Binariness and rational choice

Abstract The concept of numerical representability of preferences together with maximality is at the heart of the concept of rationality embodied in classical optimization models. The difficulty of representing social preferences arises from inherent intransitivities thrown up by democratic voting procedures and by non-binary choice rules which need to be adopted to cope with these intransitivities. An alternative (weaker) concept of representability is developed and it is shown that this concept can partially accommodate intransitivity and non-binariness. ‘Weak transitivity’ and ‘weak binaries’ conditions are provided and it is shown that these conditions are necessary and sufficient for ‘weak representability’. While the weak transitivity condition would be violated by social aggregation procedures, the non-binary functions used by social choice theorists do indeed satisfy the condition of ‘weak binariness’.