Vote splitting

Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates, and increases the chance of winning for a dissimilar candidate.

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Vote splitting most easily occurs in plurality voting (also called first-past-the-post) in which each voter indicates a single choice and the candidate with the most votes wins, even if the winner does not have majority support.[1] For example, if candidate A1 receives 30% of the votes, similar candidate A2 receives another 30% of the votes, and dissimilar candidate B receives the remaining 40% of the votes, plurality voting declares candidate B as the winner, even though 60% of the voters prefer either candidate A1 or A2.

Under such systems vote pairing (also called vote swapping, co-voting or peer to peer voting) can mitigate the effect, but it requires two voters in different districts to agree, and identifying probabilities of candidates winning in those districts. A vote swap effectively preserves the total support for each party but moved it to where it is most effective. It is legal and practiced in US [2], Canadian [3] & especially UK elections.[4]

Cardinal voting methods are immune to vote splitting, since each candidate is rated independently of each other.[5] Pairwise-counting Condorcet methods minimize vote splitting effects.[6][1] Plurality-runoff voting methods (like Exhaustive ballot, Two-round system/Top-two primary,[1] Instant-runoff voting,[5] Supplementary vote, and Contingent vote) still suffer from vote-splitting in each round, but can somewhat reduce its effects compared to single-round plurality voting.[6]

A well-known effect of vote splitting is the spoiler effect, in which a popular candidate loses an election by a small margin because a less-popular similar candidate attracts votes away from the popular candidate, allowing a dissimilar candidate to win. As a result, the notion of vote splitting is controversial because it can discourage third party candidates.

Strategic nomination takes advantage of vote splitting to defeat a popular candidate by supporting another similar candidate.

Vote splitting is one possible cause for an electoral system failing the independence of clones or independence of irrelevant alternatives fairness criteria.

Vote splitting and electoral systems

Different electoral systems have different levels of vulnerability to vote splitting.

Plurality voting

Vote splitting most easily occurs in plurality voting because the ballots gather only the least bad preference of the voter.[7] In the United States vote splitting commonly occurs in primary elections.[6] The purpose of primary elections is to eliminate vote splitting among candidates in the same party before the general election. If primary elections or party nominations are not used to identify a single candidate from each party, the party that has more candidates is more likely to lose because of vote splitting among the candidates from the same party. Primary elections occur only within each party and so vote splitting can still occur between parties in the secondary election. In open primaries, vote splitting occurs between all candidates.

In addition to applying to single-winner voting systems (such as used in the United Kingdom, the United States and Canada), a split vote can occur in proportional representation methods that use election thresholds, such as in Germany, New Zealand and Turkey. In those cases, "fringe" parties that do not meet the threshold can take away votes from larger parties with similar ideologies.

Ordinal voting methods

When ranked ballots are used, voters can vote for a minor party candidate as their first choice and indicate their order of preference for the remaining candidates, without regard ro whether a candidate is in a major political party. For example, voters who support a very conservative candidate can select a somewhat-conservative candidate as their second choice, thus minimising the chance that their vote will result in the election of a liberal candidate.

Runoff voting is less vulnerable to vote splitting than plurality voting, but vote splitting can occur in any round of runoff voting.

Vote splitting rarely occurs when the chosen electoral system uses [ranked ballots and a pairwise-counting method, such as a Condorcet method.[6] Pairwise counting methods do not involve distributing each voter's vote between the candidates. Instead, pairwise counting methods separately consider each possible pair of candidates, for all possible pairs. For each pair of candidates there is a count for how many voters prefer the first candidate (in the pair) to the second candidate and how many voters have the opposite preference. The resulting table of pairwise counts eliminates the step-by-step distribution of votes, which facilitates vote splitting in other voting methods.

Voting methods that are vulnerable to strategic nomination, especially methods that fail independence of clones, are vulnerable to vote splitting. Vote splitting also can occur in situations that do not involve strategic nomination, such as talent contests (such as American Idol) in which earlier rounds of voting determine the current contestants.

Cardinal voting methods

Cardinal voting methods require an independent score to be given to candidates, as opposed to a ranking. The three primary methods are approval voting, with a range between 0-1, score voting with an arbitrary range, and STAR voting.

All cardinal voting methods are immune to vote splitting, as each candidate is evaluated independently of each other candidate.

Historical examples
  • When the cities of Fort William and Port Arthur merged and (in 1969) voted on a name for the new town, the vote was split between the popular choices of "Lakehead" and "The Lakehead", allowing the third option to win, creating the town of Thunder Bay, Ontario.[8]
  • In 1987, Roh Tae-woo won the South Korean presidential election with just under 36% of the popular vote because his two main rivals split the vote.
  • In the 2000, spoiler candidate Ralph Nader is believed to have split votes away from Democratic candidate Al Gore, contributing to the victory of Republican candidate George W. Bush.[9]
  • In the 2000 presidential election in Taiwan, James Soong left Kuomintang (KMT) party and ran as an independent against KMT's candidate Lien Chan. This caused vote-splitting among KMT voters and resulted in victory for Democratic Progressive Party's candidate, Chen Shui-bian. It is the first time in Taiwan history that the KMT did not win a presidential election, and it became the opposition party.
  • In the 2002 presidential election in France, the left-wing vote was fragmented among the Socialist Party and several smaller parties, relegating the most successful left-wing candidate, Lionel Jospin, to third place, and precipitating a runoff between two right-wing candidates, incumbent president and RPR candidate Jacques Chirac, and FN candidate Jean-Marie Le Pen. The total vote for the two candidates advancing to the runoff totaled less than forty percent of the votes cast in the first round.
  • In the special 2003 California gubernatorial race won by Republican Arnold Schwarzenegger, which did not involve a primary election and which listed 135 candidates on the ballot, concerns about vote splitting caused the Democrats to withdraw all but one of their major candidates and the Republicans to withdraw most of their candidates. Likewise, many supporters of Republican Tom McClintock changed their mind at the last minute and voted for Schwarzenegger for fear of the Democratic candidate, Cruz Bustamante, winning.
  • From 1993 to 2004, the conservative vote in Canada was split between the Progressive Conservatives and the Reform (later the Alliance) Party. That allowed the Liberal Party to win almost all seats in Ontario and to win three successive majority governments.
  • Similarly, in Quebec, it is argued that the success of the Bloc Québécois in elections from 1993 to 2008 was because of the federalist vote being split between the Liberals and the Conservatives.
  • In the 2004 Philippine presidential election, those who were opposed to Gloria Macapagal-Arroyo's presidency had their vote split into the four candidates, thereby allowing Arroyo to win. The opposition had film actor Fernando Poe, Jr. as its candidate, but Panfilo Lacson refused to give way and ran as a candidate of a breakaway faction of the Laban ng Demokratikong Pilipino. Arroyo was later accused of vote-rigging.
  • In the 2010 special election for the 1st congressional district of Hawaii, the Republican Charles Djou won against Democrats Colleen Hanabusa and Ed Case.
  • In the 2012 Egyptian presidential election, the two candidates who qualified for the runoff election, Freedom and Justice Party candidate Mohamed Morsi (24.8%) and the independent candidate Ahmed Shafik (23.7%), each received more votes than any other candidate, but they failed to get enough votes to prove that each winning candidate was actually more popular than the Dignity Party candidate Hamdeen Sabahi (20.7%), the independent candidate Abdel Moneim Aboul Fotouh (17.5%), or the independent candidate Amr Moussa (11.1%).
  • In the 1994 European Elections, Richard Huggett stood as a "Literal Democrat" candidate for the Devon and East Plymouth seat, with the name playing on that of the much larger Liberal Democrats. Huggett took over 10,000 votes, and the Liberal Democrats lost by 700 votes to the Conservative Party. The Registration of Political Parties Act 1998, brought in after the election, introduced a register of political parties and ended the practice of deliberately confusing party descriptions.[10]
  • In Australia, the 1918 Swan by-election saw the conservative vote split between the Country Party and Nationalist Party, which allowed the Australian Labor Party to win the seat. That led the Nationalist government to implement preferential voting in federal elections to allow Country and Nationalist voters to transfer preferences to the other party and to avoid vote splitting.[11] Today, the Liberal Party and National Party rarely run candidates in the same seats, which are known as three-cornered contests.

Spoiler effect

The spoiler effect is the effect of vote splitting between candidates or ballot questions[n 1] who often have similar ideologies. One spoiler candidate's presence in the election draws votes from a major candidate with similar politics, thereby causing a strong opponent of both or several to win.[12][13][14][15] The minor candidate causing this effect is referred to as a spoiler.[n 2] However, short of any electoral fraud, this presents no grounds for a legal challenge.

The spoiler effect is a problem in plurality voting systems because they enable a candidate to win with less than half of the vote.

The problem also exists in instant-runoff voting, also known as ranked-choice voting or alternative vote,[14][16][17][18][19][20] though it is reduced, because voters are allowed to rank their candidate choices, with their vote transferring to their second choice if their first choice does not win, to their third choice if their second choice does not win, and so on. Other preferential voting or ranked ballot voting systems also suffer from variations of the spoiler effect, as they fail the independence of irrelevant alternatives (IIA) criterion (see § Mathematical definitions).

The problem does not exist in cardinal voting methods like approval voting, score voting, or majority judgment, since the rating of each candidate is independent of the ratings of other candidates.

Relationship with other effects

The spoiler candidate takes votes away from a more viable[n 3] candidate or candidates, a common effect called vote splitting. If one opposing candidate is ideologically or politically similar and therefore receives far fewer votes than other opposing candidates to the spoiler candidate, vote splitting has a spoiler effect.

In some cases, even though spoiler candidates cannot win themselves, their influence upon the voters may enable the candidate to determine deliberately the more viable candidate who wins the election, a situation known as a kingmaker scenario. With a first-past-the-post voting system, that is particularly feasible when spoiler candidates recommend tactical voting or run on a false manifesto to bolster the prospects for their secretly-preferred candidate to win.

In a preferential voting system, voters can feel more inclined to vote for a minor party or independent as their first choice and can record a preference between the remaining candidates, whether they are in a major or established party or not. For example, voters for a minor left-wing candidate might select a major left-wing candidate as their second choice, thus minimizing the probability that their vote will result in the election of a right-wing candidate, or voters for an independent candidate perceived as libertarian, or simply as the voter prefers that ideology might select a particular libertarian candidate as their second choice, thus minimizing the probability of an authoritarian candidate being elected. Approval voting and proportional representation systems can also reduce the spoiler effect.

One of the main functions of political parties is to mitigate the effect of spoiler-prone voting methods by winnowing on a local level the contenders before the election. Each party nominates at most one candidate per office since each party expects to lose if they nominate more than one.[n 4] In some cases, a party can expect to "lose" by "suffering a rival elected opponent" if they nominate more than zero, where two opponents exist and one is considered a candidate they can "work with" — a party may prefer the candidate who would win if the party nominates zero.[n 5]

Thus, empirical observations of the frequency of spoiled elections do not provide a good measure of how prone to spoiling a particular voting method is, since the observations omit the relevant information about potential candidates who did not run because of not wanting to spoil the election.

Mathematical definitions
Further information on the mathematics of elections: Decision theory and Social choice theory

Possible mathematical definitions for the spoiler effect include failure of the independence of irrelevant alternatives (IIA) axiom, and vote splitting.

Arrow's impossibility theorem states that rank-voting systems are unable to satisfy the independence of irrelevant alternatives criterion without exhibiting other undesirable properties as a consequence. However, different voting systems are affected to a greater or lesser extent by IIA failure. For example, instant runoff voting is considered to have less frequent IIA failure than First Past the Post (also known as Plurality Rule). The independence of Smith-dominated alternatives (ISDA) criterion is much weaker than IIA; unlike IIA, some ranked-ballot voting methods can pass ISDA.

A possible definition of spoiling based on vote splitting is as follows: Let W denote the candidate who wins the election, and let X and S denote two other candidates. If X would have won had S not been one of the nominees, and if (most of) the voters who prefer S over W also prefer X over W (either S>X>W or X>S>W), then S is a spoiler. Here is an example to illustrate: Suppose the voters' orders of preference are as follows:

33%: S>X>W 15%: X>S>W 17%: X>W>S 35%: W>X>S

The voters who prefer S over W also prefer X over W. W is the winner under Plurality Rule, Top Two Runoff, and Instant Runoff. If S is deleted from the votes (so that the 33% who ranked S on top now rank X on top) then X would be the winner (by 65% landslide majority). Thus S is a spoiler with these three voting methods.

Spoiler effect in American elections

A 2014 analysis by Philip Bump for the Washington Post found that 1.5% of general election races in the U.S. from 2006 to 2012 were spoiled by third-party candidates.[21]

Historically, the Democratic and Republican parties have benefited from the alleged spoiler effect created by the existing U.S. plurality voting system.[22][23] This benefit is based in the theory that not voting for other parties and for independents and that third parties and independent candidates themselves declining to run, means to avoid "wasting votes" or splitting the vote causing an election result not wanted.

There are third-party candidates who have been accused of denying victory to a major nominee in U.S. Presidential Elections; a notable case among these is the 1912 election, where Progressive Party candidate Theodore Roosevelt won almost 700,000 votes more than did the Republican incumbent, William Howard Taft,[24] and thus it could be said that Taft was the spoiler for Roosevelt in that election. This argument worried Republicans, who, after Woodrow Wilson won the 1912 election, became concerned that Roosevelt might return to split the Republican vote again.[25]

In 1968, George Wallace ran for president as the American Independent Party's nominee. He received numerous votes from Southern demographics that typically voted for Democratic candidates, thereby undercutting the candidacy of that election's Democratic nominee, Hubert Humphrey.[26]

Bush, Gore, and Nader (2000 U.S. presidential election)

The 2000 U.S. Presidential election is often cited as an example of the spoiler effect. In that election, Al Gore, the Democratic candidate, received more popular votes than George W. Bush, the Republican candidate, but lost in the electoral college. In the state of Florida, the final certified vote count showed Bush with just 537 more votes than Gore.[27] Because Bush defeated Gore in Florida, he won the state, received more votes in the electoral college, and became president of the United States.

Gore supporters argued that had candidate Ralph Nader, a progressive, not run in the election, the majority of the 97,421 votes he received in Florida would have been cast for Gore. Thus, they contend that Nader's candidacy spoiled the election for Gore by taking away enough votes from Gore in Florida to swing the election to Bush. Their argument is bolstered by a poll of Nader voters, asking them for whom they would have voted had Nader not run, which said 45 percent of Nader voters would have voted for Gore, 27 percent would have voted for Bush, and the rest would not have voted.[28]

Nader himself and many of his supporters argued that most Nader voters would either have chosen another minor party candidate or abstained from voting, had Nader not been on the ballot. All other third party candidates on the ballot in Florida received more than the 537 vote difference between Bush and Gore.[29] Still, some observers began to refer to the spoiler effect as the "Nader effect" after the 2000 election.[30][31][32] A 2006 study found that at least 40% of Nader voters in Florida would have voted for Bush if Nader had not run, while the other 60% would have voted for Gore. The study concluded that this 60% "did indeed spoil the 2000 presidential election for Gore but only because of highly idiosyncratic circumstances, namely, Florida’s extreme closeness."[33]

Other US elections
  • In the 1884 presidential election the Prohibition Party's presidential nominee, former Republican Governor John St. John, took 147,482 votes with 25,006 votes coming from New York where Grover Clevland only defeated James G. Blain by 1,149 votes. Republicans were angered by John St. John's party switching causing their first presidential defeat since 1856 that on November 27, 1884 an effigy of him was burned in Topeka, Kansas in front of a crowd of three thousand people.[34]
  • In the 1934 Oregon gubernatorial election, Republican Peter Zimmerman ran as an independent, receiving 31.7% of the vote compared to Democratic victor Charles Martin's 38.6% and Republican nominee Joe Dunne's 28.7%. Altogether, the Republicans received 60.3% of the vote.
  • A similar trend was seen in the 1990 Oregon gubernatorial election when conservative activist Al Mobley ran as an independent and received 144,062 votes for 13.0% of the vote while in the same election Democrat Barbara Roberts defeated Republican David B. Frohnmayer by 64,103 votes.
  • In the 1992 presidential election Ross Perot ran as an independent and due to his conservative beliefs was considered to be a spoiler candidate that cost George H. W. Bush the election. However, a 1999 study in the American Journal of Political Science estimated that Perot's candidacy hurt the Clinton campaign, reducing "Clinton's margin of victory over Bush by seven percentage points."[35]
  • Marshall Coleman, a moderate Republican, ran in 1994 for Virginia's senate seat as an independent and received 235,324 votes for 11.44% while in the same election Democratic Chuck Robb defeated Republican Oliver North by 56,163 votes.
  • In 2008, Democrat Al Franken was elected the junior senator from Minnesota, defeating Norm Coleman by only 0.1%. Independent candidate Dean Barkley received over 15% of the vote, and a 2014 analysis by Time found that without Barkley in the race, Franken would have lost the election to Coleman.[36]
  • In 2010, Green Party candidate Bill Scheurer ran for Illinois 8th Congressional District against Democratic incumbent Melissa Bean. Republican Joe Walsh won the election in a surprising upset with only a 291-vote (0.1%) difference with Bean, while Scheurer received 6,494 votes (3.2%).
  • As a result of the 2011 Wisconsin protests and subsequent recall elections, the Wisconsin Republican Party has encouraged spoiler candidates to run in the recall elections on the Democrat ticket in order to force the Democrats into a primary election. Republicans argued that this would even the playing field in the recalls, as incumbents facing recall did not have the time to campaign due to their work load in the state senate.[37]
  • In Maine's 2010 and 2014 gubernatorial elections Eliot Cutler ran as a left-wing independent. In the 2010 election Paul LePage narrowly defeated him with 218,065 votes to 208,270 votes with the Democratic nominee Libby Mitchell receiving 109,387 votes and possibly spoiling the election for Cutler. However, in 2014 Cutler performed worse and only received 51,518 votes, but it was still greater than the difference between LePage and Mike Michaud causing a possible spoiler effect. These elections lead to an increase support in ranked choice voting leading to Maine adopting the voting system due to LePage's unpopularity and him winning twice only with pluralities.[38][39][40][41][42]
  • Several races in the 2014 election cycle were allegedly influenced by spoiler candidates, most notably Hawaii's gubernatorial elections and the Kansas senatorial race. In the Mississippi senatorial Republican primary, a paper candidate, Thomas Carey, who received less than two percent of the vote prevented both top contenders, incumbent Thad Cochran and challenger Chris McDaniel, from avoiding a runoff. Had the Carey not run, the race between McDaniel and Cochran would have avoided a runoff.
  • In both the 2013 Virginia gubernatorial election and the 2014 Virginia US Senate Election, Libertarian Robert Sarvis received a number of votes greater than the difference between the Republican and Democratic candidates.[43][44] Given the similarity in Republican and Libertarian views, it is likely that the Republican would have won each election if not for the inclusion of Sarvis on the ballot.
  • In the 2016 New Hampshire Senate election, conservative independent candidate Aaron Day won about 18,000 votes. Given his political leanings, it is likely that the vast majority of his voters otherwise would have voted for incumbent Senator Kelly Ayotte, who lost to Governor Maggie Hassan by about 1,000 votes, thus costing Ayotte reelection.

Other countries

In the German presidential election of 1925, Communist Ernst Thälmann refused to withdraw his candidacy although it was extremely unlikely that he would have won although the leadership of the Communist International urged him not to run. In the second (and final) round of balloting, Thälmann won 1,931,151 votes, or 6.4 percent. Centrist candidate Wilhelm Marx won 13,751,605, or 45.3 percent. The independent candidate Paul von Hindenburg, endorsed by the German National People's Party and German People's Party shared 14,655,641 votes, or 48.3 percent.[45] If most of Thälmann's supporters had voted for Marx, instead of Hindenburg, Marx would have won the election. The election of 1925 had great significance because in 1933 Hindenburg appointed Adolf Hitler as chancellor and then died the following year, giving Hitler unchecked control of the German government.[46] By contrast, Marx, who was dedicated to republican democracy, lived until 1946.

In New Zealand, there have been two notable cases of the spoiler effect. In the 1984 general election, the free-market New Zealand Party deliberately ran for office to weaken support former Prime Minister Robert Muldoon, the incumbent. Later, the 1993 general election saw the New Zealand Labour Party's vote split by The Alliance, which has been attributed to the vagaries of the plurality vote. In response to these problems, New Zealand has since adopted mixed-member proportional representation.

Likewise, in France, the 2002 presidential elections have been cited as a case of the spoiler effect: the numerous left-wing candidates, such as Christiane Taubira and Jean-Pierre Chevènement, both from political parties allied to the French Socialist Party, or the three candidates from Trotskyist parties, which altogether totalled around 20%, have been charged with making Lionel Jospin, the Socialist Party candidate, lose the two-round election in the first round to the benefit of Jean-Marie Le Pen, who was separated from Jospin by only 0.68%. Some also cite the case of some districts in which the moderate right and the far right had more than half of the votes together, but the left still won the election; they accuse the left of profiting from the split.

In Hong Kong,vote-splitting is very common for the pro-democracy camp, which caused it to suffer greatly in many elections, including the 2016 Hong Kong legislative election and the 2015 Hong Kong local elections. Pro-democracy supporters typically have different ideologies and suffer from factional disputes that are exacerbated after the advent of localist groups. However, many have wider aggregate support fewer seats are earned than the pro-Beijing camp, an example being in Kowloon East in which pro-democracy parties got over 55% of cast ballots but won only 2 seats out of 5.

In Canada, in the 2004 federal election, the right-wing Conservative Party won power with 29.63% of the popular vote. Its two major left-wing competitors, the Liberal Party and the New Democratic Party, won respectively 36.73% and 15.68% of the vote. Similar vote splits between the two major left-wing parties continued to assist the Conservative Party in maintaining power in the 2006, 2008, and 2011 federal elections, despite most of the popular vote going to left-wing parties in each race.

Also in Canada, the 2015 provincial election in Alberta saw the left-wing New Democratic Party win 62% of the seats with 40.6% of the province's popular vote after a division within the right-wing Progressive Conservative Party, which left it with only 27.8% of the vote, and its breakaway movement, the Wildrose Party, with 24.2% of the vote. In 2008, the last election in which the Progressive Conservative Party had been unified, it won 52.72% of the popular vote.

In Greece, Antonis Samaras was the Minister for Foreign Affairs for the liberal conservative government of New Democracy under Prime Minister Konstantinos Mitsotakis but ended up leaving and founding the national conservative Political Spring in response to the Macedonia naming dispute, resulting in the 1993 Greek legislative election where PASOK won with its leader Andreas Papandreou making a successful political comeback, which was considered to be responsible for the Greek government debt crisis.

In the run up to 2019 UK General Election, the Brexit Party, led by former UKIP leader Nigel Farage, initially put up candidates in 600 seats after a strong showing for the newly-formed party in the 2019 European Elections, but days later, he reversed his position after Conservative British Prime Minister Boris Johnson stated that he would not consider an electoral pact with the Brexit Party. That was seen as benefiting the Conservative Party and disadvantaging the Labour Party.[47] Farage later encouraged voters not to vote for the Labour Party in areas that traditionally favoured it but voted to leave in the 2016 EU Membership Referendum but instead to vote tactically.[48] After the Conservatives' decisive victory, it was suggested by some media outlets and political analysts that Farage had acted as "kingmaker" and stalking horse and effectively won the election for the Tories, as Farage's decision avoided splitting the vote.[49][50]

gollark: Oh no. Do we have a Delta Scenario?
gollark: Apathy is apathy is apathy.
gollark: > Apathy is only one step to the better.¿
gollark: osmarks.tk did that a while ago but the frogs seem to be the same?
gollark: Ã⅔ ≠ ∞°↑↑↑↑3

See also

Notes
  1. Examples are the first past the post electoral system and in single transferable vote or similar systems with a first-preference votes winning percentage.
  2. A term designed to appeal to a wider section of the public as a result of the widespread, often national support of political parties.
  3. More viable by common public sentiment which may sometimes be indicated in opinion polls.
  4. For example, if the Democrats had nominated both Hillary Clinton and Barack Obama for U.S. President in 2008, it would have allowed the Republican candidate (John McCain) to easily win; the voters who preferred both Clinton and Obama over McCain could not have been relied on to solve the strategy coordination problem on their own.
  5. For example, in the United Kingdom, UKIP have a policy of not standing parliamentary candidates where the incumbent is a committed eurosceptic member of the large Conservative Party; however, one rebel spoiler candidate from the party, Jake Baynes, led to the defeat of David Heathcoat-Amory in Wells in the 2010 United Kingdom general election by the Liberal Democrats (UK).

References
  1. Sen, Amartya; Maskin, Eric (2017-06-08). "A Better Way to Choose Presidents" (PDF). ISSN 0028-7504. Retrieved 2019-07-20. plurality-rule voting is seriously vulnerable to vote-splitting ... runoff voting ... as French history shows, it too is highly subject to vote-splitting. ... [Condorcet] majority rule avoids such vote-splitting debacles because it allows voters to rank the candidates and candidates are compared pairwise
  2. https://slate.com/news-and-politics/2000/11/is-vote-swapping-legal.html
  3. https://www.cbc.ca/news/canada/online-vote-swapping-legal-but-voter-beware-elections-canada-warns-1.715876
  4. https://m.huffingtonpost.co.uk/entry/vote-swapping-uk-how-tactical-voting-in-a-pair_uk_5912da4ce4b0a58297e0da25
  5. Poundstone, William. (2013). Gaming the vote : why elections aren't fair (and what we can do about it). Farrar, Straus and Giroux. pp. 168, 197, 234. ISBN 9781429957649. OCLC 872601019. IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left. ... Approval voting thus appears to solve the problem of vote splitting simply and elegantly. ... Range voting solves the problems of spoilers and vote splitting
  6. Ending The Hidden Unfairness In U.S. Elections explains why plurality and runoff voting methods are vulnerable to vote splitting.
  7. "Top 5 Ways Plurality Voting Fails". The Center for Election Science. 2015-03-30. Retrieved 2017-10-07. You likely have opinions about all those candidates. And yet, you only get a say about one.
  8. About Thunder Bay, pp. 2. Retrieved 2 September 2007.
  9. "Nader Elected Bush: Why We Shouldn't Forget | RealClearPolitics". Retrieved 2017-11-26.
  10. "The Scotsman: Challenger could spell ballot paper trouble for Tories' Davis, 21 February 2005". Archived from the original on 10 January 2006. Retrieved 20 May 2006.
  11. Reilly, Benjamin (2001). Democracy in Divided Societies: Electoral Engineering for Conflict Management. Cambridge: Cambridge University Press. p. 36. 2007-07-01.
  12. Buchler, Justin (2011-04-20). Hiring and Firing Public Officials: Rethinking the Purpose of Elections. Oxford University Press, USA. ISBN 9780199759965. a spoiler effect occurs when entry by a third-party candidate causes party A to defeat party B even though Party B would have won in a two-candidate race.
  13. King, Bridgett A.; Hale, Kathleen (2016-07-11). Why Don't Americans Vote? Causes and Consequences: Causes and Consequences. ABC-CLIO. ISBN 9781440841163. Those votes that are cast for minor party candidates are perceived as taking away pivotal votes from major party candidates. ... This phenomenon is known as the 'spoiler effect'.
  14. Borgers, Christoph (2010-01-01). Mathematics of Social Choice: Voting, Compensation, and Division. SIAM. ISBN 9780898716955. Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does not do away with the spoiler problem entirely, although it ... makes it less likely
  15. Heckelman, Jac C.; Miller, Nicholas R. (2015-12-18). Handbook of Social Choice and Voting. Edward Elgar Publishing. ISBN 9781783470730. A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.
  16. Poundstone, William (2009-02-17). Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It). Farrar, Straus and Giroux. ISBN 9781429957649. IRV is excellent for preventing classic spoilers-minor candidates who irrationally tip the election from one major candidate to another. It is not so good when the 'spoiler' has a real chance of winning
  17. "The Spoiler Effect". The Center for Election Science. 2015-05-20. Retrieved 2017-01-29.
  18. "The Problem with Instant Runoff Voting". minguo.info. Retrieved 2017-01-29. After a minor party is strong enough to win, on the other hand, a vote for them could have the same spoiler effect that it could have under the current plurality system
  19. "RangeVoting.org - Example to demonstrate how IRV leads to 'spoilers', 2-party domination". www.rangevoting.org. Retrieved 2017-01-29. IRV means betraying your true favorite third party candidate pays off. Voting third party can mean wasting your vote under IRV, just like under plurality.
  20. The Center for Election Science (2013-12-02), Favorite Betrayal in Plurality and Instant Runoff Voting, retrieved 2017-01-29
  21. Bump, Philip (8 October 2014). "How often do third-party candidates actually spoil elections? Almost never". The Fix. The Washington Post. Retrieved 17 May 2017.
  22. "THE 1992 ELECTIONS: DISAPPOINTMENT -- NEWS ANALYSIS An Eccentric but No Joke; Perot's Strong Showing Raises Questions On What Might Have Been, and Might Be". The New York Times. November 5, 1992.
  23. "Nader to Crash Dems' Party?".
  24. "United States presidential election of 1912". Encyclopedia Britannica. Retrieved 10 May 2017.
  25. Nilsson, Jeff (5 May 2016). "100 Years Ago: Fear of a Republican Spoiler". Saturday Evening Post. Retrieved 10 May 2017.
  26. Belsome, Ross; Newman, Robert J. (April 2007). "Ghosts of Elections Past: Third-Party Shepherds and Stray Voters" (PDF).
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