Unrestricted domain: Difference between revisions

[[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 hethey likeslike best along that line. HisTheir ordering of the choices is determined by theirthe distances from thatthe spot defined by the voter's preference. 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 (see "[[Median voter theory|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 the "[[independence of irrelevant alternatives]]" criterion.