The two main families of electoral systems in the world are proportional and winner-take-all. All single-winner systems are, by definition, winner-take-all. Multi-winner systems may be proportional or winner-take all.
Sometimes it makes sense to elect just one person. For example, a nation would only ever choose one president at a time. However, when electing a legislative body, there is a real decision to make between using single-winner or multi-winner districts. That choice has profound consequences.
The academic consensus is that multi-winner districts with a form of proportional representation are associated with:
On the other hand, single-winner districts are associated with:
Plurality: A system in which the candidate with the most votes wins, without necessarily a majority of votes. It is the system used for most elections in the United States and is most common system used in nation-states descended from the British and French Empires.
Two Round System: A system identical to the plurality system except that if no winner attains the majority of votes in the initial election, a second "runoff" round of voting takes place between the two candidates who received the most votes in the initial round.
Single-winner Ranked Choice Voting: A system that allows voters the option to rank candidates in order of preference: one, two, three, and so forth. If their vote cannot help their top choice win, their vote counts for their next choice.
In races where voters select one winner, if a candidate receives more than half of the first choices, that candidate wins, just like in any other election. However, if there is no majority winner after counting first choices, the race is decided by an "instant runoff." The candidate with the fewest votes is eliminated, and voters who picked that candidate as ‘number 1’ will have their votes count for their next choice. This process continues until there’s a majority winner or a candidate won with more than half of the vote.
Block voting: A system in which electors have as many votes as there are candidates to be elected. Counting is identical to a plurality system, with the candidates with the most votes winning the seats. This is widely used in the United States and is a winner-take-all system
Single Voting: A multi-winner system in which electors have one vote. The candidates with the most votes win. When electing more than one candidate, this is not a winner take all system. When a "numbered post" system where all voter participate in a series one-winner elections, it is a winner-take-all system.
List Proportional Voting: A multi-winner system in which political parties nominate candidates and electors vote for their most preferred party (or candidate nominated by a party). The seats are allocated to each party in proportion to the share received in the national vote.
When electing a legislative body, seats can be elected proportionally or by "winner-take-all".
In proportional representation, like-minded groups of winners are allocated in alignment with the proportion of the vote they receive. For example, in a five-winner district, a political party that received 38% of the vote would elect two candidates and a party that received 62% of the vote would elect three. Only multi-winner districts can be proportional.
Winner-take-all, by contrast, operates on the principle that the candidate(s) with the most votes win. This means that some voters get representation and others do not. For example, in a five-winner district using winner-take-all, all five seats could be won by a single party, even if only a bare majority of voters support that part. Indeed, this sort of outcome was common in early congressional elections.
There are a multitude of different proportional systems, including the Single Voting and List Proportional Voting described above, as well as:
Cumulative Voting: A method of election in which voters have a number of votes equal to the number of seats to be elected. Voters can assign as many of their votes to a particular candidate or candidates as they wish. In a three-seat district, for example, a voter could give all three of their votes to one candidate, two votes to one candidate and one to another, or one vote each to three different candidates. Cumulative voting is subject to distorted results due to vote-splitting and is thereby a "semi-proportional" system.
Ranked Choice Voting in Multi-Winner Districts (single transferable vote): A method of voting in which voters have one vote but are able to rank candidates in order of preference. Initially, every ballot counts as a vote for its highest ranked candidate. Those candidates who have enough votes to win are elected, their "surplus votes" are counted for next-choice candidates, and the weakest performing candidates are eliminated until all seats are filed. For instance, in a five-seat district, a candidate is elected if they receive more than 1/6 of all votes cast, as this threshold ensures that they will be one of the top five finishers. If not enough candidates as number of seats reach the threshold to win, then voters' second and additional backup choices come into play.
Winner-take-all systems include all single-winner district systems, the block vote, and the single vote system in numbered posts.
Mixed systems—which combine single-winner, winner-take-all elements with multi-winner proportional elements—are increasingly popular. Many consider them to be "the best of both worlds" because they maintain the link between constituent and representative in single-winner districts, while embracing proportionality.
The two main types of mixed systems are:
Mixed Member Proportional: An electoral system in which each voter gets two votes: one for a candidate in a local constituency and another for party. A fraction of seats are elected using plurality and the remainder from list proportional systems. The list seats are allocated after the plurality seats in such a way as to achieve proportionality with the national party vote.
Parallel Systems: An electoral system in which each voter gets two votes: one for a candidate in a local constituency and another for party. A fraction of seats are elected using plurality and the remainder from list proportional systems. The list seats are allocated proportionally with the national party vote, but the legislature itself need not reflect the party vote across the nation.