Are there other aggregation procedures that are better than pairwise majority decision, or do the different ones have shortcomings of their own? Condorcet, his contemporary Jean Charles de Borda (1781), and later Charles Dodgson (1844) and Duncan Black (1948), among others, all addressed this question by studying various procedures and comparing their properties. Arrow broke new ground by coming at it from the opposite direction. Starting with various requirements that aggregation procedures might be expected to meet, he asked which procedures fill the bill. Among his requirements is Social Ordering, which insists that the result of aggregation is always an ordering of the alternatives, never a cycle. After the introduction in  Section 2 of the technical framework that Arrow set up in order to study social choice,  Section 3.1 sets out further conditions that he imposed. Briefly, these are: Unrestricted Domain which says that aggregation procedures must be able to handle any individual preferences at all; Weak Pareto, which requires them to respect unanimous individual preferences; Non-Dictatorship, which rules out procedures by which social preferences always agree with the strict preferences of some one individual; and finally Independence of Irrelevant Alternatives, which says that the social comparison among any two given alternatives is to depend on individual preferences among only that pair. Arrow’s theorem, stated in  Section 3.2, tells us that, except in  the very simplest of cases, no aggregation procedure whatsoever meets all the requirements.