Arrow's impossibility theorem: Difference between revisions
Content added Content deleted
Dr. Edmonds (talk | contribs) (Point out that Arrows Theorem only applies to Ordinal systems. Many people think that it applies to all systems.) |
(The loopholes in Arrow's theorem were closed by Gibbard. See my comment on the Talk page.) |
||
| Line 29: | Line 29: | ||
[[MCA|MCA-P]], as a rated rather than ranked system, violates only unrestricted domain. A system which arbitrarily chose two candidates to go into a runoff would violate only sovereignty. [[Random ballot]] violates only non-dictatorship. None of the methods described on this wiki violate only monotonicity. The [[Schulze method]] violates only independence of irrelevant alternatives, although it actually satisfies the similar [[ISDA|independence of Smith-dominated alternatives]] criterion. |
[[MCA|MCA-P]], as a rated rather than ranked system, violates only unrestricted domain. A system which arbitrarily chose two candidates to go into a runoff would violate only sovereignty. [[Random ballot]] violates only non-dictatorship. None of the methods described on this wiki violate only monotonicity. The [[Schulze method]] violates only independence of irrelevant alternatives, although it actually satisfies the similar [[ISDA|independence of Smith-dominated alternatives]] criterion. |
||
==Systems |
==Systems which claim to evade Arrow's Criteria== |
||
| ⚫ | |||
| ⚫ | Some activists believe that Arrow's theorem only applies to [[Ordinal Voting|ordinal voting]] and not [[cardinal voting]]. They point out that that it is technically possible for several cardinal systems to pass all three fairness criteria. The typical example is [[score voting]] but there are also several [[Multi-Member System |multi-winner systems]] which proport to pass all three of Arrow's original criteria. Addtionally, there are cardinal systems which do not pass all criteria but this is not due to Arrow's theorem; for example [[Ebert's Method]] fails [[Monotonicity]]. |
||
However, subsequent social choice theorists have expanded on Arrow's central insight, and applied his ideas more broadly. For example, [[W:Gibbard's theorem|Gibbard's theorem]] (published in 1973) holds that any deterministic process of collective decision making will have at least one undesirable characteristic. |
|||
==See also== |
==See also== |
||
*[[Gibbard-Satterthwaite theorem]] |
*[[Gibbard-Satterthwaite theorem]] |
||