Arrow's impossibility theorem: Difference between revisions
Point out that Arrows Theorem only applies to Ordinal systems. Many people think that it applies to all systems.
Psephomancy (talk | contribs) (did you just remove it because it's a dead link?) |
Dr. Edmonds (talk | contribs) (Point out that Arrows Theorem only applies to Ordinal systems. Many people think that it applies to all systems.) |
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{{Wikipedia}}
'''Arrow’s impossibility theorem''', or '''Arrow’s paradox''' demonstrates the impossibility of designing a set of rules based on [[Ordinal Voting]] for social decision making that would obey every ‘reasonable’ criterion required by society.
The theorem is named after economist [[w:Kenneth Arrow|Kenneth Arrow]], who proved the theorem in his Ph.D. thesis and popularized it in his 1951 book ''Social Choice and Individual Values.'' Arrow was a co-recipient of the 1972 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel (popularly known as the “Nobel Prize in Economics”).
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==Systems which violate only one of Arrow's criteria==
[[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 Which Evade Arrow's Criteria==
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]].
==See also==
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