Our Condition ND is what social choice theorists call a domain restriction, but with an important twist. Typically, a domain restriction says that certain kinds of preferences are not admissible into the social choice problem. Indeed, one of the most common responses to Kenneth Arrow’s famous impossibility theorem is that if we restrict the domain of preferences – if we only allow certain kinds of preferences to enter the aggregation exercise – then the impossibility theorem goes away, and we generate a possibility theorem instead. Our Condition ND is a bit different than this: instead of putting a restriction on admissible preferences (Condition ND allows for all logically possible preference profiles), we are instead putting a restriction on admissible perspectives. If we restrict the kinds of perspectives admitted into our social choice problem such that all persons categorize objects in the external world in the same manner, then schemes of jurisdictional rights are guaranteed to satisfy Condition NC. With Condition ND only some kinds of perspectives are admitted into the social choice problem – those that all agree with one another. What happens when we allow all logically possible perspectives to be admitted? We first define the relevant condition before examining results. Condition UD (Unrestricted Domain): All social choice problems are admissible. Recall that in our model, a social choice problem includes a profile of individual perspectives along with a set of feasible social states and a profile of individual preferences. Hence, under Condition UD, not only is any profile of individual preferences or any set of feasible social states allowed, but any profile of individual perspectives is allowed as well. When Condition UD holds, we allow individuals to categorize social reality in radically different and incompatible
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