Tideman Algorithm Verified » 【Easy】

Its deep insight is that — a landslide should outweigh a squeaker in resolving circular ties, but never override a direct pairwise majority. This balance between strength and directness makes Tideman one of the most intellectually satisfying voting algorithms ever devised.

The Tideman algorithm (Ranked Pairs), invented by Nicolaus Tideman in 1987, answers this by saying: Lock in the strongest landslides first, skip any result that would create a cycle. Imagine a tournament. Candidate A beats B by 52% to 48% (a narrow win). Candidate C beats A by 80% to 20% (a landslide). Tideman argues that the landslide should have more weight in determining the winner than the squeaker. tideman algorithm

But there is a more insidious problem: (e.g., A > B, B > C, C > A). Here, no single candidate beats all others head-to-head. The question is: How do we break the cycle fairly? Its deep insight is that — a landslide

(strength of victory): [ \textmargin(a, b) = P[a][b] - P[b][a] ] If ( \textmargin(a, b) > 0 ), then ( a ) beats ( b ). Imagine a tournament

( G ): A directed acyclic graph (DAG) where an edge ( a \to b ) means "the final ranking has ( a ) above ( b )". 4. The Algorithm Step-by-Step Step 0: Input Each voter submits a ranked ballot (no ties allowed in pure Tideman). Step 1: Tally Pairwise Preferences For every ordered pair ( (a, b) ), count how many voters prefer ( a ) to ( b ). Step 2: Compute Victory Margins For each unordered pair ( a, b ), compute ( \textmargin(a, b) ) if positive. Step 3: Sort Victories by Margin (Descending) Create a list of pairs ( (a, b) ) where ( a ) beats ( b ), sorted from largest margin to smallest.