An Encyclopedia of Democratic Methods
The simplest method: each voter selects one candidate, and the candidate with the most votes wins. Used in most English-speaking democracies. Its simplicity is both its strength and its limitation -- it frequently produces winners who are opposed by the majority.
Voters may approve of as many candidates as they wish. The candidate with the most approvals wins. Eliminates the spoiler effect and encourages honest expression of preferences. Simple to implement on existing ballots.
Voters rank candidates in order of preference. If no candidate wins a majority, the last-place candidate is eliminated and their votes redistributed to the voters' next choices. This process repeats until a majority winner emerges.
A family of methods that select the candidate who would win a head-to-head contest against every other candidate. The Condorcet winner, when one exists, is the most broadly preferred candidate. Various tiebreaking rules handle cycles.
Voters assign a numerical score to each candidate. The candidate with the highest total (or average) score wins. Maximizes expressiveness -- voters can indicate both preference order and preference intensity.