Examples of Restricted Domains
Duncan Black defined a restriction to domains of social choice functions called "single-peaked preferences". Under this principle, all of the choices have a predetermined position along a line, giving them a linear ordering. Every voter has some special place she likes best along that line. Her ordering of the choices is determined by their distances from that spot. For example, if voting on where to set the volume for music, it would be reasonable to assume that each voter had their own ideal volume preference and that as the volume got progressively too loud or too quiet they would be increasingly dissatisfied. Black proved that by replacing unrestricted domain with single-peaked preferences in Arrow's theorem removes the impossibility: there are Pareto-efficient non-dictatorships that satisfy IIA.
Read more about this topic: Unrestricted Domain
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