Condorcet Theory: Exploration of Tie-breaking vote

Voting has played a crucial role in modern society, as it empowers individuals to voice their opinions and ensures representative and fair decision-making. However, no current voting algorithm can claim to be completely fair. In preferential voting systems, the Worst Defeat and Ranked Pair methods are often used to determine election outcomes. Due to fundamental differences in their principles, both algorithms exhibit distinct strengths and weaknesses, particularly regarding the weighting of tie-breaking votes. This paper delves into the specific cases of Worst Defeat and Ranked Pair in tie-breaking scenarios, offering an integrated analysis and proof of related issues. Furthermore, it identifies the most suitable contexts for each algorithm, aiming to provide general recommendations for the usage of voting algorithms across various situations.