Independence of Irrelevant Alternatives severely limits which information about individual preferences may be used for what. It requires a social welfare function, when assembling the social preference among a pair of alternatives, to take into account only those of people’s preferences that concern just this pair. This Section discusses two kinds of information that is implicit in preferences for other alternatives, and illustrates their use in social decision making: information about the positions of alternatives in individual orderings, and information about the fairness of social states. 