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Dodgson's method: Difference between revisions

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Dodgson's method (view source)

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Fishburn's variant can be computed in polytime
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Dodgson's method passes the Condorcet criterion. It fails the [[independence of clones criterion]],<ref>{{Cite journal|last=Brandt|first=Felix|date=2009|title=Some Remarks on Dodgson's Voting Rule|url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.149.5624&rep=rep1&type=pdf|journal=Mathematical Logic Quarterly|volume=55|issue=4|pages=460–463|doi=10.1002/malq.200810017|issn=1521-3870|via=}}</ref> the [[Smith criterion]], the [[monotonicity criterion]], and also fails the [[homogeneity criterion]]:<ref name="PCFishburn">{{Cite journal|last=Fishburn|first=Peter C.|date=1977-11-01|title=Condorcet Social Choice Functions|url=https://epubs.siam.org/doi/abs/10.1137/0133030|journal=SIAM Journal on Applied Mathematics|volume=33|issue=3|pages=477-479|doi=10.1137/0133030|issn=0036-1399|via=}}</ref> an election with 100 voters may return a different result to an election with 10 voters, even if the relative size of the factions is the same.
 
P. C. Fishburn proposed a variant that passes homogeneity,<ref name="PCFishburn" /> and where the winner can be found in polynomial time,<ref>{{Cite journal|last=Rothe|first=Jörg|last2=Spakowski|first2=Holger|last3=Vogel|first3=Jörg|date=2003-08-01|title=Exact Complexity of the Winner Problem for Young Elections|url=https://arxiv.org/pdf/cs/0112021|journal=Theory of Computing Systems|language=en|volume=36|issue=4|pages=375–386|doi=10.1007/s00224-002-1093-z|issn=1433-0490|via=}}</ref> but the variant fails the other three criteria mentioned above.
 
==References==
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