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Condorcet Domain Archive

Explore the stored preference domains as adjacent-swap graphs. Each node is one permutation; edges connect permutations that differ by a single adjacent transposition. Start with the connected four-alternative example, and select a node to inspect its neighbours.

Archive note: filenames marked n=5 contain permutations of six symbols, including a leading 0. The original naming convention has not been verified. All stored symbols are displayed; these files are not presented as a verified five- or six-alternative census.

Read a preference domain as a graph

Start with The Assembly →
First visit · three things to try
  1. Keep the four-alternative example. It opens with nine rankings. Each node is one whole preference order, read from most to least preferred.
  2. Select a ranking. An edge means swapping two adjacent entries. For example, 0123 and 1023 differ by one adjacent swap.
  3. Compare another domain. Change the domain number or dataset. The graph describes relationships between rankings, not a majority vote. Table rows can be selected with Enter or Space.
How to read the results

A Condorcet domain prevents majority cycles for every odd electorate using its allowed rankings. Maximal means no extra ranking can be added; largest means greatest possible size. This archive viewer does not prove maximality or certify uploaded data. Filename n=5 files store six symbols; their naming convention remains unresolved. For the verified seven-alternative collection, open the Condorcet atlas.

Adjacent-Swap Graph
layout labels colors size edges
Load data to draw a graph.
Two nodes are adjacent exactly when one permutation is obtained from the other by swapping one neighboring pair.
Permutations in Current Domain
No domain loaded.
Neighbors of Selected Permutation
Select a node to inspect its adjacent neighbors.