (hypothetically) available (feasible as to resource quantity and productivity), not merely conceivable. The social ordering R then selects the top-ranked social state(s) from the subset as the social choice set. Less informally, the social choice function is the function mapping each environment S of available social states (at least two) for any given set of orderings (and corresponding social ordering R) to