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 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.