Dodgson's method: Difference between revisions
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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 some provided ballot to make X the Condorcet winner. The candidate with the least number of necessary swaps wins. |
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 some provided ballot to make X the Condorcet winner. The candidate with the least number of necessary swaps wins. |
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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 |
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. |
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For more information, see [[w:Dodgson's method|Dodgson's method on Wikipedia]]. |
For more information, see [[w:Dodgson's method|Dodgson's method on Wikipedia]]. |
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==Criterion compliances== |
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Dodgson's method passes the Condorcet criterion. It fails [[Smith criterion|Smith]], is [[Monotonicity criterion|nonmonotonic]] and also fails the [[homogeneity criterion]]:<ref>{{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. |
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==References== |
==References== |
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Revision as of 12:09, 25 August 2020
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 some provided ballot 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,[1] and thus NP-hard.
For more information, see Dodgson's method on Wikipedia.
Criterion compliances
Dodgson's method passes the Condorcet criterion. It fails Smith, is nonmonotonic and also fails the homogeneity criterion:[2] 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.
References
- ↑ Hemaspaandra, Edith; Hemaspaandra, Lane A.; Rothe, Jörg (1997). Degano, Pierpaolo; Gorrieri, Roberto; Marchetti-Spaccamela, Alberto (eds.). "Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP". Automata, Languages and Programming. Lecture Notes in Computer Science. Berlin, Heidelberg: Springer: 214–224. doi:10.1007/3-540-63165-8_179. ISBN 978-3-540-69194-5.
- ↑ Fishburn, Peter C. (1977-11-01). "Condorcet Social Choice Functions". SIAM Journal on Applied Mathematics. 33 (3): 477–479. doi:10.1137/0133030. ISSN 0036-1399.