A NOTE ON THE EXISTENCE OF AN ISLAMIC SOCIAL WELFARE FUNCTION

This paper aims at examining the possibility of constructing an Arrow‐social welfare function (SWF) in an Islamic community, that is abide by the Islamic tradition (i.e. the Shari'ah), where the domain of the individuals is defined in the context of Islamic framework. This domain is defined by the Shari'ah, where part of that domain is constrained, such that those actions that lie in the wajib (i.e. obligatory) or haram (i.e. prohibited), where the individual has no choice, must be thoroughly explored with respect to such a welfare function to consistency with the Shari'ah. Individual choice functions only within that segment of the domain that Islamic law leaves to the individual; the individual makes choices concerning actions in which they will not lose any praise or reward if they do or do not act one way or another. My concern in this regard will be the Mubah (i.e. permissible) range of the individual domain. In the process of examining the possibility of constructing an Arrow form (SWF) in an Islamic community, I have added a new Axiom to those suggested by Arrow (1951, pp.22–31). Kenneth J. Arrow, in his book Social Choice and Individuals Values (1951), has argued that five requirements of ‘fairness’ must characterize an acceptable social welfare function. He finds that these are inconsistent with each other. In fact, no welfare function exists that will satisfy all of those conditions simultaneously. As laid out by Arrow, these five conditions are, respectively: (1) universal domain; (2) positive association of individuals' values; (3) independence of irrelevant alternatives; (4) citizens' sovereignty; (5) nondictatorship. These conditions, characterized by Arrow as “seemingly innocuous” together rule out the possibility of deriving a complete and consistent (SWF) (Luce and Raiffa, 1957, p.328). The new axiom which I will refer to as Islamically imposed axiom such that, in the process of formulating an Arrow form social welfare function, it is important to be consistent with the Shari'ah. The Islamically imposed condition will thus guarantee the consistency with the Shari'ah in the process of formulating a social welfare function. This axiom implies that to maintain consistency the following must hold: When ti, (which refers to actions that individuals must do) is an element of the choice set (xi, ti), ti will always be chosen over xi (which refers to the feasible set of alternatives that individuals can choose from), and when tio is an element of the choice set (which refers to actions that individuals must not do), it will never be chosen. I came to the conclusion that when the choice set contains alternatives that the individual must do (wajib) or must not do (haram), the former will be chosen and the latter will never be chosen. Thus, for the general case, Arrow's negative results follow. If these elements are not in the choice set (i.e. all elements in the choice set belongs to Mubah activities), then Arrow's results follow in a straightforward fashion.