Relation To Arrow's Impossibility Theorem
Unrestricted domain is one of the conditions for Arrow's impossibility theorem. Under that theorem, it is impossible to have a social choice function that satisfies unrestricted domain, Pareto efficiency, independence of irrelevant alternatives, and non-dictatorship. However, the conditions of the theorem can be satisfied if unrestricted domain is removed.
Read more about this topic: Unrestricted Domain
Famous quotes containing the words relation, arrow and/or theorem:
“The instincts of the ant are very unimportant, considered as the ant’s; but the moment a ray of relation is seen to extend from it to man, and the little drudge is seen to be a monitor, a little body with a mighty heart, then all its habits, even that said to be recently observed, that it never sleeps, become sublime.”
—Ralph Waldo Emerson (1803–1882)
“... and the next summer she died in childbirth.
That’s all. Of course, there may be some sort of sequel but it is not known to me. In such cases instead of getting bogged down in guesswork, I repeat the words of the merry king in my favorite fairy tale: Which arrow flies for ever? The arrow that has hit its mark.”
—Vladimir Nabokov (1899–1977)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)