View source for Dodgson's method

Dodgson's method is a Condorcet method that ranks a candidate X according to the number of times adjacent candidates have to be swapped on a ballot (not necessarily the same ballot each time) to make X the Condorcet winner. The candidate with the least number of necessary swaps wins.

If X is the Condorcet winner, the number of swaps is zero, so the method passes Condorcet. However, determining the winner in the general case is complete for parallel access to NP,<ref>{{Cite journal|last=Hemaspaandra|first=Edith|last2=Hemaspaandra|first2=Lane A.|last3=Rothe|first3=Jörg|date=1997|editor-last=Degano|editor-first=Pierpaolo|editor2-last=Gorrieri|editor2-first=Roberto|editor3-last=Marchetti-Spaccamela|editor3-first=Alberto|title=Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP|url=https://arxiv.org/abs/cs/9907036|journal=Automata, Languages and Programming|series=Lecture Notes in Computer Science|language=en|location=Berlin, Heidelberg|publisher=Springer|volume=|pages=214–224|doi=10.1007/3-540-63165-8_179|isbn=978-3-540-69194-5|via=}}</ref> and thus NP-hard.

For more information, see [[w:Dodgson's method|Dodgson's method on Wikipedia]].

==Criterion compliances==
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" /> but the variant fails the other three criteria mentioned above.

==References==
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[[Category:Condorcet methods]]
[[Category:Ranked voting methods]]