Graph theory: Difference between revisions
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== Pairwise counting ==
A graph can be used to show which candidates (or winner sets, when discussing [[Proportional representation|proportional]] or non-proportional multi-winner methods) are pairwise preferred over others. Within such a graph, each candidate is considered to be a node (a point), and when an edge (a line) with an arrow points from one candidate's node towards another candidate's node, that indicates that the former candidate is preferred by more voters than the latter candidate in their pairwise matchup. If the arrow points both ways, this means that both candidates are in a [[Pairwise counting#Terminology|pairwise tie]].
One can optionally also indicate on a graph, for each pair of candidates, how many voters prefer one candidate over another by putting that number near or in the middle of the edge that connects the two candidates.
Some common concepts from Condorcet methods interpreted through graph theory:<blockquote>[[Condorcet winner]] - a candidate who has arrows pointing away from them towards every other candidate, and no arrows from any other candidate pointing back to them.
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