Plurality voting

Plurality voting refers to electoral systems in which a candidate who polls more than any other (that is, receives a plurality) is elected. In systems based on single-member districts, it elects just one member per district and may also be referred to as first-past-the-post voting|first-past-the-post (FPTP), single-member plurality (SMP/SMDP),^[1] or single-choice (choose-one) voting. A system that elects multiple winners elected at once with the plurality rule and where each voter casts multiple X votes in a multi-seat district is referred to as plurality block voting. A semi-proportional system that elects multiple winners elected at once with the plurality rule and where each voter casts just one vote in a multi-seat district is known as single non-transferable voting.

Plurality voting is distinguished from majority voting, in which a winning candidate must receive an absolute majority of votes: more than half of all votes (more than all other candidates combined if each voter has one vote). Under single-winner plurality voting, the leading candidate, whether or not they have a majority of votes, is elected.^[2]

Plurality voting is widely used throughout the English-speaking world as a result of its spread by the British Empire, including in most of the United States. Outside of the English-speaking world, it is slightly less popular than its close cousin, the runoff family of methods.

Social choice theorists and electoral reform advocates are generally opposed to plurality voting and its variants, citing major issues such as a high vulnerability to spoilers, a tendency towards duopoly and lesser of two evils voting, and their bias toward extremist candidates (as a result of failing the median voter theorem).

Voting

In single-winner plurality voting, each voter is allowed to vote for only one candidate, and the winner of the election is the candidate who represents a plurality of voters or, in other words, received more votes than any other candidate. That makes plurality voting among the simplest of all electoral systems for voters and vote counting officials;^[2] however, the drawing of district boundary lines can be contentious in the plurality system.

In an election for a legislative body with single-member seats, each voter in a geographically defined electoral district may vote for one candidate from a list of the candidates who are competing to represent that district. Under the plurality system, the winner of the election then becomes the representative of the whole electoral district and serves with representatives of other electoral districts.

In an election for a single seat, such as for president in a presidential system, the same style of ballot is used, and the winner is whichever candidate receives the highest number of votes.

In the two-round system, usually the top two candidates in the first ballot progress to the second round, also called the runoff.

In a multiple-member plurality election with n seats available, the winners are the n candidates with the highest numbers of votes. The rules may allow the voter to vote for one candidate, up to n candidates, or some other number.

Single-member vs multi-member plurality voting

Single-member plurality voting systems, often known as first past the post, is a simple system to use. The candidate who gets more votes than any of the other candidate(s) is the winning candidate. Depending on the number of candidates and their popularity within the community, it often happens that the winning candidate gets fewer votes than all the other candidates combined. This is sometimes called the spoiler effect.

Multi-member plurality elections are only slightly more complicated. The n candidates who get more votes than the others are elected.^[3]

Ballot types

Generally, plurality ballots can be categorized into two forms. The simplest form is a blank ballot in which the name of a candidate(s) is written in by hand. A more structured ballot will list all the candidates and allow a mark to be made next to the name of a single candidate (or more than one, in some cases); however, a structured ballot can also include space for a write-in candidate.

Examples of plurality voting

Plurality voting is used for local and/or national elections in 43 of the 193 countries that are members of the United Nations. It is particularly prevalent in the United Kingdom, the United States, Canada and India.^[4]

General elections in the United Kingdom

The United Kingdom, like the United States and Canada, uses single-member districts as the base for national elections. Each electoral district (constituency) chooses one member of parliament, the candidate who gets the most votes, whether or not they get at least 50% of the votes cast ("first past the post"). In 1992, for example, a Liberal Democrat in Scotland won a seat (Inverness, Nairn and Lochaber) with just 26% of the votes. The system of single-member districts with plurality winners tends to produce two large political parties. In countries with proportional representation there is not such a great incentive to vote for a large party, which contributes to multi-party systems.

Scotland, Wales and Northern Ireland use the first-past-the-post system for UK general elections but versions of proportional representation for elections to their own assemblies and parliaments. All of the UK used one form or another of proportional representation for European Parliament elections.

The countries that inherited the British majoritarian system tend toward two large parties: one left and the other right, such as the U.S. Democrats and Republicans. Canada is an exception, with three major political parties consisting of the New Democratic Party, which is to the left; the Conservative Party, which is to the right; and the Liberal Party, which is slightly off-centre but to the left. A fourth party that no longer has major party status is the separatist Bloc Québécois party, which is territorial and runs only in Quebec. New Zealand once used the British system, which yielded two large parties as well. It also left many New Zealanders unhappy because other viewpoints were ignored, which made the New Zealand Parliament in 1993 adopt a new electoral law modelled on Germany's system of proportional representation (PR) with a partial selection by constituencies. New Zealand soon developed a more complex party system.^[5]

After the 2015 UK general election, there were calls from UKIP for a switch to the use of proportional representation after it received 3,881,129 votes that produced only one MP.^[6] The Green Party was similarly underrepresented, which contrasted greatly with the SNP, a Scottish separatist party that received only 1,454,436 votes but won 56 seats because of more geographically concentrated support.

Example

This is a general example, using population percentages taken from one state for illustrative purposes.

Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:

Memphis, the largest city, but far from the others (42% of voters)
Nashville, near the center of the state (26% of voters)
Chattanooga, somewhat east (15% of voters)
Knoxville, far to the northeast (17% of voters)

The preferences of each region's voters are:

42% of voters Far-West	26% of voters Center	15% of voters Center-East	17% of voters Far-East
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville Memphis

If each voter in each city naively selects one city on the ballot (Memphis voters select Memphis, Nashville voters select Nashville, and so on), Memphis will be selected, as it has the most votes 42%. The system does not require that the winner have a majority, only a plurality. Memphis wins because it has the most votes even though 58% of the voters in the example preferred Memphis least. That problem does not arise with the two-round system in which Nashville would have won. (In practice, with FPTP, many voters in Chattanooga and Knoxville are likely to vote tactically for Nashville: see below.)

Disadvantages

Tactical voting

To a much greater extent than many other electoral methods, plurality electoral systems encourage tactical voting techniques like "compromising".^[7] Voters are under pressure to vote for one of the two candidates most likely to win, even if their true preference is neither of them; because a vote for any other candidate is unlikely to lead to the preferred candidate being elected. This will instead reduce support for one of the two major candidates whom the voter might prefer to the other. Electors who prefer not to waste their vote by voting for a candidate with a very low chance of winning their constituency vote for their lesser preferred candidate who has a higher chance of winning.^[8] The minority party will then simply take votes away from one of the major parties, which could change the outcome and gain nothing for the voters. Any other party will typically need to build up its votes and credibility over a series of elections before it is seen as electable.

In the Tennessee example, if all the voters for Chattanooga and Knoxville had instead voted for Nashville, Nashville would have won (with 58% of the vote). That would have only been the third choice for those voters, but voting for their respective first choices (their own cities) actually results in their fourth choice (Memphis) being elected.

The difficulty is sometimes summed up in an extreme form, as "All votes for anyone other than the second place are votes for the winner". That is because by voting for other candidates, voters have denied those votes to the second-place candidate, who could have won had they received them. It is often claimed by United States Democrats that Democrat Al Gore lost the 2000 Presidential Election to Republican George W. Bush because some voters on the left voted for Ralph Nader of the Green Party, who, exit polls indicated, would have preferred Gore at 45% to Bush at 27%, with the rest not voting in Nader's absence.^[9]

That thinking is illustrated by elections in Puerto Rico and its three principal voter groups: the Independentistas (pro-independence), the Populares (pro-commonwealth), and the Estadistas (pro-statehood). Historically, there has been a tendency for Independentista voters to elect Popular candidates and policies. This results in more Popular victories even though the Estadistas have the most voters on the island. It is so widely recognised that the Puerto Ricans sometimes call the Independentistas who vote for the Populares "melons" in reference to the party colours, because the fruit is green on the outside but red on the inside.

Such tactical voting can cause significant perturbation to the system:

Substantial power is given to the news media. Some voters will tend to believe the media's assertions as to who the leading contenders are likely to be in the election. Even voters who distrust the media know that other voters believe the media, and so those candidates who receive the most media attention will nonetheless be the most popular, and thus most likely to be one of the top two.
A new candidate, who is in principle supported by the majority of voters, may be considered unlikely to become one of the top two candidates, because of the lack of a track record. The candidate will thus receive fewer votes, which will then give them a reputation as a low poller in future elections, which perpetuates the problem.
The system may promote votes against than for a candidate. In the UK, entire campaigns have been organised with the aim of voting against the Conservative Party by voting either Labour or Liberal Democrat. For example, in a constituency held by the Conservatives, with the Liberal Democrats as the second-placed party and the Labour Party in third, Labour supporters might be urged to vote for the Liberal Democrat candidate, who has a smaller hurdle to overcome and more support in the constituency than their own party candidate, on the basis that Labour supporters would prefer an MP from a competing leftist or liberal party than a Conservative one. Similarly, in Labour/Liberal Democrat marginals in which the Conservatives are third, Conservative voters may be encouraged or tempted to vote Liberal Democrat to help defeat Labour.
If enough voters use this tactic, the first-past-the-post system becomes, effectively, runoff voting, a completely different system, in which the first round is held in the court of public opinion. A good example was the 1997 Winchester by-election.

Proponents of other single-winner electoral systems argue that their proposals would reduce the need for tactical voting and reduce the spoiler effect. Other systems include the commonly used two-round system of runoffs and instant-runoff voting, along with less-tested and perhaps less-understood systems such as approval voting, score voting and Condorcet methods.

Fewer political parties

Duverger's law is a theory that constituencies that use first-past-the-post systems will eventually become a two-party system after enough time.^[10] The two dominating parties regularly alternate in power and easily win constituencies due to the structure of plurality voting systems.^[11] This puts smaller parties who struggle to meet the threshold of votes at a disadvantage, and inhibits growth.^[11]

Plurality voting tends to reduce the number of political parties to a greater extent than most other methods do, making it more likely that a single party will hold a majority of legislative seats. (In the United Kingdom, 22 out of 27 general elections since 1922 have produced a single-party majority government or, in the case of the National Governments, a parliament from which such a single-party government could have been drawn.)

Plurality voting's tendency toward fewer parties and more-frequent majorities of one party can also produce a government that may not consider as wide a range of perspectives and concerns. It is entirely possible that a voter finds all major parties to have similar views on issues, and that a voter does not have a meaningful way of expressing a dissenting opinion through their vote.

As fewer choices are offered to voters, voters may vote for a candidate although they disagree with them because they disagree even more with their opponents. That will make candidates less closely reflect the viewpoints of those who vote for them.

Furthermore, one-party rule is more likely to lead to radical changes in government policy even though the changes are favoured only by a plurality or a bare majority of the voters, but a multi-party system usually requires more consensus to make dramatic changes in policy.

Wasted votes

Wasted votes are those cast for candidates who are virtually sure to lose in a safe seat, and votes cast for winning candidates in excess of the number required for victory. Plurality voting systems function on a "winner-takes-all" principle, which means that the party of the losing candidate in each riding receives no representation in government, regardless of the number of votes they received.^[12] For example, in the UK general election of 2005, 52% of votes were cast for losing candidates and 18% were excess votes, a total of 70% wasted votes. That is perhaps the most fundamental criticism of FPTP since a large majority of votes may play no part in determining the outcome.^[13] Alternative electoral systems, such as Proportional Representation, attempt to ensure that almost all of the votes are effective in influencing the result, which minimizes vote wastage.^[14] Such a system decreases disproportionality in election results and is credited for increasing voter turnout.^[15]

Voter turnout

Political apathy is prevalent in plurality voting systems such as FPTP.^[16] Studies suggest that plurality voting system fails to incentivize citizens to vote, which results in very low voter turnouts.^[16] Under this system, many people feel that voting is an empty ritual that has no influence on the composition of legislature.^[13] Voters are not assured that the number of seats that political parties are accorded will reflect the popular vote, which disincentivizes them from voting and sends the message that their votes are not valued, and participation in elections does not seem necessary.^[16]

Strategic voting

This is when a voter decides to vote in a way that does not represent their true preference or choice, motivated by an intent to influence election outcomes.^[17] Strategic behaviour by voters can and does influence the outcome of voting in different plurality voting systems. Strategic behaviour is when a voter casts their vote for a different party or alternative district/constituency/riding^{[clarification needed]} in order to induce, in their opinion, a better outcome. An example of this is when a person really likes party A but votes for party B because they do not like party C or D or because they believe that party A has little to no chance of winning.^[18] This can cause the outcome of very close votes to be swayed for the wrong reason. This might have had an impact on the 2000 United States election that was essentially decided by fewer than 600 votes, with the winner being President Bush. When voters behave in a strategic way and expect others to do the same, they end up voting for one of the two leading candidates, making the Condorcet alternative more likely to be elected.^[18] The prevalence of strategic voting in an election makes it difficult to evaluate the true political state of the population, as their true political ideologies are not reflected in their votes.^[8]

Gerrymandering

Because FPTP permits a high level of wasted votes, an election under FPTP is easily gerrymandered unless safeguards are in place.^[19] In gerrymandering, a party in power deliberately manipulates constituency boundaries to increase the number of seats that it wins unfairly.

In brief, if a governing party G wishes to reduce the seats that will be won by opposition party O in the next election, it can create a number of constituencies in each of which O has an overwhelming majority of votes. O will win these seats, but many of its voters will waste their votes. Then, the rest of the constituencies are designed to have small majorities for G. Few G votes are wasted, and G will win many seats by small margins. As a result of the gerrymander, O's seats have cost it more votes than G's seats.

Efficiency gap

The efficiency gap measures gerrymandering and has been scrutinized in the Supreme Court of the United States.^[20]^[21] The efficiency gap is the difference between the two parties' wasted votes, divided by the total number of votes.^[22]^[23]

Manipulation charges

The presence of spoilers often gives rise to suspicions that manipulation of the slate has taken place. The spoiler may have received incentives to run. A spoiler may also drop out at the last moment, which induces charges that such an act was intended from the beginning. Voters who are uninformed do not have a comparable opportunity to manipulate their votes as voters who understand all opposing sides, understand the pros and cons of voting for each party.

Spoiler effect

The spoiler effect is the effect of vote splitting between candidates or ballot questions with similar ideologies.^[12] One spoiler candidate's presence in the election draws votes from a major candidate with similar politics, which causes a strong opponent of both or several to win.^[12] Smaller parties can disproportionately change the outcome of an FPTP election by swinging what is called the 50-50% balance of two party systems by creating a faction within one or both ends of the political spectrum. This shifts the winner of the election from an absolute majority outcome to a plurality outcome. Due to the spoiler effect, the party that holds the unfavourable ideology by the majority will win, as the majority of the population would be split between the two parties with the similar ideology.^[12] In comparison, electoral systems that use proportional representation have small groups win only their proportional share of representation.

Issues specific to particular countries

Solomon Islands

In August 2008, Sir Peter Kenilorea commented on what he perceived as the flaws of a first-past-the-post electoral system in the Solomon Islands:

An... underlying cause of political instability and poor governance, in my opinion, is our electoral system and its related problems. It has been identified by a number of academics and practitioners that the First Past the Post system is such that a Member elected to Parliament is sometimes elected by a small percentage of voters where there are many candidates in a particular constituency. I believe that this system is part of the reason why voters ignore political parties and why candidates try an appeal to voters' material desires and relationships instead of political parties.... Moreover, this system creates a political environment where a Member is elected by a relatively small number of voters with the effect that this Member is then expected to ignore his party's philosophy and instead look after that core base of voters in terms of their material needs. Another relevant factor that I see in relation to the electoral system is the proven fact that it is rather conducive, and thus has not prevented, corrupt elections practices such as ballot buying.
— "Realising political stability", Sir Peter Kenilorea, Solomon Star, 30 August 2008

International examples

The United Kingdom continues to use the first-past-the-post electoral system for general elections, and for local government elections in England and Wales. Changes to the UK system have been proposed, and alternatives were examined by the Jenkins Commission in the late 1990s. After the formation of a new coalition government in 2010, it was announced as part of the coalition agreement that a referendum would be held on switching to the alternative vote system. However the alternative vote system was rejected 2-1 by British voters in a referendum held on 5 May 2011.

Canada also uses FPTP for national and provincial elections. In May 2005 the Canadian province of British Columbia had a referendum on abolishing single-member district plurality in favour of multi-member districts with the Single Transferable Vote system after the Citizens' Assembly on Electoral Reform made a recommendation for the reform. The referendum obtained 57% of the vote, but failed to meet the 60% requirement for passing. A second referendum was held in May 2009, this time the province's voters defeated the change with 39% voting in favour.

An October 2007 referendum in the Canadian province of Ontario on adopting a Mixed Member Proportional system, also requiring 60% approval, failed with only 36.9% voting in favour. British Columbia again called a referendum on the issue in 2018 which was defeated by 62% voting to keep current system.

Northern Ireland, Scotland, Wales, the Republic of Ireland, Australia and New Zealand are notable examples of countries within the UK, or with previous links to it, that use non-FPTP electoral systems (Northern Ireland, Scotland and Wales use FPTP in United Kingdom general elections, however).

Nations which have undergone democratic reforms since 1990 but have not adopted the FPTP system include South Africa, almost all of the former Eastern bloc nations, Russia, and Afghanistan.

List of countries

Countries that use plurality voting to elect the lower or only house of their legislature include:^[24] (Some of these may be undemocratic systems where there is effectively only one candidate allowed anyway.)

References

^ "Plurality-Majority Systems". Mtholyoke.edu. Retrieved 8 May 2010.
^ ^a ^b Cooper, Duane; Zillante, Arthur (January 2012). "A comparison of cumulative voting and generalized plurality voting". Public Choice. 150 (1–2): 363–383. doi:10.1007/s11127-010-9707-5. ISSN 0048-5829. S2CID 154416463.
^ Dulay, Dean; Go, Laurence (1 August 2021). "First among equals: The first place effect and political promotion in multi-member plurality elections". Journal of Public Economics. 200: 104455. doi:10.1016/j.jpubeco.2021.104455. ISSN 0047-2727. S2CID 236254332.
^ "The Global Distribution of Electoral Systems". Aceproject.org. 20 May 2008. Retrieved 8 May 2010.
^ Roskin, Michael, Countries and Concepts (2007)
^ "Reckless Out Amid UKIP Frustration at System". Sky News. Retrieved 8 May 2015.
^ Dolez, Bernard; Laurent, Annie; Blais, André (1 April 2017). "Strategic voting in the second round of a two-round system: The 2014 French municipal elections". French Politics. 15 (1): 27–42. doi:10.1057/s41253-016-0010-9. ISSN 1476-3427. S2CID 151584816.
^ ^a ^b Blais, André; Nadeau, Richard; Gidengil, Elisabeth; Nevitte, Neil (1 September 2001). "Measuring strategic voting in multiparty plurality elections". Electoral Studies. 20 (3): 343–352. doi:10.1016/S0261-3794(00)00017-2. ISSN 0261-3794.
^ Rosenbaum, David E. (24 February 2004). "The 2004 Campaign: the Independent; Relax, Nader Advises Alarmed Democrats, but the 2000 Math Counsels Otherwise". The New York Times. Retrieved 8 May 2010.
^ Grofman, Bernard; Blais, André; Bowler, Shaun (5 March 2009). Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States. Springer Science & Business Media. ISBN 978-0-387-09720-6.
^ ^a ^b Blais, André (2008). To keep or to change first past the post? : the politics of electoral reform. Oxford University Press. ISBN 978-0-19-953939-0. OCLC 470918525.
^ ^a ^b ^c ^d Verma, Dhruv (1 January 2021). "Reflecting People's Will: Evaluating elections with computer aided simulations". Open Political Science. 4 (1): 228–237. doi:10.1515/openps-2021-0021. ISSN 2543-8042. S2CID 236980393.
^ ^a ^b Whitelock, Amy; Whitelock, Jeryl; van Heerde, Jennifer (6 April 2010). Harris, Phil (ed.). "The influence of promotional activity and different electoral systems on voter turnout: A study of the UK and German Euro elections". European Journal of Marketing. 44 (3/4): 401–420. doi:10.1108/03090561011020499. ISSN 0309-0566.
^ Blais, André; Anduiza, Eva (25 June 2013), "Voter Turnout", Political Science, Oxford University Press, doi:10.1093/obo/9780199756223-0066, ISBN 978-0-19-975622-3, retrieved 15 April 2022
^ Blais, André (1 June 2006). "What affects voter turnout?". Annual Review of Political Science. 9 (1): 111–125. doi:10.1146/annurev.polisci.9.070204.105121. ISSN 1094-2939.
^ ^a ^b ^c Kwiatkowska, Agnieszka; Cześnik, Mikołaj (16 December 2020). "Electoral System, Political Knowledge and Voter Turnout— Complex Liaisons". Polish Sociological Review. 212 (4): 425–444. doi:10.26412/psr212.03. ISSN 1231-1413.
^ Hartvigsen, David (2008). "The Manipulation of Voting Systems". Journal of Business Ethics. 80 (1): 13–21. doi:10.1007/s10551-007-9438-9. ISSN 0167-4544. JSTOR 41219187. S2CID 153895999.
^ ^a ^b Bassi, Anna (2015). "Voting Systems and Strategic Manipulation: an Experimental Study". Journal of Theoretical Politics. 27: 58–85. doi:10.1177/0951629813514300. S2CID 4471874.
^ Johnston, Ron; Rossiter, David; Pattie, Charles; Dorling, Danny (2002). "Labour electoral landslides and the changing efficiency of voting distributions". Transactions of the Institute of British Geographers. 27 (3): 336–361. Bibcode:2002TrIBG..27..336J. doi:10.1111/1475-5661.00058. ISSN 1475-5661.
^ "Here's how the Supreme Court could decide whether your vote will count". The Washington Post.
^ McGhee, Eric (2020). "Partisan Gerrymandering and Political Science". Annual Review of Political Science. 23: 171–185. doi:10.1146/annurev-polisci-060118-045351.
^ Stephanopoulos, Nicholas; McGhee, Eric (2014). "Partisan Gerrymandering and the Efficiency Gap". University of Chicago Law Review. 82: 831–900. SSRN 2457468. Wasted votes and efficiency gap are defined pp. 850–852.
^ Stephanopoulos, Nicholas (2 July 2014). "Here's How We Can End Gerrymandering Once and for All". The New Republic. Retrieved 22 November 2016.
^ "Electoral Systems". ACE Electoral Knowledge Network. Archived from the original on 26 August 2014. Retrieved 3 November 2015.

The fatal flaws of Plurality (first-past-the-post) electoral systems – Proportional Representation Society of Australia

[:0-1] "Plurality-Majority Systems". Mtholyoke.edu. Retrieved 8 May 2010.

[:7-2] Cooper, Duane; Zillante, Arthur (January 2012). "A comparison of cumulative voting and generalized plurality voting". Public Choice. 150 (1–2): 363–383. doi:10.1007/s11127-010-9707-5. ISSN 0048-5829. S2CID 154416463.

[3] Dulay, Dean; Go, Laurence (1 August 2021). "First among equals: The first place effect and political promotion in multi-member plurality elections". Journal of Public Economics. 200: 104455. doi:10.1016/j.jpubeco.2021.104455. ISSN 0047-2727. S2CID 236254332.

[4] "The Global Distribution of Electoral Systems". Aceproject.org. 20 May 2008. Retrieved 8 May 2010.

[5] Roskin, Michael, Countries and Concepts (2007)

[6] "Reckless Out Amid UKIP Frustration at System". Sky News. Retrieved 8 May 2015.

[7] Dolez, Bernard; Laurent, Annie; Blais, André (1 April 2017). "Strategic voting in the second round of a two-round system: The 2014 French municipal elections". French Politics. 15 (1): 27–42. doi:10.1057/s41253-016-0010-9. ISSN 1476-3427. S2CID 151584816.

[:5-8] Blais, André; Nadeau, Richard; Gidengil, Elisabeth; Nevitte, Neil (1 September 2001). "Measuring strategic voting in multiparty plurality elections". Electoral Studies. 20 (3): 343–352. doi:10.1016/S0261-3794(00)00017-2. ISSN 0261-3794.

[9] Rosenbaum, David E. (24 February 2004). "The 2004 Campaign: the Independent; Relax, Nader Advises Alarmed Democrats, but the 2000 Math Counsels Otherwise". The New York Times. Retrieved 8 May 2010.

[GrofmanBlais2009-10] Grofman, Bernard; Blais, André; Bowler, Shaun (5 March 2009). Duverger's Law of Plurality Voting: The Logic of Party Competition in Canada, India, the United Kingdom and the United States. Springer Science & Business Media. ISBN 978-0-387-09720-6.

[:6-11] Blais, André (2008). To keep or to change first past the post? : the politics of electoral reform. Oxford University Press. ISBN 978-0-19-953939-0. OCLC 470918525.

[:4-12] Verma, Dhruv (1 January 2021). "Reflecting People's Will: Evaluating elections with computer aided simulations". Open Political Science. 4 (1): 228–237. doi:10.1515/openps-2021-0021. ISSN 2543-8042. S2CID 236980393.

[:2-13] Whitelock, Amy; Whitelock, Jeryl; van Heerde, Jennifer (6 April 2010). Harris, Phil (ed.). "The influence of promotional activity and different electoral systems on voter turnout: A study of the UK and German Euro elections". European Journal of Marketing. 44 (3/4): 401–420. doi:10.1108/03090561011020499. ISSN 0309-0566.

[14] Blais, André; Anduiza, Eva (25 June 2013), "Voter Turnout", Political Science, Oxford University Press, doi:10.1093/obo/9780199756223-0066, ISBN 978-0-19-975622-3, retrieved 15 April 2022

[15] Blais, André (1 June 2006). "What affects voter turnout?". Annual Review of Political Science. 9 (1): 111–125. doi:10.1146/annurev.polisci.9.070204.105121. ISSN 1094-2939.

[:3-16] Kwiatkowska, Agnieszka; Cześnik, Mikołaj (16 December 2020). "Electoral System, Political Knowledge and Voter Turnout— Complex Liaisons". Polish Sociological Review. 212 (4): 425–444. doi:10.26412/psr212.03. ISSN 1231-1413.

[17] Hartvigsen, David (2008). "The Manipulation of Voting Systems". Journal of Business Ethics. 80 (1): 13–21. doi:10.1007/s10551-007-9438-9. ISSN 0167-4544. JSTOR 41219187. S2CID 153895999.

[:1-18] Bassi, Anna (2015). "Voting Systems and Strategic Manipulation: an Experimental Study". Journal of Theoretical Politics. 27: 58–85. doi:10.1177/0951629813514300. S2CID 4471874.

[19] Johnston, Ron; Rossiter, David; Pattie, Charles; Dorling, Danny (2002). "Labour electoral landslides and the changing efficiency of voting distributions". Transactions of the Institute of British Geographers. 27 (3): 336–361. Bibcode:2002TrIBG..27..336J. doi:10.1111/1475-5661.00058. ISSN 1475-5661.

[20] "Here's how the Supreme Court could decide whether your vote will count". The Washington Post.

[21] McGhee, Eric (2020). "Partisan Gerrymandering and Political Science". Annual Review of Political Science. 23: 171–185. doi:10.1146/annurev-polisci-060118-045351.

[82UofCLawReview-22] Stephanopoulos, Nicholas; McGhee, Eric (2014). "Partisan Gerrymandering and the Efficiency Gap". University of Chicago Law Review. 82: 831–900. SSRN 2457468. Wasted votes and efficiency gap are defined pp. 850–852.

[NewRepublic20140702-23] Stephanopoulos, Nicholas (2 July 2014). "Here's How We Can End Gerrymandering Once and for All". The New Republic. Retrieved 22 November 2016.

[24] "Electoral Systems". ACE Electoral Knowledge Network. Archived from the original on 26 August 2014. Retrieved 3 November 2015.

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