Tideman Algorithm [2021] Site

: ( O(n^3) ) with Floyd-Warshall, ( O(n^2 \log n) ) with clever topological sorting.

: If there is a Condorcet winner (beats all others head-to-head), Tideman elects them. Proof : All edges from Condorcet winner to others have positive margins; they'll be locked before any contradictory edges can form a cycle. tideman algorithm

The process typically follows three core phases after votes are collected: : ( O(n^3) ) with Floyd-Warshall, ( O(n^2

First, we look at every possible pair of candidates. For each pair (e.g., Alice vs. Bob), we count how many voters prefer Alice over Bob, and how many prefer Bob over Alice. The process typically follows three core phases after

( G ): A directed acyclic graph (DAG) where an edge ( a \to b ) means "the final ranking has ( a ) above ( b )".

Maintain a boolean matrix reach[u][v] meaning "is there a path from u to v in the locked graph?"

In a standard "plurality" election (where you vote for just one person), a candidate can win even if the majority of voters actually prefer someone else. Even in basic ranked-choice systems, "cycles" can occur: Candidate A beats B, B beats C, but C beats A (like Rock-Paper-Scissors). The Tideman algorithm uses graph theory to resolve these cycles by prioritizing the strongest victories first. How the Algorithm Works