Ranked Pairs

What the ballot looks like with Ranked Pairs

Ranked Pairs is a ranked-choice voting system, meaning voters rank the candidates from their most preferred to their least preferred.

Here is an example of a ranked-choice ballot.

How the winner is determined

Instead of assigning votes or points to candidates, Ranked Pairs looks at the relative ranking between pairs of candidates. If you rank Alice higher than Bob, that comparison is recorded.

For your ballot above, the following table of comparisons is computed showing which canidate is preferred between two.

This is done for every ballot, and the points for each of the comparisons can then be summed to produce this comparison table.

Once you have these results, you know who would win in a head-to-head election between every pair of candidates.

Ranked Pairs works by prioritizing the head-to-head elections with the strongest margin of victory.

You'll then begin constructing a directed acyclic graph, working from the top of this list down to the bottom, where the candidates are the nodes and edges are the pairwise elections. Skip any connection that would create a cycle in the graph. (e.g. Dave > Carol, Carol > Alice, and Alice > Dave).

After constructing this graph, the candidate whose node is a source node is deemed the winner.

Where Ranked Pairs performs best

As a ranked-choice voting system, Ranked Pairs performs best when the voters have a ranked preference between the options.

An example of this is in the election of government officials, where many candidates are running and voters are likely to have an opinion on each (or at least many) of the candidates.

Ranked Pairs is special among voting systems in that it satisfies the Condorcet Criterion. This means that it will always elect the candidate that would beat every other candidate in a head-to- head election if such a candidate exists (which they usually do). This makes Ranked Pairs a very strong and stable voting system.

Where Ranked Pairs performs worst

As a ranked-choice voting system, Ranked Pairs should not be used in situations where the options are mutually exclusive to the voter. For example, when looking at the number of senior citizens in a population, a voter will either fall into the bucket of "Below 65" or "65 and Over". It should also not be used when voters unlikely to have a ranked preference between options.

Try Ranked Pairs

Create your own poll and send it to your friends to see how Ranked Pairs performs.

Learn about other voting systems