# Electoral system

Map showing the electoral systems used to elect candidates to the lower house of national legislatures, as of 2019.
Majoritarian system
Semi-proportional system
Proportional system
Mixed system
Majority bonus system
Mixed-member proportional representation
Parallel voting
Other

No direct election
No information

An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Political electoral systems are organized by governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted (electoral method), limits on campaign spending, and other factors that can affect the outcome. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.

Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as members of parliament or boards of directors. There are many variations in electoral systems, but the most common systems are first-past-the-post voting, the two-round (runoff) system, proportional representation and ranked voting. Some electoral systems, such as mixed systems, attempt to combine the benefits of non-proportional and proportional systems.

The study of formally defined electoral methods is called social choice theory or voting theory, and this study can take place within the field of political science, economics, or mathematics, and specifically within the subfields of game theory and mechanism design. Impossibility proofs such as Arrow's impossibility theorem demonstrate that when voters have three or more alternatives, it is not possible to design a ranked voting electoral system that reflects the preferences of individuals in a global preference of the community, present in countries with proportional representation and plurality voting.

## Types of electoral systems

### Plurality systems

Countries using first-past-the-post for legislatures.

Plurality voting is a system in which the candidate(s) with the highest number of votes wins, with no requirement to get a majority of votes. In cases where there is a single position to be filled, it is known as first-past-the-post; this is the second most common electoral system for national legislatures, with 58 countries using it to elect their legislatures,[1] the vast majority of which are current or former British or American colonies or territories. It is also the second most common system used for presidential elections, being used in 19 countries.[1]

In cases where there are multiple positions to be filled, most commonly in cases of multi-member constituencies, plurality voting is referred to as block voting or plurality-at-large.[1] This takes two main forms: in one form voters have as many votes as there are seats and can vote for any candidate, regardless of party – this is used in eight countries.[1] There are variations on this system such as limited voting, where voters are given fewer votes than there are seats to be filled (Gibraltar is the only territory where this system is in use)[1] and single non-transferable vote (SNTV), in which voters can vote for only one candidate in a multi-member constituency, with the candidates receiving the most votes declared the winners; this system is used in Afghanistan, Kuwait, the Pitcairn Islands and Vanuatu.[1] In the other main form of block voting, also known as party block voting, voters can only vote for the multiple candidates of a single party. This is used in five countries as part of mixed systems.[1]

The Dowdall system, a multi-member constituency variation on the Borda count, is used in Nauru for parliamentary elections and sees voters rank the candidates depending on how many seats there are in their constituency. First preference votes are counted as whole numbers; the second preference votes divided by two, third preferences by three; this continues to the lowest possible ranking.[2] The totals achieved by each candidate determine the winners.[3]

### Majoritarian systems

Majoritarian voting is a system in which candidates have to receive a majority of the votes to be elected, although in some cases only a plurality is required in the last round of counting if no candidate can achieve a majority. There are two main forms of majoritarian systems, one using a single round of ranked voting and the other using two or more rounds. Both are primarily used for single-member constituencies.

Majoritarian voting can take place in a single round using instant-runoff voting (IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in Australia and Papua New Guinea. If no candidate receives a majority of the vote in the first round, the second preferences of the lowest-ranked candidate are then added to the totals. This is repeated until a candidate achieves over 50% of the number of valid votes. If not all voters use all their preference votes, then the count may continue until two candidates remain, at which point the winner is the one with the most votes. A modified form of IRV is the contingent vote where voters do not rank all candidates, but have a limited number of preference votes. If no candidate has a majority in the first round, all candidates are excluded except the top two, with the highest remaining preference votes from the votes for the excluded candidates then added to the totals to determine the winner. This system is used in Sri Lankan presidential elections, with voters allowed to give three preferences.[4]

The other main form of majoritarian system is the two-round system, which is the most common system used for presidential elections around the world, being used in 88 countries. It is also used in 20 countries for electing the legislature.[1] If no candidate achieves a majority of votes in the first round of voting, a second round is held to determine the winner. In most cases the second round is limited to the top two candidates from the first round, although in some elections more than two candidates may choose to contest the second round; in these cases the second round is decided by plurality voting. Some countries use a modified form of the two-round system, such as Ecuador where a candidate in the presidential election is declared the winner if they receive 40% of the vote and are 10% ahead of their nearest rival,[5] or Argentina (45% plus 10% ahead), where the system is known as ballotage.

An exhaustive ballot is not limited to two rounds, but sees the last-placed candidate eliminated in each round of voting. Due to the potentially large number of rounds, this system is not used in any major popular elections, but is used to elect the Speakers of parliament in several countries and members of the Swiss Federal Council. In some formats there may be multiple rounds held without any candidates being eliminated until a candidate achieves a majority, a system used in the United States Electoral College.

### Proportional systems

Countries by type of proportional system

Proportional representation is the most widely used electoral system for national legislatures, with the parliaments of over eighty countries elected by various forms of the system.

Party-list proportional representation is the single most common electoral system and is used by 80 countries, and involves voters voting for a list of candidates proposed by a party. In closed list systems voters do not have any influence over the candidates put forward by the party, but in open list systems voters are able to both vote for the party list and influence the order in which candidates will be assigned seats. In some countries, notably Israel and the Netherlands, elections are carried out using 'pure' proportional representation, with the votes tallied on a national level before assigning seats to parties. However, in most cases several multi-member constituencies are used rather than a single nationwide constituency, giving an element of geographical representation; but this can result in the distribution of seats not reflecting the national vote totals. As a result, some countries have leveling seats to award to parties whose seat totals are lower than their proportion of the national vote.

In addition to the electoral threshold (the minimum percentage of the vote that a party must obtain to win seats), there are several different ways to allocate seats in proportional systems. There are two main types of system: highest average and largest remainder. Highest average systems involve dividing the votes received by each party by a series of divisors, producing figures that determine seat allocation; for example the D'Hondt method (of which there are variants including Hagenbach-Bischoff) and the Webster/Sainte-Laguë method. Under largest remainder systems, parties' vote shares are divided by the quota (obtained by dividing the total number of votes by the number of seats available). This usually leaves some seats unallocated, which are awarded to parties based on the largest fractions of seats that they have remaining. Examples of largest remainder systems include the Hare quota, Droop quota, the Imperiali quota and the Hagenbach-Bischoff quota.

Single transferable vote (STV) is another form of proportional representation; in STV, voters rank candidates in a multi-member constituency rather than voting for a party list; it is used in Malta and the Republic of Ireland. To be elected, candidates must pass a quota (the Droop quota being the most common). Candidates that pass the quota on the first count are elected. Votes are then reallocated from the least successful candidates, as well as surplus votes from successful candidates, until all seats have been filled by candidates who have passed the quota.[3]

### Mixed systems

In several countries, mixed systems are used to elect the legislature. These include parallel voting and mixed-member proportional representation.

In parallel voting systems, which are used in 20 countries,[1] there are two methods by which members of a legislature are elected; part of the membership is elected by a plurality or majority vote in single-member constituencies and the other part by proportional representation. The results of the constituency vote have no effect on the outcome of the proportional vote.[3]

Mixed-member proportional representation, in use in eight countries, also sees the membership of the legislature elected by constituency and proportional methods, but in this case the results of the proportional vote are adjusted to balance the seats won in the constituency vote in order to ensure that parties have a number of seats proportional to their vote share.[1] This may result in overhang seats, where parties win more seats in the constituency system than they would be entitled to based on their vote share. Variations of this include the Additional Member System and Alternative Vote Plus, in which voters cast votes for both single-member constituencies and multi-member constituencies; the allocation of seats in the multi-member constituencies is adjusted to achieve an overall seat total proportional to parties' vote share by taking into account the number of seats won by parties in the single-member constituencies. A form of mixed-member proportional representation, Scorporo, was used in Italy from 1993 until 2006.

Some electoral systems feature a majority bonus system to either ensure one party or coalition gains a majority in the legislature, or to give the party receiving the most votes a clear advantage in terms of the number of seats. In Greece the party receiving the most votes is given an additional 50 seats,[6] San Marino has a modified two-round system, which sees a second round of voting featuring the top two parties or coalitions if there is no majority in the first round. The winner of the second round is guaranteed 35 seats in the 60-seat Grand and General Council.[7]

In Uruguay, the President and members of the General Assembly are elected by on a single ballot, known as the double simultaneous vote. Voters cast a single vote, voting for the presidential, Senatorial and Chamber of Deputies candidates of that party. This system was also previously used in Bolivia and the Dominican Republic.

### Primary elections

Primary elections are a feature of some electoral systems, either as a formal part of the electoral system or informally by choice of individual political parties as a method of selecting candidates, as is the case in Italy. Primary elections limit the risk of vote splitting by ensuring a single party candidate. In Argentina they are a formal part of the electoral system and take place two months before the main elections; any party receiving less than 1.5% of the vote is not permitted to contest the main elections. In the United States, there are both partisan and non-partisan primary elections.

### Indirect elections

Some elections feature an indirect electoral system, whereby there is either no popular vote, or the popular vote is only one stage of the election; in these systems the final vote is usually taken by an electoral college. In several countries, such as Mauritius or Trinidad and Tobago, the post of President is elected by the legislature. In others like India, the vote is taken by an electoral college consisting of the national legislature and state legislatures. In the United States, the president is indirectly elected using a two-stage process; a popular vote in each state elects members to the electoral college that in turn elects the President. This can result in a situation where a candidate who receives the most votes nationwide does not win the electoral college vote, as most recently happened in 2000 and 2016.

### Systems used outside politics

In addition to the various electoral systems in use in the political sphere, there are numerous others, some of which are proposals and some of which have been adopted for usage in business (such as electing corporate board members) or for organisations but not for public elections.

Ranked systems include Bucklin voting, the various Condorcet methods (Copeland's, Dodgson's, Kemeny-Young, Maximal lotteries, Minimax, Nanson's, Ranked pairs, Schulze), the Coombs' method and positional voting. There are also several variants of single transferable vote, including CPO-STV, Schulze STV and the Wright system. Dual-member proportional representation is a proposed system with two candidates elected in each constituency, one with the most votes and one to ensure proportionality of the combined results. Biproportional apportionment is a system whereby the total number of votes is used to calculate the number of seats each party is due, followed by a calculation of the constituencies in which the seats should be awarded in order to achieve the total due to them.

Cardinal electoral systems allow voters to score candidates independently. The complexity ranges from approval voting where voters simply state whether they approve of a candidate or not to range voting, where a candidate is scored from a set range of numbers. Other cardinal systems include proportional approval voting, sequential proportional approval voting, satisfaction approval voting, majority judgment and the Janeček Method where voters can cast positive and negative votes.

Historically, weighted voting systems were used in some countries. These allocated a greater weight to the votes of some voters than others, either indirectly by allocating more seats to certain groups (such as the Prussian three-class franchise), or by weighting the results of the vote. The latter system was used in colonial Rhodesia for the 1962 and 1965 elections. The elections featured two voter rolls (the 'A' roll being largely European and the 'B' roll largely African); the seats of the House Assembly were divided into 50 constituency seats and 15 district seats. Although all voters could vote for both types of seats, 'A' roll votes were given greater weight for the constituency seats and 'B' roll votes greater weight for the district seats. Weighted systems are still used in corporate elections, with votes weighted to reflect stock ownership.