Arrow’s theorem, it has been said, is about the impossibility of trying to do too much with too little information. This remark directs attention towards two main avenues leading from Arrow-inspired gloom toward a sunnier view of the possibilities for collective decision making: not trying to do so much, and using more information. One way of not trying to do so much is to relax the requirement, it is a part of SO, that all social preferences are transitive.  Section 4.2 briefly considered this idea but found it unpromising. Another way is to soften the demand of U that there be a social ordering for each “logically possible” preference profile. That is, we can restrict the domains of social welfare functions. Section 5.1 discusses this important “escape route” from Arrow’s theorem in some detail. One way of using more information is to loosen the independence constraint I. This allows social welfare functions to make use of more of the information that is carried by individual preference orderings. See Section 5.2. Another way is to extend Arrow’s framework so as to allow individuals to contribute richer information than is carried by preference orderings. This information can come in the form of scores or grades, as discussed in Section 5.3, or in the form of cardinal measurements of individual utilities, in Section 5.4.