A multi-dimensional approach toward collective choice

If we look carefully at Arrow's definition of independence of irrelevant alternatives, we are often puzzled as to why he does not examine collective choice in terms of a multi-dimensional framework. There is no reason why we should not employ a multi-dimensional approach as far as the definition is concerned. When we reconsider his original framework in terms of a multi-dimensional point of view, his other definition of unrestricted domain looks too demanding. Our actual preference relations may change according to the change of our view and our preference orderings seem rather independent even toward the same set of alternatives. Once we recognise this, it may be almost impossible to accept his unrestricted domain demanding free choice from all logically possible orderings of all alternatives, which may justify the notion that our choices are dimensionally separated. Our flexibility of choice may be rather restricted in an actual choice situation. By introducing a multidimensional approach, it is possible to have a more realistic explanation of our actual choice behaviour in the framework of collective choice theory. In this paper, the difference between the traditional single-dimensional approach and a new multi-dimensional approach is theoretically clarified.