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Thomas (Tom) C. Gorordo 2026-05-25 07:39:51 -07:00
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@ -5,10 +5,13 @@ The Smith set is the minimal set of election candidates which can beat all other
(by simple majority ranking preference) - if there is a single winner in the set they are
guaranteed the standard Condorcet i.e. Majority winner (they beat all others pairwise).
`smithy` currently identifies the set by brute-force search which is combinatoric complexity
in the worst case (TODO: better [algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm))
but appears approximately O(n^2) on-average in the number of candidates for typical/random ballots,
and linear in the number of ballots.
`smithy` identifies the Smith set via graph Strongly Connected Component (SCC) analysis of
the pairwise majority graph using [`rustworkx`](https://www.rustworkx.org/).
Pairwise majority comparisons scale quadratically in the number of candidates and linearly
in the number of ballots, while while the SCC and condensation graph analysis is
approximately quadratic in the number of candidates for the dense tournament graphs typical
of Condorcet elections. Internally, repeated ballots are compressed/cache-counted before
pairwise evaluation to improve performance over duplicate rankings.
## Usage