Here are the voting methods I mentioned in the various aborted replies to Raul: Definitions from http://www.barnsdle.demon.co.uk/vote/vote.html Defn: An "unbeaten set" is a set of options none of which is beaten [in a pairwise contest] by anyone outside that set. Defn: A "small unbeaten set" is an unbeaten set that doesn't contain a smaller unbeaten set. Defn: The "Schwartz set" is the set of options which are in small unbeaten sets. Defn: The "Smith set" is the smallest set of options such that every option in the set beats every option outside the set. Note: In some cases, the Smith Set can contain the entire set of options. Given: A set of preferential ballots, modifed by eliminating all options that are not in the Smith set. ============================================ Option: Plurality, or First-Across-The-Post (FatP) ============================================ Examine the 1st choice on all ballots. The choice with the highest vote total wins. Advantages: Easy to understand. Disadvantages: Does not take into account complete knowledge of voters preferences. Requires re-examination of the ballots after the initial tally. Other factors: Strongly favors first choice preferences. Plurality encourages "strategic voting" when used as a general voting method and can choose an option that is disliked by a majority; I am uncertain how limiting it to the Smith Set affects this. ======================= Option: Instant Runoff (IRV) ======================= Examine the 1st choice on all ballots. If a single choice has more than half the total votes cast, it wins. If not, eliminate from all ballots the choice that has the fewest number of 1st choice votes, and repeat until there is a winner. Advantages: Current system in place. Disadvantages: Does not take into accout complete knowledge of voters preferences. Requires re-examination of the ballots after the initial tally. Other factors: When used as a general voting method, can cause an option to win that would have lost if voted higher, and vice versa. Does not meet -any- of the "academic criteria" espoused by Condorcet-favorable experts. I am uncertain how limiting it to the Smith Set affects this. ======================== Option: Runoff-Pairwise (R-P) ======================== Conduct a second vote using Approval Voting, with the options chosen solely from the Smith set. Advantages: Allows voters to compromise and readjust their voting after seeing the outcome of the initial balloting. Disadvantages: Requires second vote. May encourage strategic voting in second vote. ======================== Option: Smith/Condorcet (SC) ======================== Of the n options in the Smith set, order the n*(n-1) pairwise results by number of votes for the winning choice, strongest to weakest. (e.g., if A beat B by 100:50, and B beat C by 76:74, order them as AB first, BC second, because 100 is bigger than 76). Drop the weakest defeat iteratively until one option is unbeaten. That unbeaten option is the winner. Advantages: Variants have been studied for 200+ years. Generally regarded as a good method. Disadvantages: Not certain. Other factors: The various Condorcet-based methods (SC, SD, SSD, Tideman) will usually give similar results. SC itself is a variant on the proposal Condorcet made (called "Plain Condorcet" (PC)). PC does not limit itself to just the Smith set. ================================ Option: Sequential Dropping (SD) ================================ Order the pairwise results as in the Smith/Condorcet option. Drop the weakest defeat that is part of a cycle until one option is unbeaten. That option wins. Advantages: Favored over PC because only defeats part of a cycle reflect the ambiguity of the result. Disadvantages: Doesn't work well when the pairwise contests result in ties. Not usually a problem except when there is a small number of voters. Other factors: This is basically PC limited to options part of a cycle. ==================================== Option: Schwartz Sequential Dropping ==================================== Order as in Smith/Condorcet Drop the weakest defeat among members of the current Schwartz Set. Repeat until one option is unbeaten. The Schwartz set is recomputed after each dropping based on remaining pairwise contests considered. Advantages: Works better than SD in the face of ties. Some people feel that the winner should come from a Schwartz Set. This method guarantees that. Disadvantages: Not certain. Other factors: This is basically PC limited to the Schwarz Set. ======================== Option: Tideman's Method ======================== Order the results as in Smith/Condorcet. >From strongest to weakest, drop defeats which form a cycle with remaining stronger defeats. The remaining undefeated candidate will win. Advantages: Experts say it represents the will of the voters better than any PC, SC, SD, or SSD. I have not yet found any online theoretical discussions that say why, though. Disadvantages: Is not guaranteed to find unique winner in face of tied pairwise voting. Other factors: This is the only method discussed that was developed specifically for Condorcet that isn't based on PC. ------------------------- Apparantly, Tideman's is considered the best method among people who have studied voting methods. David Barnsdale's site above lists some criteria that people feel are important. http://www.fortunecity.com/meltingpot/harrow/124/ describes a large number of election methods, as well as a large number of possible criterion. 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