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Arrow's impossibility theorem: Difference between revisions
The loopholes in Arrow's theorem were closed by Gibbard. See my comment on the Talk page.
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.) |
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[[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
It is important to note that Arrow's theorem only applies to [[Ordinal Voting]] and not [[Cardinal voting]]. This means there are several Cardinal systems which pass all three fairness criteria. The typical example is [[Score voting]] but there are also several [[Multi-Member System | multi-winner systems]] which pass all three. There are of course Cardinal systems which do not pass all criteria but this is not due to Arrow's theorem. For example [[Ebert's Method]] fails [[Monotonicity]]. ▼
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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==
*[[Gibbard-Satterthwaite theorem]]
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