At a general level, the information that may be required to enable a planner to judge which of two states is socially preferable may be of a diverse character. It is convenient to partition this information into the welfare and non-welfare characteristics of social states. Welfare characteristics consist of the individual welfares achieved in different states; minimally, individual welfares will be ordinal and interpersonally non-comparable, but it is possible to consider situations where information about the cardinality and/or interpersonal comparability of welfares is also relevant. Non-welfare characteristics are more difficult to describe; as well as a physical description of a particular state, they may also be a description of the evolution of a state. Thus, for example, non-welfare characteristics may include information about whether claims bestowed in the past are settled in the state under consideration. In the language of social choice theory, if welfare characteristics are not always deemed relevant then the SWF (the rule for moving from characteristics to an ordering of social states) is said to be imposed, and if non-welfare characteristics are not deemed relevant then the SWF is said to be neutral. Social choice theory is conventionally concerned with nonimposed SWFs; although rarely mentioned, much of it also deals with non-neutral SWFs. For instance, in the problem studied by Arrow (1963), neutrality is not invoked and it does not follow from the axioms that he lays down. Arrow showed that there exists a dictator but, when this dictator is indifferent between two states, it is possible that non-welfare characteristics of the states will determine the social ordering. On the other hand, Arrow took welfares to be ordinal and non-comparable so that a considerable amount of information about welfares was deemed irrelevant, given that such information might be available. In a series of recent papers, the implications of allowing information concerned with the cardinal and comparable nature of welfares to influence the social ordering have been considered. Most of these studies have dealt with the characterization of either utilitarianism (d'Aspremont and Gevers (1977), Deschamps and Gevers (1978), Maskin (1978)) or the lexicographic extension to the Rawlsian maximin criterion (leximin) (Hammond (1976a), Sen (1976) and (1977), Strasnick (1976), d'Aspremont and Gevers (1977), Deschamps and Gevers (1978), Gevers (1979)). As these rules are neutral, conditions must be invoked which ensure the neutrality of the derived social ordering. This paper considers the derivation of non-imposed and non-neutral social orderings when individual welfares satisfy various measurability/comparability assumptions. The axioms used by Arrow are modified so as to admit the influence of different types of information. Section 2 deals with the formulation of the problem and there is a discussion of the various assumptions that can be made about the measurability/comparability of welfares. Section 3 considers the influence that non-welfare characteristics can have upon the social ordering. Further, a procedure is developed which allows permissible rules to be