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 to, relation, arrow and/or theorem:
“In relation to God, we are like a thief who has burgled the house of a kindly householder and been allowed to keep some of the gold. From the point of view of the lawful owner this gold is a gift; From the point of view of the burglar it is a theft. He must go and give it back. It is the same with our existence. We have stolen a little of God’s being to make it ours. God has made us a gift of it. But we have stolen it. We must return it.”
—Simone Weil (1909–1943)
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)
“O Russia! O my wife! Our long and narrow Road lies clear though distressed.
Our road with an old Tatar freedom’s arrow Has deeply pierced our breast.”
—Alexander Blok (1880–1921)
“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)