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In the context of elections, voting fairness is all about ensuring that the outcome reflects the true preferences of the electorate. This involves selecting a winner who genuinely represents the majority's choice when candidate comparisons are made. However, an election can sometimes result in the selection of a candidate who may not be the most preferred when compared head-to-head with others. This raises questions about fairness and whether the election method used has honored the principles of fair representation.
Consider a situation where a candidate, let’s call them Candidate B, is preferred by the majority over others like A and C when they are examined individually. If the final election result overlooks Candidate B in favor of others, it suggests a potential fairness issue, such as non-compliance with the Condorcet criterion. Fair voting systems aim to avoid such inconsistencies to maintain electoral integrity.

Candidate preference is the individual voter's ranking or choice of candidates, often reflecting who they wish to see elected into office. Preferences can be complex, involving not just a simple first-choice pick but a ranked ordering where voters express their direct comparisons between candidates.
In an ideal election, the winner aligns with the preferences of the majority in these one-on-one comparisons. For instance, if Candidate B is preferred head-to-head against both Candidates A and C, then intuitively, B should be the optimal choice according to the preferences expressed by the electorate. However, capturing these preferences accurately can be challenging depending on the election methods and systems in use.
Understanding and respecting candidate preferences are crucial for deriving outcomes that best reflect the collective will of the voters.

Election methods are the procedures and rules used to determine the winner of an election based on the votes cast by the electorate. These methods include various systems like plurality, runoff, approval voting, and the Condorcet method, each having its strengths and challenges.
The Condorcet method, named after the French mathematician and philosopher, involves pairwise comparisons to evaluate which candidate wins head-to-head against others. The candidate who can beat each other candidate in these comparisons is deemed the Condorcet winner and is viewed as the most favorable choice across the electorate.
Despite its theoretical appeal in reflecting voters' preferences, not all election systems incorporate the Condorcet criterion. For example, the traditional plurality system can elect a candidate who isn't the Condorcet winner, leading to outcomes that may not always satisfy principles of fairness and representative accuracy. Understanding different election methods helps in choosing systems that appropriately address the electorate's preferences.