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