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
Famous quotes containing the words examples of, examples, restricted and/or domains:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“Love is like some fresh spring, first a stream and then a river, changing its aspect and its nature as it flows to plunge itself in some boundless ocean, where restricted natures only find monotony, but where great souls are engulfed in endless contemplation.”
—Honoré De Balzac (1799–1850)
“I shall be a benefactor if I conquer some realms from the night, if I report to the gazettes anything transpiring about us at that season worthy of their attention,—if I can show men that there is some beauty awake while they are asleep,—if I add to the domains of poetry.”
—Henry David Thoreau (1817–1862)