First-past-the-post or plurality voting is the dominant system in the US and in the UK's national government. You vote for one candidate, and the winner is whoever gets the largest fraction of the votes. While that is a simple system, and while it works well when there are only two candidates, it does not work so well for more than two candidates. In fact, fear of wasting votes on unlikely-to-win candidates usually leads to a two-party system. This behavior was described in the 1950's and 1960's by a certain Maurice Duverger, and it's now called Duverger's law (Wikipedia). However, there are several alternatives that are much more multiple-candidate-friendly, and many nations and regions and cities and organizations now use some of them. Approval Voting: you can vote for more than one candidate. As with FPTP, whoever gets the most votes wins. It's a subset of Range Voting, where one can give each candidate a fraction of a vote from 0 to 1. It can be extended to include "disapproval voting", where you can cast a vote of -1 as well as 0 or +1. The UN Security Council has used that system to vote for a Secretary General: RangeVoting.org - Election (via approval voting) of UN secretary general Polls created with the vBulletin software can be either FPTP (single choice) or approval voting (multiple choice). Runoff elections. If nobody gets a majority in FPTP-style voting, then have a second election between the top candidates. Preference voting. Rank the candidates by preference, then find an overall winner with some algorithm. Borda: for n candidates, one's kth preference gets a value (n-k+1), and these values are added for all candidates. Condorcet or Virtual Round Robin: from each ballot construct a matrix of who beats whom. Add all these matrices together, and from the total one, find who beats the others. There are various algorithms for disambiguating ambiguous cases, like the Schulze beatpath algorithm. Instant Runoff: each ballot gets a pointer that's started off at its top preference. In each round, count the pointed-to preferences, and if a candidate gets a majority, then that candidate wins. Otherwise, remove the candidate with the fewest votes, bump the pointers of that candidate's ballots down to the first candidate still in the race, and then have another round of counting. These algorithms can be extended to multiseat elections in various ways. Single Transferable Vote: set a quota of (total votes) / ((number of seats) + 1). Count like IRV, but first remove candidates with more than the quota as winners. Over-quota ballots get their pointers bumped down like defeated candidates' ones. Party-List Proportional Representation: you vote for a party, and each party gets a number of seats in proportion to how many votes it had received. There are various algorithms for coming up with integer numbers of seats for each party, like the d'Hondt method. Party-list PR can be closed list, where the parties select who gets the seats, or open list, where you can vote for whomever you think ought to have priority. Mixed-Member Proportional Representation: a mixture of single-member districts and party-list PR. Wikipedia's Voting system has a comprehensive list. Wikipedia's contributors have collected a Table of voting systems by country. It's rather eye-opening to see what different countries have chosen. For presidents, runoff elections are most common, though FPTP ones are common. If the US had popular-vote presidential elections with runoffs, then several of them would have gone into runoff. Would Carter have beaten Reagan? Bush I or Dole beaten Clinton? Gore beaten Bush II? For legislatures, party list is the most common, though mixed member and FPTP have sizable showings, followed by runoff elections. Most of the FPTP users are the UK and former British-Empire countries, including certain well-known rebellious British colonies. But even in the Anglosphere, as it may be called, some nations have moved to PR and PR-like systems, like Australia and New Zealand, and in the UK, Northern Ireland, Scotland, and Wales. In the US, it is easier than one might think to implement PR. The US Constitution nowhere mandates single-member districts for Representatives; it states that they are to be elected state-by-state. So a state could elect is Representatives by PR if it so chose. A big plus of PR is that it enables minorities to be more easily represented; not only racial and ethnic and religious ones, but also political and ideological ones. One can see this in action in PR systems, which sometimes have several parties. This means that Libertarians, for instance, can more easily get seats under PR than under FPTP.