What condition would lead to a "run-off election" in Georgia?

In Georgia, a run-off election is required when no candidate receives a majority of the votes cast in an election. A majority is defined as more than 50% of the total votes. If none of the candidates surpasses this threshold, the top two candidates will then compete in a subsequent election, known as the run-off, to determine the winner. This process ensures that the elected candidate has a clear mandate supported by a majority of the voters.

The other situations described do not trigger run-off elections. For instance, a tie in votes can lead to different resolutions depending on local rules, but it does not automatically result in a run-off; a candidate's withdrawal also does not necessitate a run-off and would typically affect the number of candidates in the race. Additionally, while having third-party candidates may influence the distribution of votes, it does not directly lead to a run-off unless it prevents any candidate from achieving a majority. Thus, the requirement for a run-off election is specifically tied to the absence of a majority winner.