Spoiler effect

See Spoiler effect on Wikipedia

The spoiler effect can broadly be thought of as a situation where, when a particular candidate or set of candidate(s) are running, some candidate not in the set (call him X) wins, but when that particular set of candidate(s) aren't running, some different candidate who's also not in the set wins (call him Y). The Independence of irrelevant alternatives article has more information on this broad interpretation of the spoiler effect.

In some sense, much of voting theory is really just an attempt to mitigate the effects of various things that might be considered "spoiler effects". For example, Condorcet methods and many rated methods attempt to elect a candidate who can beat all other candidates in a head-to-head matchup (assuming voters cast the same ballots no matter which candidates are in the race); this arguably reduces the ability of losing candidates to drop out to impact the race.

The situation where there are only two or fewer candidates competing for a single seat i.e. to be the single winner (or more generally, any time there are N + 1 or fewer candidates competing for N seats) is often compared to the situation where there are more than two (or more than N + 1) candidates when discussing the spoiler effect. For example, majority rule guarantees a winner or a tie when there are two or fewer candidates, but when there are three or more, it is possible not to have a "majority winner" for any straightforward generalization of majority rule (i.e. maybe no candidate has a majority of 1st choices, or no candidate is a beats-all Condorcet winner, etc.), and moreover, in the event of a Condorcet cycle, if certain candidates in the cycle drop out, the winner can change.