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Electoral Systems

South African Ballot PaperThe way you vote at your local polling place may seem like the natural and only way to vote. But there are thousands of different ways to cast and count votes.

Votes may be cast for candidates or for political parties. Votes may be indicated by check marks, crossing out names, writing in names, or ranking candidates in order of choice. Votes may be cast on paper in pencil, on a punch card machine or a modern touch screen.

When it is time to count votes, thousands of workers may tabulate the results by hand over the course of days or weeks--or computers might calculate the result, almost instantly. Importantly, winners might be required to win a majority of the vote, or more votes than the other candidates (but not a majority); they might need to be the candidate most preferred by the electorate overall (taking into account voters' rankings), or alternatively, winners might be decided by reference to the proportion of the total vote they receive.

This page summarizes some of the most common electoral systems around the world and in the United States. 

Click on a topic to begin.

1870s ballot boxElectoral Systems 101

There are two main families of electoral systems in the world: 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.

Single-winner systems vs Multi-winner systems

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 and multi-winner districts. That choice has profound consequences.

The academic consensus is that multi-winner districts are associated with: 

  • Larger and more populous districts; 
  • Districts contested by multiple parties and candidates;
  • Legislatures that more proportionately reflect voters' political preferences;
  • Governing by a coalition of parties rather than one single majority party;
  • The election of more women to the legislature. 

 On the other hand, single-winner districts are associated with: 

  • Smaller districts, with a closer link between elected representative and constituents;
  • Uncontested districts and two-party systems (see Duverger 1972);
  • A lack of proportionality between votes cast across the country for a party and seats won by that party;
  • Governing by single-party majorities;
  • The election of fewer women to the legislature.

Common single-winner systems include:

Plurality: A system in which the candidate with the most votes wins without necessarily a majority of votes. It is the most common system used in nation-states descended from the British and French Empires, including the United States and Canada. 

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 in which voters rank candidates in order of preference. A candidate who receives over 50% of the first preference votes will be declared the winner; if this does not occur, the ballot count simulates a series of runoff elections. The candidate with the fewest first-place votes is eliminated, and ballots cast for that candidate are "transferred" to second choices as indicated on voters' ballots. This process of transferring votes continues until one of the candidates has a majority.

Common multi-winner systems include: 

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. 

Single Voting: A multi-winner system in which electors have one vote. The candidates with the most votes win. 

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. 

Proportional vs Winner-take-all

Another choice, in addition to the one between single- and multi- winner districts, is whether to elect legislators proportionally or using something called "winner-take-all". 

In proportional representation, 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. Naturally, then, 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 one party with just over half of the vote. Indeed, this sort of outcome was quite common in early congressional elections. 

There are a multitude of different proportional systems, including the Single Voting and List Proportional Voting, 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 to three different candidates. 

Ranked Choice Voting in Multi-Winner Districts: 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 and the weakest performing candidates are eliminated.  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 choices come into play.  

Winner-take-all systems include all single-winner district systems and the block vote. 

Mixed Systems

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 proportionality with the national party vote, but the legislature itself need not reflect the party vote across the nation. 

 

Electoral_Systems_Chart.JPG

Further reading: 

  • Cox, Gary. 1997. Making Votes Count: Strategic Coordination in the World's Electoral Systems. Cambridge: Cambridge University Press. 
  • Lijphart, Arend, and Don Aitkin. 1994. Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945-1990. Oxford University Press.
  • Reilly, Ben, Andrew Ellis, and Andrew Reynolds. 2005. Electoral System Design: The New International IDEA Handbook. International Institute for Democracy and Electoral Assistance.
  • Shugart, Matthew, and Martin P. Wattenberg, eds. 2001. Mixed-Member Electoral Systems: The Best of Both Worlds?: The Best of Both Worlds?. Oxford University Press.

German ballot 2012

Electoral Systems around the World

There are many different electoral systems in use around the world.  Most countries have chosen an electoral system very different to the one used in national elections in the United States.

Single-winner systems vs Multi-winner systems

Most nations around the world choose to have at least some multi-winner districts in their national legislatures. Fifty-four of the 195 countries in the map below use only single-winner districts. Ninety use only multi-winner districts, and 38 use a mix of multi- and single-winner districts. 

infogram_0_multi_and_single_winner_districtsMulti and Single winner districts//e.infogr.am/js/embed.js?2Fhtext/javascript

 

Proportional vs Winner-take-all

Internationally, proportional representation is the most common type of electoral system with 89 of the 195 countries below using it. Of those 84 countries, 79 use list proportional systems, with two using multi-winner RCV and three using other proportional systems. An additional 34 countries mix proportionality and winner-take all. Sixty-four countries use winner-take-all, including 37 that use plurality, including the United States, the United Kingdom, and Canada. 

infogram_0_electoral_systems_of_the_worldElectoral Systems of the World//e.infogr.am/js/embed.js?HeStext/javascript

Useful Sources:

Electoral Systems of 35 Major Democracies

The following chart lists the different voting systems used by the world's 35 major, well-established democracies to elect their most powerful legislative chamber. These 35 democracies were chosen because they had a population of at least 2 million and received a 2012 Freedom House Average Freedom Ranking of 1 or 2.

Among these 35 major democracies, proportional representation (PR) systems are by far the most common way to elect legislatures.

infogram_0_electoral_sys_maj_dems_2012Electoral sys maj dems 2012//e.infogr.am/js/embed.js?UbHtext/javascript

 

infogram_0_es_of_35_dems_2012ES of 35 Dems 2012//e.infogr.am/js/embed.js?gt8text/javascript

 

Of the six nations that do not use PR to elect representatives in their most powerful national legislative body, only three countries (US, Ghana, and Canada) don't use it for at least one of their national elections (PR is used in the upper house in Australia and European Parliament in UK and France).

Electoral Systems Reform is Possible

The structure of elections and a nation's choice of electoral system can have profound implications for the effectiveness of democratic governance. It is no surprise, then, that reformers in many nations continuously strive to improve the way their governments are elected. Most countries regularly reflect on how well their systems are working and consider structural improvements--and such changes are implemented more often than many casual observers may realize. In recent decades, major changes in electoral systems have been adopted in New Zealand, France, Italy and Japan. Scotland, Wales and Northern Ireland have adopted electoral systems vastly different from that in the United Kingdom. Furthermore, the United Kingdom conducted a referendum on electoral reform in 2011, many Canadian provinces have voted on reform in the last decade, and the Canadian Parliament is currently considering electoral systems reform. (Matthew Shugart and Justin Reeves (2015) "Electoral System Reform in Advanced Democracies" Oxford Bibliographies)

Electoral Systems in the United States

Historically, Americans have been innovators in the design of electoral systems. In its day, the Electoral College was an impressive innovation. Several vote counting methods, including Cumulative Voting, Bucklin Voting and Coombs' Method originated in the United States. Today, the U.S. is less innovative nationally, but there is much diversity in the electoral systems in use in state and local jurisdictions.  

Winner-take-all in single winner districts ("plurality") is the norm in America

Used to elect the U.S. House Representatives, as well as many state and local legislatures, plurality is the most common and best-known electoral system currently in use in America. Under the plurality system, an area is divided into a number of geographically defined voting districts, each represented by a single elected official. Voters cast a single vote for their district’s representative, with the highest total vote-getter winning election, even if he or she has received less than half of the vote. 

There are two main weaknesses in the plurality system. 

First, where the boundaries of districts are drawn can have a huge effect on who is likely to win election. As a result, gerrymandering to protect incumbents or weaken political enemies is common practice under plurality rules. This is a problem inherent in any single-winner system. 

Second, plurality elections are prone to the spoiler effect. Where three or more viable candidates run and split the vote within a district, the “winner” of an election can often be the candidate whom the majority of voters liked least. This characteristic of plurality elections leads to a further problem. In order to prevent the spoiler effect from negatively impacting their chances, political parties will limit the number of candidates running. This in turn leaves voters with no effective choice as elections often involve voters merely ratifying the candidate chosen by the majority party (typically at a low turnout primary) in their district.

There are other voting systems that are identical to plurality in every way, except that they use a runoff after the general election or instant runoff voting to increase the chances that the winner of an election has the support of the majority of voters. While this eliminates the spoiler effect, it does nothing to stop the negative effects of gerrymandering or the limitations inherent in making geography the primary districting criteria. 

Many multi-winner systems can, however, overcome the pernicious impacts of gerrymandering -- as well as prevent the spoiler effect. They do this by (1) ensuring that geography is not the main criterion for representation and (2) assigning winners proportionally and/or based on the voters' ranking of candidates. 

Multi-winner systems are widely used in the United States

While single-winner districts are used in most American legislative elections, eleven state chambers and a majority of municipalities use some form of multi-winner districts. These jurisdictions include: 

  • Eleven state legislative chambers (the state houses in Arizona, Idaho, Maryland, New Hampshire, New Jersey, North Dakota, South Dakota, Vermont, Washington and West Virginia and the state senate in Vermont).  
  • Hundreds of cities, including Cincinnati OH, Portland OR, Seattle WA, and Irvine CA, that use multi-winner districts (called "at-large") to elect their city councils. 
  • Hundreds more cities, including Atlanta GA, Houston TX, Philadelphia PA, and Washington DC, that use multi-winner districts (called "at-large") to elect some members of their city councils.  
  • Many counties, including 47 counties in Pennsylvania, and several in each of North Carolina and Alabama, that use multi-winner districts (called "at-large") to elect some members of their county commissions.

Historically, multi-winner districts were used to elect members of the U.S. House of Representatives and to elect most state legislators.

infogram_0_states_using_multiwinner_districtsStates using multiwinner districts//e.infogr.am/js/embed.js?y0xtext/javascript

Further reading: 

Proportional vs Winner-take-all Systems

Winner-take-all is the norm in American jurisdictions, and is currently used for all national and state elections. However, proportional representation voting has been used to elect public officials in the United States since the nineteenth century. Numerous cities, including Cincinnati OH, Boulder CO, and New York City, used proportional representation--the polar opposite to winner-take-all--in the 20th century. At the state level, Illinois used multi-member districts and cumulative voting to elect their House of Representatives for over one hundred years.

Currently, voters use at-large ranked choice voting, cumulative voting, and the single vote or other forms of "limited voting" to elect city councils, school boards, and other local offices in over two hundred United States jurisdictions to achieve proportional representation in their communities. You can visit our page on proportional representation for a brief history of proportional representation voting in the United States, and the full list of jurisdictions using proportional representation voting, including what specific election method they use and when their next election will be.

 

Further reading: 

Presidential Elections around the World

The office of president combines the head of state and head of government functions into one office. The office of president is often the most prominent, and focal, political office in a country.

Presidents may indirectly elected through an electoral college, or directly elected. The United States indirectly elects its president using an electoral college. Mexico and Brazil elect their presidents directly. 

Additionally, some countries require that their directly elected president win a majority--either an absolute majority, or some large plurality--of votes.

Indirect Election: Pros and Cons

The U.S. Founding Fathers decided on an indirectly elected president because they believed voters would vote according to parochial, state-based, interests, because they feared the "tyranny of the majority", and because they were concerned that the office could become too powerful with a direct mandate from the people. The Founding Fathers designed the elaborate and, at times misfiring, Electoral College to ensure that the president has broad support across the many states.

Nowadays, the Electoral College is often criticized as being outdated and contravening principles of majority rule. For more on the Electoral College, and proposals for its reform see our "Electoral College" page. 

Majority Requirements in Presidential Elections

Of the 28 freest presidential democracies, 21 require the president to win with a majority of votes. Two more mandate presidents be elected with relatively high minimum pluralities. Only five allow pure plurality winners. One of them, the United States, permits the winner of the popular vote to lose the election through an Electoral College system. The 23 countries with majority and minimum plurality requirements all employ runoff elections. 22 use delayed runoff elections and one, Ireland, builds both rounds into one with instant runoff voting (IRV). 

Download Our Report: Majority Rule in International Presidential Elections

 

 

infogram_0_presidential_and_parliamentaryPresidential and Parliamentary//e.infogr.am/js/embed.js?D6mtext/javascript

Single-winner Voting Method Comparison Chart

There are many different ways to elect a single office, such as a president, governor or mayor. This chart compares the most widely discussed voting methods for electing a single winner (and thus does not deal with multi-seat or proportional representation methods). There are countless possible evaluation criteria. 

  Plurality Two-Round Runoff Ranked Choive Voting (RCV) Approval Range Condorcet methods Borda Count
Resistance to spoilers Low Medium High Medium Medium High Low
Later-no-harm criterion Yes Yes Yes No No No No
Resistance to strategic voting Low High High Low Low High Low
Majority-favorite criterion Yes Yes Yes No No Yes No
Mutual-majority criterion No No Yes No No Yes/No No
Prospects for U.S. adoption High High High Medium Low Low Low
Condorcet-loser criterion No Yes Yes No No Yes/No Yes
Condorcet-winner criterion No No No No No Yes No
Independence of clones criterion No No Yes Yes/No Yes/No Yes/No No
Monotonicity criterion Yes No No Yes Yes Yes/No

Yes

References

Austen-Smith, David, and Jeffrey Banks (1991). “Monotonicity in Electoral Systems”. American Political Science Review, Vol. 85, No. 2 (June): 531-537.

Brewer, Albert P. (1993). “First- and Second-Choice Votes in Alabama”. The Alabama Review, A Quarterly Review of Alabama History, Vol. 46 (April 1993): 83 - 94

Burgin, Maggie (1931). The Direct Primary System in Alabama. Masters thesis, University of Alabama.

Green-Armytage, James (n.d.). “A Survey of Basic Voting Methods”. Web page at http://fc.antioch.edu/~james_green-armytage/vm/survey.htm (last visited November 20, 2008).

Green-Armytage, James (2008). “Strategic Voting and Strategic Nomination: Comparing seven election methods”. Unpublished manuscript, University of California at Santa Barbara. http://fc.antioch.edu/~james_green-armytage/vm/svn.pdf (last visited November 20, 2008).

Nagel, Jack (2007). “The Burr Dilemma in Approval Voting”. Journal of Politics, Vol. 69, No. 1 (February): 43-58.

Robert, Henry M., William J. Evans, Daniel H. Honemann, Thomas J. Balch (2000). Robert's Rules of Order Newly Revised, 10th Edition. Cambridge, MA, Da Capo Press.

Tideman, Nicolaus (2006). Collective Decisions and Voting: The Potential for Public Choice

 

For a full explanation, refer to our archived site.

Notes:

Plurality Voting is the most prevalent method of voting in the U.S. In a single seat election, the voter picks one candidate, and the candidate selected by the largest number of voters is elected, regardless of whether that candidate is favored by a majority or not. Because of its supposed similarity to a horse race this method is sometimes referred to as "First Past the Post" or FPTP.

Two-Round Runoff: Two-round Runoffs are intended to prevent split majorities resulting in the election of a candidate that the majority opposes. The winner of the second round is considered a majority winner, although, due to drop-off in turnout, this "winner" could receive fewer votes in the runoff than the loser received in the first round. Thus the "majority" is manufactured by preventing voters from voting for eliminating candidates and discounting all voters who do not turn out for the second round.

Ranked Choice Voting (RCV): Ranked choice voting has several variants and other names, including Instant Runoff Voting (IRV), Preferential Voting, and the "Alternative Vote." Voters are allowed to rank candidates in order of choice using a single transferable vote. If no candidate is the first choice of a majority of voters, candidates are sequentially dropped from the bottom, with ballots that were credited towards these candidates then being credited to those voters' next choice who has not been eliminated. This simulation of a series of runoffs ends when one candidate receives a majority or only one candidate remains. This method of voting was invented in Massachusetts around 1870, based on the "single transferable vote" innovation developed some decades previously. It is described in Robert's Rules of Order (Robert, et al., 2000: 411-414), and is used for government elections in places such as the U.S., Ireland and Australia.

Approval: Approval Voting allows voters to vote for as many candidates as they wish in a single-seat election, with the candidate receiving the most votes being elected. Thus some voters may cast one vote, while others effectively may cast several. Since this method is not used in government elections it has not been constitutionally tested as to whether it complies with the one-person, one-vote mandate.

Range: Range Voting asks each voter to assign a score (such a 0 - 10) to each candidate, with the candidate with the highest average score being elected. It is used in sporting events with impartial judges and Internet scoring of various products or services. Because this method is highly susceptible to strategy, it is most appropriate when voting is conducted by disinterested judges, rather than voters with a stake in the outcome.

Condorcet methods: Named after the Marquis de Condorcet who invented it around the time of the French Revolution. Voters are asked to rank all candidates. There rankings can be used to do a pair-wise comparison of how each candidate would theoretically do in a head-to-head match up with each other candidate one at a time. If there is one candidate who would defeat each of the others in a one-on-one contest, this candidate is termed the "Condorcet winner." In some scenarios there is no such winner, as a cycle where A would beat B, B would beat C and C would beat A exists (think of rock, paper, scissors). In this case a variety of different procedures (often named for the inventor) have been proposed for settling which candidate should win.

Borda Count: Borda Count, named after its inventor Jean-Charles de Borda around the time of the French revolution, asks voters to rank all candidates in order of preference. Based on this order, the candidates are assigned a score, with the first choice receiving the most points, the second choice receiving a smaller, number, etc. with the last candidate receiving no points. In one sense, it is like Range voting, except that the points are inflexibly tied to the ranking order, rather than set by the voters individually. Because it is highly susceptible to strategy, like Range Voting, it is most suitable for elections by impartial judges, rather than voters with a stake in the outcome.

 

Glossary of Terms

ALTERNATIVE VOTE (AV) : An alternative name for "Single-Winner Ranked Choice Voting".
APPROVAL VOTING: A voting system used in single-winner district systems and single-office elections in which voters can vote for, or approve of, as many candidates as they wish. Each candidate approved receives one vote and the candidate with the most votes wins. The winner need not garner a majority of the votes.
AT-LARGE : A type of electoral jurisdiction where representatives are elected from the whole political region (i.e.: a city, county, state or nation).
BALLOT IMAGE DATA: Records of the contents of each individual vote cast by each and every voter in a jurisdiction (with all identifying information removed).
BALLOT STRUCTURE: The way in which electoral choices are presented on the ballot paper.
BLOCK VOTE: A winner-take-all voting system used in multi-winner districts where electors have as many votes as there are candidates to be elected. Voting can be either candidate-centered or party-centered. Counting is identical to a plurality system, with the candidates with the highest vote totals winning the seats. Also known as the Bloc Vote.
BORDA COUNT : A non-proportional form of preferential voting where voters rank candidates. These ranking are converted into points; the candidate with the most points wins. Candidates score one point for being ranked last, two for being next-to-last and so on, with the first-choice candidate receiving points equal to the total number of candidates. For example, in an election with five candidates, a first ranked candidate would receive five points, a second ranked office seeker four and so on.
BULLET VOTING: A vote in which the voter has selected only one candidate, despite the option to indicate a preference for more than one candidates. Voters may bullet vote strategically (in block voting systems), in a misguided attempt to vote strategically (in the case of ranked choice voting) or because the voter lacks the information or will to evaluate more than one candidate on the ballot.
CANDIDATE-CENTERED BALLOT: A form of balloting where an elector chooses between candidates.
CHOICE VOTING : Another term for "Multi-winner Ranked Choice Voting".
CLOSED LIST : A form of list proportional representation in which electors are restricted to voting for a party only, and cannot express a preference for any candidate within a party list.
COMPENSATORY SEATS : The party list seats in a mixed-member proportional (MMP) system awarded to parties based on their proportion of the national vote. These seats are designed to correct the often disproportionate results of plurality-majority elections.
CONTIGUOUS DISTRICTS : Districts comprised of areas geographically adjoined or touching.
CUMULATIVE VOTE : A semi-proportional system, used in some American localities, that uses multi-winner districts. Voters have the same number of votes as seats and may allocate them among the candidates in any way they see fit including giving more than one vote to a particular candidate.
DESCRIPTIVE REPRESENTATION: The idea that a body of elected representatives should reflect the outward characteristics, such as such as occupation, race, ethnicity, or gender, of the populations they represent.
DISTRIBUTION REQUIREMENTS: The requirement that a winning candidate must not merely win a specified proportion of the vote nationally but also a specified degree of support from different regions.
DISTRICT : The geographical regions into which a city, state, or country is divided for election purposes. Single-winner districts elect one member of the legislature whereas multi-winner districts elect two or more.
DISTRICT MAGNITUDE : The number of candidates to be elected in each district.
DROOP QUOTA : Used in highest average method and multi-winner ranked choice voting elections to determine the number of votes necessary to win a seat. The threshold is intended to be the lowest vote total that only the winning number of candidates can get. The quota is ascertained by the following formula: total vote divided by the number of seats plus one, then one is added to the product.
ELECTORAL FORMULA : That part of the electoral system dealing specifically with the translation of votes into seats.
ELECTORAL LAW : The constitutional and legal provisions governing all aspects of the electoral process.
ELECTORAL SYSTEM: A set of rules and procedures that govern the election of public officials by specifying, chiefly, the electoral formula, the ballot structure, and district magnitude.
FIRST PAST THE POST (FPTP) : Another name for "Plurality".
FREE LIST : A form of list system PR providing for cumulative voting.
FULL REPRESENTATION: A term used by proportional representation proponents to describe electoral systems that aim to reduce the disparity between a party's share of the national vote in a legislative election and its share of seats. For example, if a party wins 40% of the votes, it should win approximately 40% of the seats.
GENDER PARITY: The political condition under which women and men are just as likely to hold elected office.
GERRYMANDERING : The manipulation of district boundary lines in order to advantage or disadvantage a candidate or political group. Gerrymandering is typically used to create a district that is favorable to an incumbent, advantage a particular party or political group to receive more seats than its proportion of the vote, or to conversely disenfranchise a group or party by weakening or dividing that subset of the electorate.
HAGENBACH-BISCHOFF FORMULA : Another term for the Droop Quota.
HARE QUOTA : Used in largest remainder full representation systems to determine how many votes are needed to win a seat. The quota is ascertained by dividing the total vote by the number of seats.
HIGHEST AVERAGE METHOD : A family of formulas used with list systems to translate votes into seats, including the d'Hondt formula and the Sainte-Lague Formula. Party vote totals are divided by a series of divisors, which differ according to the system used. After each stage, the party with the highest average wins the seat.
IMPERIALI QUOTA : Sometimes used in largest remainder systems to determine how many votes are necessary to win a seat. The quota is ascertained by dividing the total vote by the number of seats plus two.
INDEX OF DISPROPORTIONALITY: A figure illustrating the collective disparity between the votes cast for parties in an election and the seats in a legislature they win.
INSTANT RUNOFF VOTING (IRV) : Another term for "Single-winner Ranked Choice Voting".
INVALID VOTES : Ballots cast that are unable to be included in the vote total due to accidental or deliberate errors on the ballot.
LARGEST REMAINDER METHOD : General term for the Hare Quota, and the Droop and Imperiali calculation methods, which translate votes into seats within List PR systems. There are two stages to the count. First, parties are awarded seats in proportion to the number of quotas they fulfill (quotas vary depending on which of the three systems are used). Second, remaining seats are awarded to parties on the basis of the leftover votes they possess after the 'quota' stage of the count. Largest remainder seats are allocated in order of vote size.
LIMITED VOTE : A voting system used in multi-winner districts; electors have more than one vote but fewer votes than there are candidates to be elected. Counting is identical to a plurality system, with the candidates with the highest vote totals winning the seats. When voters have only one vote, it is also known as the Single Vote system or the single non-transferable vote (SNTV).
LIST PROPORTIONAL REPRESENTATION : A form of proportional representation used in multi-winner elections where the party submits lists of candidates to be elected. Voters vote for the party. The seats are allocated to each party in proportion to the share received in the national vote. Party lists of candidates can be open, closed, or free. List proportional representation are also known as party list proportional or list systems or List PR.
MAJORITY-RUNOFF: Another name for the "Two Round System".
MALAPPORTIONMENT : The uneven distribution of voters between electoral districts.
MIXED MEMBER PROPORTIONAL (MMP): A hybrid electoral system where some legislative seats are elected from single-winner districts suing winner-take-all rules (i.e. plurality) and the remainder from party list proportional systems. MMP combines geographic representation with proportional representation of ideological interests. Party list seats are allocated in such a way as to achieve proportionality in the legislative chamber overall.
MONOTONICITY: The characteristic of a voting system in which it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot).
MULTI-WINNER DISTRICT : A district from which more than one member is elected.
MULTI-WINNER PLURALITY VOTING SYSTEM : Another name for "Block Voting".
MULTI-WINNER RANKED CHOICE VOTING: A proportional voting system used in at-large or multi-winner district elections where voters rank candidates in order of preference. Candidates win by reaching a threshold through a process of surplus transfers and eliminations.
NUMBERED POSTS : An electoral system in which candidates run for a particular post but are elected at-large. Some numbered posts require that the candidate be a resident of a particular geographical area.
ONE VOTE SYSTEM : Another term for the "Single Vote".
OPEN LIST : A form of List PR in which electors can express a preference for the order of candidates within a party list, as well as voting for the party.
OVERVOTE: A vote in which the voter has indicated a preference for more than the maximum number of selections allowed.
Parallel System: A hybrid electoral system where some legislatives seats are elected from single-winner districts suing winner-take-all rules (i.e. plurality) and the remainder from party list proportional systems. Unlike MMP, proportionality is confined to the party lists seats, rather than applying to the legislative chamber overall.
PARTY-CENTERED BALLOT : A form of ballot in which an elector chooses between parties.
PLURALITY: A voting system used in single-winner elections in which the candidate with the most votes wins, without necessarily receiving a majority of votes. It is the most common system used in countries descended from the British and French Empires, including the United States and Canada. Certain jurisdictions couple the use of plurality with runoff elections if no winner attains the majority of votes in the initial election (this is called the "Two Round System").
POLARIZATION : In voting rights, polarization describes a division where voters cast their votes along racial lines. For example, an area would exhibit polarized voting if most white voters support a particular candidate and most black voters support another candidate.
PREFERENTIAL VOTING: Electoral systems in which voters can rank-order candidates on the ballot paper in order of their choice. Ranked choice voting, Borda count, Bucklin Voting, and Coomb's method are all examples of preferential voting. In other contexts, preferential voting may be a synoym for single-winner ranked choice voting (in Australia) or open list proportional representation (in some parts of Europe).
PROPORTIONAL REPRESENTATION : A group of voting systems used in many democracies whose major goal is to ensure that parties and political groups are allocated seats in legislative bodies in proportion to their share of the vote. For example, a party receiving 30% of the national vote should receive approximately 30% of the seats in the national legislature.
RANKED CHOICE VOTING: Two voting systems in which voters express their preferences for candidates by ranking them. Ranked choice voting may be single- or multi-winner. See also "Multi-winner Ranked Choice Voting" and "Single-winner Ranked Choice Voting"
REFLECTIVE REPRESENTATION: Another term for "descriptive representation".
RESERVED SEATS : Seats in which some ascriptive criterion such as religion, ethnicity, language, gender etc. is a requirement for election.
RESIDUAL VOTES: Total number of votes that cannot be counted for a specific contest. There are multiple types of residual votes, including overvotes and undervotes.
RUNOFF ELECTIONS : An election method where the top two candidates face off in a second round of voting if no candidate wins a majority (or lower, pre-determined vote) in the first round.
SAINTE-LAGUE FORMULA : A highest-average formula for allocating seats proportionally in a list system. The available seats are awarded one at a time to the party with the largest average number of votes as determined by dividing the number of votes won by the party by the number of seats the party has been awarded plus one. Each time a party wins a seat, the divisor for that party increases by two, which thus reduces its chances of winning the next seat. The first seat is awarded to the party with the largest absolute number of votes, since, no seats having been allocated, the average vote total as determined by the formula will be largest for this party (see also d'Hondt formula).
SEMI-PROPORTIONAL SYSTEMS : Those electoral systems where proportional outcomes (groups winning seats according to their population percentage) in elections may be produced, but are not guaranteed. Semi-proportional systems generally produces electoral results that are between the proportionality of full representation systems and the disproportionality of winner-take-all systems. These systems include cumulative voting and limited voting.
SINCERE VOTING : A term used to describe votes cast by voters for their most preferred candidate. This contrasts with "insincere" or "strategic" voting where voters must cast a vote for a candidate other than their first preference in order to best pursue their political interests.
SINGLE NON-TRANSFERABLE VOTE (SNTV) : Another term for "Single Vote".
SINGLE TRANSFERABLE VOTE (STV): Another tem for "Multi-winner Ranked Choice Voting".
SINGLE VOTE: A multi-winner system in which electors have one vote. The candidates with the most votes win.
SINGLE-WINNER DISTRICT : A district from which only one member is elected.
SINGLE-WINNER RANKED CHOICE VOTING: An electoral system used in single-winner elections where voters rank candidates in order of preference. If a candidate has more than half of the vote based on first-choices, that candidate wins. If no candidate has more than half of those votes, then the candidate with the fewest first choices is eliminated. The voters who selected the defeated candidate as a first choice will then have their votes added to the totals of their next choice. This process continues until a candidate has more than half of the active votes or only two candidates remain. The candidate with a majority among the active candidates is declared the winner.
SPOILER EFFECT : A phenomenon in plurality elections in which an independent or third party candidate takes enough votes away from one major party candidate to ensure the victory of the other major party candidate, who would not have won otherwise.
STRATEGIC (OR TACTICAL) VOTING : Occurs when a voter votes for a candidate other than her sincere choice to prevent an unwanted outcome. For example, in a plurality election, there is often a strong incentive for supporters of a minor party to throw their vote to a larger party with a greater chance of victory; this prevents a party or candidate the voter dislikes from winning. Generally speaking, proportional voting systems are designed to reduce strategic voting, as the results will closely match the total share of votes cast for each party.
THRESHOLD : The minimum numbers of the votes needed to receive any seats in the legislature under a proportional representation system. Known technically as the threshold of exclusion in List PR, because if a party reaches this threshold they cannot be excluded from winning a seat. Under choice voting, the threshold is the fewest number of votes that only the winning number of candidates can obtain (roughly the number of votes divided by the number of seats.
TWO-ROUND SYSTEM: A winner-take-all system in which a second election is held if no candidate achieves an absolute majority of votes in the first election. Also known as "runoff elections".
TWO-TIER DISTRICTING: Where seats are awarded to parties from both single member districts and national lists, or both regional and national lists.
UNDERVOTE: A vote in which the voter has selected fewer candidates than allowed or has skipped voting for the office entirely.
WASTED VOTES : A political science term used to describe votes that are not useful in the election of the winning candidate or party. Those votes include ballots cast for a losing candidate(s) along with any extraneous votes cast in support of winning candidates.
WINNER-TAKE-ALL: A term used to describe election systems that award seats to the highest vote getters without ensuring fair representation for minority groups. In the United States, these are typically single-winner district schemes or at-large, block-voting systems.

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