Final answer:
In the event of a tie for an executive officer such as the President of the United States, the House of Representatives decides the winner, each state casting one vote. For a Senate tie, including the election of the Vice President, the sitting Vice President can break the tie. These rules apply to the majority election system; a plurality election would not require such measures as the candidate with the highest votes wins.
Step-by-step explanation:
If the results of an election for an executive officer show a tie, the method to decide the winner can vary based on the specific rules governing the election. In the context of United States presidential elections, if no candidate receives the majority of electoral votes, the decision goes to Congress. The sitting House of Representatives elects the president, with each state receiving one vote. This approach was considered during historical elections, such as those in 1800 and 1824. However, if there is a tie in the Vice President election, the Senate is responsible for breaking the tie, with the Vice President presiding and having a chance to vote in the case of a Senate tie.
Different rules may apply for plurality and majority elections. In a plurality election, the candidate with the most votes wins even if they do not have a majority. In contrast, a majority election requires a candidate to secure at least 50 percent plus one vote to win. If no candidate achieves this, a runoff election between the top two candidates may occur. Certain states like Georgia use this majority rule for statewide offices.