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How does a majority electoral system choose a winner?

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Map of Canada displaying the results of the 2008 federal election by province and territory, with regions shaded to indicate the leading party's share of the popular vote: blue for Conservative, red for Liberal, light blue for Bloc Quebecois, and orange for New Democratic Party. Each area is labeled with the number of seats won by each party, and a legend at the bottom summarizes national seat totals for each party. — election Canada's 2008 federal election results.

Under a majority system, a candidate or party must secure more than 50 percent of the vote in a constituency to be awarded the seat. Because this absolute-majority criterion can be difficult to satisfy when more than two candidates are running, several methods are used to determine a winner:1

Alternative (Preferential) Vote: Voters rank candidates by preference. If no candidate achieves a majority of first-preference votes, the weakest candidate is eliminated and their votes are redistributed based on the next preferences. This process repeats until one candidate secures a majority.1
Double-Ballot System: If no candidate wins a majority in the first round, a second round is held. Only candidates meeting a specific threshold of support in the first round may compete, and the winner is determined by the vote in the second round.1
Supplementary-Vote System: Voters rank their top two choices. If no majority is reached, ballots not including the top two candidates are discarded, and the remaining first and second preferences are combined to determine the winner.1

These formulas are typically applied within single-member constituencies.1