Search results
Results from the WOW.Com Content Network
Arrow's impossibility theorem is a key result in social choice theory, ... Hansen, Paul (2002). "Another Graphical Proof of Arrow's Impossibility Theorem".
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility, negative proofs, or negative results. Impossibility theorems often resolve decades or centuries of work spent looking for a solution by proving there is no solution.
The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible ...
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 the "independence of irrelevant alternatives" criterion. However, Black's 1948 proof was published before Arrow's impossibility theorem was published in 1950 ...
Arrow's impossibility theorem shows that no reasonable (non-random, non-dictatorial) ranked voting system can satisfy IIA. However, Arrow's theorem does not apply to rated voting methods. These can pass IIA under certain assumptions, but fail it if they are not met. Methods that unconditionally pass IIA include sortition and random dictatorship.
Non-dictatorship is one of the necessary conditions in Arrow's impossibility theorem. [1] In Social Choice and Individual Values , Kenneth Arrow defines non-dictatorship as: There is no voter i {\displaystyle i} in { 1 , ..., n } such that, for every set of orderings in the domain of the constitution, and every pair of social states x and y , x ...
Sen's proof, set in the context of social choice theory, is similar in many respects to Arrow's impossibility theorem and the Gibbard–Satterthwaite theorem. As a mathematical construct, it also has much wider applicability: it is essentially about cyclical majorities between partially ordered sets, of which at least three must participate in ...
Gibbard's theorem can be proven using Arrow's impossibility theorem. Gibbard's theorem is itself generalized by Gibbard's 1978 theorem [ 11 ] and Hylland's theorem , which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance.