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@ -3,7 +3,7 @@
The [Smith set](https://en.wikipedia.org/wiki/Smith_set) is the minimal set of election candidates which can beat all others pairwise The [Smith set](https://en.wikipedia.org/wiki/Smith_set) is the minimal set of election candidates which can beat all others pairwise
(by simple majority ranking preference) - if there is a single winner in the set they are (by simple majority ranking preference) - if there is a single winner in the set they are
guaranteed the standard [Condorcet i.e. Majority winner](https://en.wikipedia.org/wiki/Condorcet_winner) (they beat all others pairwise). guaranteed the standard [Condorcet i.e. Majority winner](https://en.wikipedia.org/wiki/Condorcet_winner) (they beat all others pairwise).
`smithy` identifies the Smith set via graph Strongly Connected Component (SCC) analysis of `smithy` identifies the Smith set via graph Strongly Connected Component (SCC) analysis of
the pairwise majority graph using [`rustworkx`](https://www.rustworkx.org/). the pairwise majority graph using [`rustworkx`](https://www.rustworkx.org/).
@ -12,9 +12,7 @@ in the number of ballots, while the SCC and condensation graph analysis is
approximately quadratic in the number of candidates for the dense tournament graphs typical approximately quadratic in the number of candidates for the dense tournament graphs typical
of Condorcet elections. Internally, repeated ballots are compressed/cache-counted before of Condorcet elections. Internally, repeated ballots are compressed/cache-counted before
pairwise evaluation to improve performance over duplicate rankings. pairwise evaluation to improve performance over duplicate rankings.
This is all overkill for small elections, but is fun. This is all overkill for small elections, but is fun.
(TODO: for small elections -because enumerating all tie resolution paths scales badly in the event of many tied counts-, optionally resolve nontrivial Smith sets -majoritarian ties- via IRV within the set, at least reducing to an IRV winner set within the Smith set if not likely identifying a unique delegate who wins all paths, having built a plurality coalition amongst the majority winners. This should identify a winning candidate as the best possible focal point for voluntary coordination; if your elections have other priorities you may want to resolve amongst the smith set differently).
## Usage ## Usage