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Methods

See my note about strategies in the introduction .

Name: Approval

Definition:

A voter can vote for as many alternatives as he or she wishes. The alternative that receives the most votes wins. There is no justification for entering a ballot approving of all alternatives or disaproving of all alternatives. Although ballots that do not do this may or may not be considered spoiled, I do not consider them for the purposes of this site.

Strategy:

compromising, burying

Name: Average Rating

Definition:

Each alternative is given a score (for example from 0 to 100) by each voter. The alternatives with the highest total score wins. There is no justification for not giving the lowest score to the least favourite candidate, and the highest score to the most favourite. Although ballots that do not do this may or may not be considered spoiled, I do not consider them for the purposes of this site.

Strategy:

burying, compromising

Name: Black

Definition:

Choose the Condorcet winner if one exists. Otherwise, find the Borda winner.

Strategy:

compromising, teaming, crowding

Name: Borda

Definition:

For each ballot, each alternative is given one point for every other alternative it is ranked above, and 1/2 point for every other alternative it is ranked as equal to. The alternative with the highest total score wins. This score is often called the Borda Count.

Strategy:

teaming, crowding, burying, compromising

Name: Borda-Elimination
Nanson's Modified Method
Baldwin
Nanson

Definition:

The alternative with the lowest Borda count is eliminated. This is repeated until only one alternative is left.

Strategy:

push-over, burying, compromising, crowding, vote-splitting

Name: Bucklin

Definition:

Candidates are given points based on the rank ballots of the voters. At every stage, if any candidates has a number of points greater than half the number of voters, the candidate with the greatest number of points wins. Start by giving one point for each first preference vote, then add 1 for every second and so on until a winner can be declared.

Strategy:

burying, compromising, crowding, teaming

Name: Coombs

Definition:

Start with no alternatives eliminated . If one candidate has a majority of first-place votes, it is the winner. Otherwise, find the total for each alternative of how many ballots it is the lowest ranked non-eliminated alternative. Eliminate the alternative with the highest score.  Repeat the process until an alternative has a majority in first-place votes among non-eliminated candidates.

Strategy:

compromising, push-over, teaming,

Name: Copeland

Definition:

Each alternative's Copeland score is calculated by subtracting the number of alternatives that pairwise beat it from the number that it beats. The alternatives with the highest Copeland score win.

Strategy:

burying, compromising, crowding

Name: Dodgson

Definition:

Each alternative is given a score equal to the smallest number of swaps in adjacent preferences necessary to make it the Condorcet Winner. The alternative with the lowest score wins.

Strategy:

compromising, burying, teaming, crowding

Name: IRV
Instant Run-off Voting (IRV)
Majority Preference Voting (MPV)
Alternative Vote (AV)
Single Transferable Ballot
Plurality-Elimination

Definition:

Start with no alternatives eliminated . Find the total for each alternative of how many ballots it is the highest ranked non-eliminated alternative. Eliminate the alternative with the lowest score. Repeat the process until only one alternative is left.

Strategy:

compromising, push-over

Name: Kemeny-Young Maximum Likelihood Method

Definition:

Each possible complete ranking of the candidates is given a "distance" score. For each pair of candidates, find the number of ballots that order them the the opposite way as the given ranking. The distance is the sum across all such pairs. The ranking with the least distance wins.

Strategy:

compromising, burying, crowding

Name: Median Rating

Each alternative is given a score (for example from 0 to 100) by each voter. The alternative with the highest median score wins. There is no justification for not giving the lowest score to the least favourite candidate, and the highest score to the most favourite. Although ballots that do not do this may or may not be considered spoiled, I do not consider them for the purposes of this site.

Strategy:

burying, compromising

Name: Minmax

Definition:

Each alternative is given a score equal to the greatest margin of victory by which that alternative loses a pairwise contest. A score of 0 is given if no losses exist for the candidate. The alternative with the lowest score wins.

Strategy:

compromising, burying, vote-splitting

Name: Nanson (original)
Nanson's Original Method
Nanson

Definition:

All alternatives whose Borda counts are equal to or below the average Borda count for the alternatives are eliminated. This is repeated until only one alternative remains.

Strategy:

push-over, burying, compromising, crowding, vote-splitting

Name: Pairwise-Elimination

Definition:

Repeatedly eliminate the alternative with the highest score in Minmax.

Strategy:

push-over, compromising, burying

Name: Plurality
First Past the Post (FPP)

Definition:
Each voter votes for only one alternative. The alternative with the most votes wins.

Strategy:
compromising, vote-splitting

Name: Random

Definition:

Choose one of the alternatives at random with each having an equal chance of winning.

Strategy:

teaming

Name: Random Ballot

Definition:

Choose one ballot at random. If the ballot does not rank a candidate with respect to another, and this ranking is desired, choose another ballot. If no ballot ranks a set of candidates with respect to each other, ranking can be decided randomly.

Strategy:

None.

Name: Ranked Pairs
Tideman's method

Definition:

Ranked Pairs finds a complete ranking. pairwise victories are processed starting from the greatest margin, and working down. These victories are locked, which means that the final ranking will agree with this pairwise decision. If a victory is processed that is incompatible with the previously locked victories, it is skipped. Once all victories are processed, a complete ranking is left.

Strategy:

compromising, burying

Name: Schulze

Definition:

If for a pairwise contest X either beats or ties Y, then we say that X has a path to Y, with a strength equal to the number of voters ranking X over Y.

If X has a path to Y of strength m, and Y has a path to Z of strength n, then we say that X has a path to Z equal to the minimum of m and n.

Of all the paths from X to Y, a maximum path strength can be found. If the maximum path strength from X to Y is greater than the maximum path strength from Y to X, then Y cannot win. The winner is the candidate that does not lose any such maximum path strength comparisons.

Strategy:

compromising, burying

Name: Smith

Definition:

All members of the Smith set are winners. Usually combined with another method.

Strategy:

compromising

Name: Smith//Minmax

Definition:

First eliminate all alternatives who are not in the Smith set. Then find the Condorcet winner for the remaining alternatives based on Minmax.

Strategy:

compromising, burying, vote-splitting

Name: Sum of Defeats

Definition:

Each alternative is given a score equal to the sum of all its margins of defeat in pairwise contests against other alternatives. Its margins of victory do not affect its score. The alternative with the lowest score wins.

Strategy:

compromising, burying, crowding, vote-splitting

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