Important elections whose results (probably) would have differed under different voting systems

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How much damage and distortion of history is being caused by the use of poor voting systems? Assess for yourself... we list a large number of elections in which poor voting systems such as plurality yielded the wrong winner. This has nothing necessarily to do with fraud or fakery; it is purely a matter of the mathematical properties of good and bad voting systems. The plurality voting system used in the USA is well known to be among the worst while range voting is one of the best.

Election Official Result What the voters actually most-wanted
Romania 2009 Presidential T.Basescu won the runoff against M.Geoana 50.33% to 49.66%. This election was extremely interesting in that (with confidence 99.9% according to our analysis) it featured at least one Condorcet cycle including both Basescu and Geoana. The third member of the cycle, Bucharest mayor Sorin Oprescu, officially finished 6th but probably would have been the winner with either approval or range voting. The one Romania wanted was either Oprescu or Antonescu (officially 3rd). The plurality+top2runoff system used made it a "waste" to vote for anybody not perceived to be in the "leading three," hence the decision by the major parties and media only to allow Antonescu, Basescu, and Geoana in the debates thus (unjustly) was the kiss of death for Oprescu.
Afghanistan 2009 Presidential Hamid Karzai "won." The election was blatantly fraudulent. Karzai under pressure from the USA and UN agreed to hold a runoff versus his top challenger A.Abdullah (initially, his stance had been that no runoff was required, since he had over 50%). However Abdullah refused to participate in the runoff, claiming it would probably again be fraudulent. With 41 candidates and a mostly-illiterate electorate this plurality+top2runoff election was inherently silly even if there had been no fraud.
French 2007 Presidential The first round (22 April) was won by N.Sarkozy with 31.2% followed by S.Royal with 25.9%. These two advanced to the second and final round. The third-place finisher, F.Bayrou, with 18.6% of the vote – and all the further even-worse finishers – were eliminated. The New York Times described Sarkozy as "rightist," Bayrou as "centrist," and Royal as "leftist." Finally, in the second round (5 May), Sarkozy won. According to an IPSOS poll ending 21 April, Bayrou would have beaten Sarkozy in a head-to-head (i.e. potential second-round) election by 52.5% to 47.5%, and this conclusion was true no matter what time the poll was taken from early March until late April. According to a CSA poll ending 20 April, a head-to-head Sarkozy v. Royal matchup – which in fact happened – would be a tossup (50%-50%), while the IFOP poll (also ending 20 April) gave a 51-49 edge to Sarkozy. The IFOP poll also indicated Bayrou would have beaten Sarkozy 55-45 head to head, and Bayrou would have beaten Royal 58-42 head-to-head. At least 9 other polls also examined a possible Bayrou-Sarkozy runoff and all also concluded Bayrou would win it. From these polls we conclude that Bayrou would have beaten either major opponent in a head to head contest and thus was the Condorcet winner. However, Bayrou was eliminated in the first round, in a clear failure of France's plurality+top2runoff system. The same pathology would also have happened with "instant runoff" at least if we restrict attention to the (31.2+25.9+18.6=75.7)% of the electorate who voted for these three only (because in a 3-candidate election with self-consistent voters, plurality+top2runoff and IRV are the same thing). Indeed an IRV exit-poll study shows IRV would have behaved almost exactly the same as the official election, also electing Sarkozy. Range voting apparently would have elected Bayrou as was shown by the results of Balinski & Laraki's Orsay experiment.
Nicaragua 2006 Presidential Daniel Ortega won with a plurality of 38% of the vote. The anti-Ortega vote was split among 4 major rivals, the top two of whom got 29% and 26%. It was generally suspected that Ortega would have lost in a runoff. Indeed quite possibly Ortega would have lost to any of his 4 major rivals in a runoff (i.e. Ortega was the Condorcet loser). But since his 38% total was above 35%, a top-2 runoff was not triggered and we did not find that out.
Mexico 2006 Presidential After 6 July the Instituto Federal Electoral officially claimed Calderon won by 0.6% margin with full count completed, but Obrador demanded a recount.
To see that this election is likely to remain disputed, consider the fact that in the 2004 USA Bush v. Kerry presidential election, one hour past midnight on election night, CNN's exit polls called the nationwide popular vote for Kerry by a >2.5% margin (based on 11027 respondents) but the official results gave it to Bush by a 2.4% margin.
Under IRV, Condorcet, range, or approval, it appears likely that either Andres M. Lopez Obrador would have won (because Patricia Mercado served as a "spoiler") or (under the latter three methods) R.Madrazo might have won (because the rightist Calderon voters would have preferred him as the "lesser evil" over the leftist Obrador, whereas the leftist Obrador voters might similarly have preferred Madrazo over Calderon, so that Madrazo in net would be preferred pairwise over every opponent). In view of both of these possibilities (more details) it is very likely Calderon's victory was merely an artifact of the plurality system.
Peru 2006 presidential Alan Garcia Perez won under plurality with separate top-2 runoff (and presumably also would have won under IRV) despite the fact that Humala won the first round, i.e. would have won a straight-plurality single election. [Incidentally, every time a top-2 runoff is won by the second finisher in the first round, that demonstrates the failure of the plain-plurality single-round system, but the plur+runoff two-round system also can fail dramatically, as here.] Lourdes Flores Nano was the clear Condorcet winner, beating every other candidate pairwise by at least a 55-45 margin according to numerous pre-election polls. She probably also would have won under Range or Approval voting. However, in a huge miscarriage of the people's will, she was eliminated in the first round, whereupon Garcia beat Humala in the runoff.
Iran 2005 Presidential Mahmoud Ahmadinejad won under plurality with separate top-2 runoff, beating Akbar Hashemi Rafsanjani by an huge 62-36 margin in the runoff despite the fact Rafsanjani won the first round with 21.0% to Ahmadinejad's 19.5%, followed by Karroubi (17.3%), Ghalibaf (13.9%), Moeen (13.8%), Larijani (5.9%), and Mehralizadeh (4.4%). [Undemocratically, many candidates were not permitted to run at all due to rejection by the Guardian Council, but the election among the remaining candidates may have been tolerably democratic.] Unclear; perhaps Karroubi. There obviously were large distortions caused by strategic voting and/or vote-splitting in the official election. You can also compare the election results to these opinion poll results to see some more large distortions.
Liberia 2005 Presidential In the plurality election, George Weah placed top with 28.4%, beating Ellen Johnson-Sirleaf (19.7%) and Charles Brumskine (13.7%). But then in the subsequent top-2 runoff, Johnson-Sirleaf won convincingly 59.4% to 40.6% over Weah (with 2.5% invalid votes). We agree Johnson-Sirleaf was the correct winner; but the fact she lost the first round to Weah demonstrates the failure of the plain plurality single-round system.
[In Puerto Rico's 2000 and 2004 governor elections, and Malawi's 2004, Kiribati's 2003, Costa Rica's 1998 and 2006, Bolivia's 1997 and 2002, Zambia's 2001, Mexico's 2000, Iceland's 1980 and 1996, Nigeria's 1979, Ghana's 1979, Colombia's 1978, Chile's 1958, Panama's 1948, 1964, and 1984, and Venezuela's 1958, 1968, 1978, and 1993 presidential elections, similar stuff happened but no second round was held, which meant it was highly unclear who "should" have won, all 23 times. It might be interesting to look at some of these more deeply. There are also suspicious S.Korea and Singapore elections of this sort.]
Romania 2004 Presidential In the plurality election, Adrian Nastase placed top with 40.9%, beating out Traian Basescu's 33.9%. But then in the subsequent top-two runoff, Basescu won 51.2% to 48.8%. We agree Basescu was the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Slovakia 2004 Presidential In the plurality election, Vladimir Meciar placed top with 32.74%, followed by Ivan Gasparovic (22.28%), Eduard Kukan (22.10%), R.Schuster (7.43%), etc. But then in the subsequent top-two runoff, Gasparovic won 59.91% to 40.09%. Gasparovic or Kukan. The fact Gasparovic lost the first round demonstrates the failure of the plain plurality single-round system, but it is by no means obvious from this data that Gasparovic "should" (or would) have beaten Kukan.
Argentina 2003 Presidential In the plurality election, Carlos S. Menem placed top with 24.34%, beating out Nestor Kirchner's 21.99%. But then Menem agreed to forfeit his victory to Kirchner because he was trailing in opinion polls and believed he would lose a subsequent runoff election. (That runoff then was canceled.) We agree Kirchner was probably the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system – and apparently it was a very obvious failure indeed if Menem was willing to forfeit without even trying to win.
France 2002 Presidential J.Chirac won under plurality with separate top-2 runoff, beating J-M. Le Pen by an enormous 82-18 margin in the runoff. Under approval or range voting, there is no question the top two instead would have been Chirac and L.Jospin, although which among these two was most preferred, is not clear. (Under Condorcet or IRV, the possibility of strategic voting muddies the picture. IRV with 15 rounds instead of just 2 would have transferred almost all the votes from the eliminated candidates to non-Le-Pen candidates, which would have caused the two final-round contenders to be candidates other than Le Pen, so in that sense IRV clearly would have been superior to top-2-runoff in this case. That would have made more sense and might have led to a different election result.) Pre-election polls had shown that a hypothetical Jospin-Chirac runoff would be too close to call, but seemed to favor Jospin. It was clear Le Pen would lose big in a runoff with either.
USA 2000 presidential George W. Bush won thanks to a 537-vote margin over Al Gore in Florida. Ralph Nader served as a "spoiler."
Also John McCain was, according to polls, more popular than either Bush or Gore and would have beaten either by 7-to-9 percent. But he failed to win the Republican Nomination, and in view of the fact that the USA's flawed plurality-voting system would have caused a third-party run to be futile, dropped out of the race. In retrospect, McCain, who had military/war experience and a strong record as a fiscal conservative, would probably have been a better match to the needs of the Nation than Bush.
Gore would have won Florida, and hence nationwide, under IRV, Range, Approval, Borda, Plurality with separate top-2 runoff, or Condorcet. (If even 1% more of the Nader voters preferred Gore than Bush, that would have been enough.) Also Gore did win nationwide in terms of the popular vote total and hence would have won if the USA did not have the "electoral college." In short, Bush's victory was purely an artifact of the electoral college combined with the use of the plurality voting system.
Taiwan 2000 presidential Chen Shui-bian won with 39.3% of the popular vote, thanks to a split of the pro-Chinese reunification vote between James Soong (36.8%) and Lien Chan (23.1%), who together received nearly 60% of the vote. Soong probably would have won under either IRV, Range, Approval, Plurality with separate top-2 runoff, or Condorcet (also probably Borda, depending on how much strategic voting happened). However, after 4 years in office, Chen Shui-bian gained popularity and was able both to survive an assassination attempt and to win re-election in 2004 versus former-rivals but now-running-mates Soong and Chan by a tiny margin (50.11% to 49.89%).
Senegal 2000 presidential Abdou Diouf won with 41.33%, followed by Abdoulaye Wade (30.97%), Moustapha Niasse (16.76%), Djibo Ka (7.08%), etc. But that was the first plurality round. In the runoff round, Wade beat Diouf 58.7% to 41.3%. We agree Wade was the correct winner; but the fact he lost the first round by a large margin then won the second by an even larger one, demonstrates the failure of the plain plurality single-round system.
Uruguay 1999 Presidential In the plurality election, Tabare Vazquez placed top with 38.51%, beating out Jorge Batlle Ibanez (31.32%), L.Alberto Lacalle (21.29%), and R.Michelini (4.36%). But in the subsequent top-2 runoff Batlle Ibanez beat Tabare Vazquez 51.59% to 44.07%. We agree Batlle Ibanez was probably the correct winner; but the fact he lost the first round by a large margin demonstrates the failure of the plain plurality single-round system.
Macedonia 1999 Presidential In the plurality election, Tito Petkovski placed top with 33.2%, beating out Boris Trajkovski (20.6%), Vasil Tupurkovski (16.0%), M.Nexipi (14.8%) etc. But in the subsequent top-2 runoff Trajkovski won 52.9% to Petkovski's 45.9%. We agree Trajkovski was probably the correct winner; but the fact he lost the first round by a large margin demonstrates the failure of the plain plurality single-round system.
Cyprus(Greek) 1998 Presidential In the plurality election, Georges Iacovou won with 40.6%, beating Glafcos Clerides (40.1%), V.Lyssarides (10.6%), etc. But in the subsequent top-2 runoff Clerides won with 50.8% over Iacovou's 49.2%. We agree Clerides was probably the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Colombia 1998 Presidential In the plurality election, Horacio Serpa Uribe placed top with 34.8%, beating out Andres Pastrana Arango with 34.4% and N.Sanin Posada De Rubio with 26.8%. But in the subsequent top-2 runoff Pastrana won 50.3% to 46.6% (with 3.1% spoiled uncounted ballots). We agree Pastrana was probably the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Moldova 1996 Presidential In the plurality election, Mircea Snegur placed top with 38.7%, beating out Petru Lucinschi (27.7%) V.Voronin (10.3%), A.Sangheli (9.5%), etc. But then in the subsequent top-two runoff, Lucinschi won 54.0% to Snegur's 46.0%. We agree Lucinschi was the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Romania 1996 Presidential In the plurality election, Ion Iliescu placed top with 32.2%, beating out Emil Constantinescu's 28.2%. But then in the subsequent top-two runoff, Constantinescu won 54.4% to 45.6%. We agree Constantinescu was the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Niger 1993 Presidential In the plurality election, Mamadou Tandja won with 34.22%, beating Mahamane Ousmane (26.59%), Mahamadou Issoufou (15.92%), and M.A.Djermakoye (15.24%). But in the subsequent top-2 runoff Ousmane won with 54.46% over Tandja. We agree Ousmane was probably the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Cyprus(Greek) 1993 Presidential In the plurality election, Georges Vassilou won with 44.15%, beating Glafcos Clerides (36.74%) and P.Pascalides (18.64%). But in the subsequent top-2 runoff Clerides won with 50.31% over Vassilou's 49.69%. We agree Clerides was probably the correct winner; but the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Estonia 1992 Presidential Arnold Ruutel won (42.2%), followed by Lennart Meri (29.8%), Rein Taagepera (23.7%), etc. But then the newly elected Riigikogu gave the presidency to Meri. Who knows?
Kiribati 1991 Presidential Kiribati was the only country in the world to adopt the Borda Count system. It failed immediately as a consequence of massive "strategic voting" (which everybody already knew was the Achilles heel of the Borda system, but this confirmed that dramatically). Consequently, Kiribati soon abandoned the Borda system and went back to plain plurality voting. We have no idea who "should have" won. We quote the pathology-description from Reilly's paper (pdf): As a result, of the four candidates nominated to contest the presidential election, "only two were genuine candidates and actually campaigned for President: Teatao Teannaki and Roniti Teiwaki. The other two candidates (Boanareke Boanareke and Beniamina Tinga) simply returned to their home islands, where they remained until election day. They did not campaign and were not regarded as serious candidates." This process illustrates a clear case of strategic manipulation of the Borda count at work. As leaders of their respective parties, Teburoro Tito and Tewareka Tentoa were two of the more popular politicians throughout Kiribati, and their elimination from the presidential contest was a surprise to many voters. By contrast, two of the nominated contestants were comparatively not serious and together received less than 10 percent of the vote at the resulting presidential election, won by Teatao Teannaki. As Van Trease commented, "It remains to be seen just how long such a system will be tolerated which has the effect of eliminating popular candidates through backroom political maneuvering." Kiribati later abandoned the Borda system.
Ireland 1990 Presidential In this election, conducted with the instant runoff (IRV) system, Mary Robinson won the final round by 52.8% versus Brian Lenihan's 47.2%. Lenihan, however, would have won had the election been conducted with plain plurality voting (he got 44.1% of the top-rank votes, while the next contender had 38.9%). Robinson's victory thus depended on vote transfers from the eliminated Fine Gael candidate A.Currie, whose supporters evidently viewed Robinson as the "lesser evil."

But thanks to IRV pathologies in this election, Lenihan could have claimed to be the legitimate winner:
  1. If a whole new county had magically appeared, all of them supporting Lenihan's most-hated rival Currie and ranking Lenihan in last place... then Lenihan would have won!
  2. If a slightly-smaller Currie-county had appeared and 12% of Lenihan's voters had instead voted for his most-hated rival Currie while ranking Lenihan last... then Lenihan would have won!
  3. So, since those handicaps actually were not present – why didn't Lenihan win?
We do not dispute that Robinson was the right winner. We are including this (a) an interesting example of IRV improving over plain plurality by actually electing a (superb) third-party candidate, but only at the cost of (b) exhibiting several pathologies including non-monotonicity. Generally speaking, IRV leads to 2-party domination, just like plurality. And indeed, in every Irish presidential election besides 1990, the Fianna Fail party's candidate always won, despite the fact that Ireland as a PR country had more than two parties. This 1990 election seems to indicate that IRV, despite leading to 2-party domination, does so with somewhat less oomph than plurality voting and hence permits a third-party candidate to win in exceptional circumstances. These certainly were exceptional circumstances:
  1. Mary Robinson enjoyed worldwide fame and respect (winner of Nobel Peace prize)
  2. The FF candidate Lenihan was afflicted by two scandals: (a) scandal involving PM Charles Haughey and phone tapping/jamming, and (b) was caught lying about that on tape,
  3. Unusually, the Fine Gael party failed to put forward a credible candidate (both their top choices FitzGerald and Barry declined to run; Currie had only been a member of the Dail since 1989).
Even all these factors together were not enough to overcome Duverger's law to permit Robinson to win under plurality voting, but they were enough with Instant Runoff Voting. (Robinson probably would have won under Approval and Range voting too.)
Peru 1990 Presidential Mario Vargas Lhosa won with 27.61%, followed by Alberto Keinya Fujimori with 24.62%, L.J.Alva Castro with 10.17%, and others. But in the runoff round, Fujimori beat Vargas Lhosa 56.5% to 33.9%. (Note the enormous percentage of spoiled votes.) If Fujimori was the correct winner, then still the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
Bolivia 1989 Presidential Gonzalo Sanchez de Lozada won the plurality election with 23.07% of the votes, followed by Hugo Banzer Suarez with 22.70% and Jaime Paz Zamora with 19.64% in third place. However, the Bolivia Congress then awarded the victory to Paz Zamora. Who knows?
Cyprus(Greek) 1988 Presidential In the plurality election, Glafcos Clerides won with 33.32%, beating Georges Vassilou (30.11%), S.Kyprianou (27.09%), and V.Lyssarides (9.22%). But in the subsequent top-2 runoff Vassilou won with 51.53% over Clerides. Perhaps Vassilou was the correct winner, but it is not clear; but even if so, the fact he lost the first round demonstrates the failure of the plain plurality single-round system.
S.Korea 1987 Presidential Roh Tae Woo, the heir of a military dictatorship, won with 35.9%, beating two liberals (Kim Dae Jung and Kim Young Sam) who split the vote with about 27% each. [Years later, the militarist party's leaders Roh and Chun were convicted of crimes for ordering the tragic shooting of pro-democracy demonstrators, role in the earlier 1979 coup, and bribery charges.] Under IRV, Condorcet, Range, Approval, or Plurality with separate top-2 runoff, one of the two liberals would have won. [And S.Korea may have elected the "wrong winner" because of its plurality system on other occasions too.]
Portugal 1986 Presidential Diogo Freitas do Amaral won the plurality election with 46.3% of the vote, followed by Mario Soares (25.4%), Francisco Salgado Zenha (20.9%) and Maria de Lourdes Pintasilgo (7.4%). However, in the subsequent top-2 runoff, Soares beat Amaral by 51.3% to 48.7% thanks to near-total support of the leftist Soares by the supporters of the two eliminated candidates, against the rightist Amaral. We agree Soares was the correct winner; but the fact he hugely lost the first round demonstrates the failure of the plain plurality single-round system. This is interesting in that it plausibly would have been a "Burr's dilemma" scenario in which approval voting would have enthroned Amaral.
Bolivia 1985 Presidential The plurality election was won by Hugo Banzer Suarez with 28.6% of the vote, followed by Victor Paz Estennsoro with 26.4% and numerous others. The Bolivian Congress then stepped in and gave the victory to Paz Estennsoro. Who knows?
Colombia 1982 Presidential Luis Carlos Galan Sarmiento (running for a split-off fragment of the Liberal party) managed to split enough leftist votes off Lopez Michelsen (Liberal) to allow the Conservative Belisario Betancur Cuartes to win with 3.19 million votes. One of the liberals (they got 2.80 and 0.75 million votes for a total of 3.55 million).
France 1981 Presidential Francois Mitterand won the runoff over V.G. de'Estaing by 51.76% to 48.24%. We agree Mitterand was probably the correct winner. We merely point out that in the first round, de'Estaing and Mitterand were the top two finishers in that reversed order – thus demonstrating the failure of the plain plurality single-round system. This failure fortunately was repaired by France's second round.
USA 1980 Presidential Ronald Reagan won with 50.7% of the popular vote, beating Jimmy Carter (41.0%) John Anderson (6.6%) and Ed Clark (1.1%). A NY Times/CBS news exit poll found the Anderson voters would have gone R=49, C=41, abstain=10 if Anderson had not been on ballot, so presumably "instant runoff" would also have elected Reagan (by an even clearer margin than plurality). We do not deny Reagan was the right winner, but we'll see there are substantial grounds for questioning Carter's second-place finish! Brams & Fishburn devote chapter 9 of their book to an analysis of the top three finishers in this election. An ABC News exit poll (unpublished data given to B&F) found these results in hypothetical 2-candidate contests: RvA 53:41 (6 abstain), AvC: 49:46 (5 abstain), RvC: 54:43 (3 abstain), so Reagan was the clear Condorcet winner with Anderson second! (Polls also showed Anderson was preferred pairwise over Carter everywhere but the South.) Brams & Fishburn after a long analysis concluded Anderson probably also would have beat Carter also under approval voting despite the fact a Time Magazine poll 2 weeks before the election found the percentages of voters rating each candidate "acceptable" were R=61, C=57, and A=49. In any event, it is clear that Anderson got enormously less support, due to plurality-system distortions, than he deserved.
Also, Brams & Fishburn mention on p.11 (based on ABC News polls), that in the New Hampshire Republican primary, James Baker would have come in second behind Reagan with Approval Voting (Reagan=58, Bush=39, Baker=41). However, under the plurality system that was used, the results were Reagan=50, Bush=23, Baker=13 which in view also of Iowa (where Bush had won with Reagan 2nd) caused Baker to quit the race, leaving it to Bush and Reagan.
USA 1976 Presidential Jimmy Carter(D) won versus Gerald Ford(R) by a narrow but undisputed 50.1% to 48.0% popular-vote margin (and a rather wider electoral vote margin). The dubious part of this election was Ford's victory over R.Reagan in the 1976 Republican party primary. Keech (p.254, citing the Congressional Quarterly Weekly Report of 13 Mar 1976 pages 547 and 1661) noted that Reagan actually got more primary votes than Ford, but Ford won the nomination because he had more delegates (1187 versus 1070, the closest ever). This pathology is somewhat analogous to the way the electoral college makes it possible for a US president to win with fewer popular votes than his opponent, as happened in 2000, 1888, 1876, and probably 1824.
Was Ford (who lost) really the best GOP choice to run against Carter? Or might Reagan (who in the next contest beat Carter by a huge landslide) have been a better choice?
USA 1974 Presidential Gerald Ford became president when Richard Nixon (facing almost-certain impeachment) resigned. While this was not an "election" at all, one can argue that the only reason Ford became president was because of an earlier "wrong-way election." [This comes from Lowell B. Anderson: Voting Theory, Handbooks in OR & MS 6 (S.M. Pollock, et al. eds.) Elsevier Science BV 1994.] In 1966, Thomas Finan and Carlton Sickles (two relatively liberal candidates from leftish Maryland) split the state Democratic party gubernatorial nomination vote, causing conservative Democrat George P. Mahoney to win it. Mahoney then was beaten in the (secondary) election by Spiro Agnew. Agnew later became Richard Nixon's Vice President. When Agnew resigned in 1973 (convicted of bribery), Nixon appointed Ford Vice President. This connection to the presidency is admittedly rather indirect, but it is quite real: If it were not for (what almost certainly was a) "wrong-way" gubernatorial primary in 1966, the US probably would have gotten a different president in 1974.
France 1974 Presidential V.G. de'Estaing won the runoff over Francois Mitterand by 50.81% to 49.19%. Same scenario as 1981, but in reverse! We agree de'Estaing was probably the correct winner. We merely point out that in the first round, Mitterand and de'Estaing were the top two finishers in that reversed order (and by large margin: M: 43.24%, d'E: 32.60%) – thus again demonstrating the failure of the plain plurality single-round system, repaired by France's second round head-to-head contest.
USA 1972 Presidential In the Democratic Party primary, G.McGovern won with 33.0% of the plurality votes, beating H.Humphrey (29.4%), G.Wallace (25.1%) and E.Muskie (12.6%). McGovern then lost the real election by an enormous "landslide" to R.M.Nixon, the Republican Party's nominee. Humphrey had broader support than McGovern and hence probably would have done better against Nixon. Studies based on various pre- & post-election polls, and exit polls (especially the National Election Study "feeling thermometer"), concluded that Humphrey would have won the Democratic nomination under essentially any voting system besides plurality, e.g. range voting, approval voting, plurality-with-top-2-runoff, instant runoff, Condorcet, Borda, and "adjusted Borda," all of these with either sincere or strategic voters. See
Richard A. Joslyn: The impact of decision rules in multi-candidate campaigns, the case of the 1972 Democratic Presidential Nomination, Public Choice 25 (1976) 1-17;
Samuel Merrill III: Strategic decisions under one-stage multicandidate voting systems, Public Choice 36,1 (1981) especially table 1 p.127. Merrill calls 0-100 range voting "cardinal ratings" and works under the assumption "don't know" voters would have awarded a score of 50 (but a more realistic assumption would have been 20); Joslyn calls it "interval measure."
Chile 1970 Presidential The plurality election official vote totals were Allende 36.3%, Allesandri 35.8%, and Tomic 27.9%. Because the winner Allende did not reach 50%, the election then went to the Chilean congress, which awarded him the victory over Allesandri by a 153-to-35 vote thanks to Tomic throwing the weight of his Christian Democrat party behind Allende. Then in 1973 Allende died in a CIA-aided coup that plunged Chile into a long dark dictatorial period. According to Michael J. Francis, author of The Allende Victory, an analysis of the 1970 Chilean presidential election, U. Arizona Press (Comparative government studies, #4) Tucson 1973 (ISBN=0816504113), Allesandri was rightist, Tomic centrist, and Allende leftist. Therefore, each A's supporters (if their candidate were removed) would have viewed Tomic as the "lesser evil." Therefore, Tomic would have beaten either opponent head-to-head despite the fact he placed dead last in the official plurality vote. Hence Tomic probably would have won under Condorcet, Borda, Range or Approval voting. But Tomic would wrongly have lost (eliminated in the first round) with either IRV or plurality plus separate top-2 runoff. This defect of the IRV system has been called the "center squeeze" effect. (Despite this, Chile later adopted the delayed top-2 runoff system.)
USA 1968 Presidential R.M.Nixon won a narrow (in terms of the popular vote) plurality victory with 43.4% versus H.Humphrey (42.7%) and and G.Wallace (13.5%). We are not going to claim this was a wrong-way election – Nixon indeed was the right winner – but we are going to claim it nearly was since Humphrey came far closer to victory than he would have under better voting systems. Based on a set of 10 rules for assigning approval votes based on NES "feeling thermometer" data, D.Roderik Kiewiet [Approval voting: the case of the 1968 Presidential Election, Polity 12,1 (Fall 1979) 170-181] found that Nixon was the clear Condorcet winner (would have beat Humphrey head-to-head 53.4-to-46.6%, and Wallace 81.5-to-18.5%) and would have won an Approval Voting (and presumably also Range Voting) election easily: Nixon=69.8%, Humphrey=60.8%, Wallace=21.3%. In the actual plurality election both Nixon and Wallace suffered due to a vote-split with each other, and also Wallace suffered due to strategic plurality voting (21% said they'd vote Wallace 2 months before the election, but he only got 13.5%; Kiewiet found voters were more likely to stay with Wallace if they thought he had chances to win).
USA 1964 Presidential Barry Goldwater won the Republican Party nomination (defeating W.Scranton and N.Rockefeller) but lost the real election by a "landslide" to Democrat L.B.Johnson. Indeed, Johnson's 61.1% of the popular vote was the largest ever recorded in US popular-vote history. There is good reason to believe (also see p.131 of Brams & Fishburn's book) that Goldwater might not have won the Republican nomination if other voting systems had been employed, and indeed that William Scranton was the "Condorcet Winner" and would have beaten Goldwater in a head-to-head contest by an enormous margin. Goldwater was a far right candidate who, e.g. in a 1963 television interview called for the defoliation of forests covering National Liberation Front supply lines in Vietnam through the use of "low-yield atomic weapons." His opponents were more moderate but split the anti-Goldwater vote. Undoubtably most or all of them would have done better against Johnson.
USA 1960 Presidential J.F.Kennedy won over R.M.Nixon in an extremely narrow popular-vote victory (34,220,984 to 34,108,158 according to Wikipedia; other sources differ) which, however, was not so narrow when it came to the "electoral vote," (which is what mattered), which Kennedy won 303 to Nixon's 219 (with 15 electoral votes cast for others). A large number of the Kennedy-Johnson votes in Illinois and Texas were fraudulent (see Campbell's book), which may or may not have been enough to tip one of both of those states. (If Nixon had won them both, he would have won by 270 to 252.) Our best guess is Kennedy really was the "right" winner, but it is only a guess. Interestingly, if all states had been using the "electoral vote by district" semi-proportional scheme currently only used by Nebraska and Maine (one elector per district votes according to his district's vote, plus the two "senatorial" electors vote according to their statewide vote, as opposed to the "winner take all" scheme) then Nixon would have won with 282 to Kennedy's 269.
USA 1916 Presidential Woodrow Wilson(D) was re-elected with 49.2% of the popular vote, defeating Charles E. Hughes(R) with 46.1%. However, Hughes would have won by 270 electoral votes versus Wilson's 263 if he'd carried California (which Hughes lost by 3966 votes, i.e. 0.3%) and New Hampshire (lost by only 56 votes!). Both losses were probably due to the spoiler effect of the single-issue Prohibition Party candidate James F. Hanly (who got 27698 California votes, 303 New Hampshire votes, and 1.2% nationally; James Bryce's American Commonwealth vol. 2 p.26, 1910 edition noted that "Republicans suffer by the starting of a Prohibitionist candidate since he draws more strength away from them than from the Democrats.") Hanly was almost definitely a spoiler in the sense that had he not run, then almost certainly Hughes would have won. Hughes probably would have been considerably better for the USA and world because Wilson failed miserably in his second term. Nevertheless, Wilson still seems to have been the "right winner" because he would then still have been the popular vote winner (only losing due to the electoral college system) – even Hughes and Hanly's votes combined added up to only 47.31% as opposed to Wilson's 49.24%. Further, because the Socialist Allan L. Benson (who got 3.19% nationally) exerted a counter-spoiler anti-Wilson effect which tended to cancel out Hanly's anti-Hughes effect, that's more reason to regard Wilson as the "right" winner despite Hanly being a spoiler considered alone. (An October poll of Labor leaders found they thought most of their members would vote Wilson.) Summary: Hanly was a spoiler for Hughes; Hughes would have won if Hanly had not run. But nevertheless in a larger democratic sense we would contend Wilson was the "right" winner based on those voters at that time. Postscript [from Richard Winger]: Republicans in Congress passed the Constitutional amendment in 1917 to impose nationwide prohibition of alcoholic beverages. The proposal had been introduced in every Congress starting in 1875, but had never come close to passing by the necessary two-thirds majority. But the Republicans (who generally gave prohibition lip service but never actually did much), having lost two presidential elections due to Prohibition Party spoilers, decided to end that problem once and for all, by accepting the amendment and thus killing the rationale for the Prohibition Party to continue to exist. (It worked: Hanly was the last Prohibition Party candidate to get substantial votes.) Prohibition turned out to be a massive failure and was repealed in 1933. Thus, in one of the few known instances where a major party pandered to a minor party to prevent its spoiler effect, the result was a huge national failure.
USA 1912 Presidential Woodrow Wilson won with 41.8% of the popular vote when his opponents Theodore Roosevelt (27.4%), William H. Taft (23.2%), Eugene V. Debs (6.0%), and others (2.6%) split the vote. Probably Roosevelt would have won under either IRV, Plurality with separate top-2 runoff, approval, Condorcet, or range voting since the Roosevelt (Bull Moose party, a breakaway fragment of the Republican party) and Taft(R) supporters probably both would have preferred him over Wilson(D) by large margins (it is unclear which way Debs' Socialist voters would have split, but also not very relevant).
USA 1888 Presidential Benjamin Harrison(R) won with 47.8% of the popular vote, defeating (then president) Grover Cleveland(D) with 48.6%. (This is not a misprint: Harrison indeed won with fewer votes thanks to the USA's electoral college system.) The Prohibition, Union Labor, and other parties got 4.6% in total for their candidates. It is unclear who would have won under different voting systems; that depends which way the third-party voters would have split in different states. The presumption, however, is Cleveland would have won under all of them if the electoral college were not there. Cleveland indeed did win in 1892, becoming the first US president to win re-election to a nonconsecutive term.
USA 1884 Presidential Grover Cleveland(D) won with 48.5% of the popular vote, defeating James G. Blaine(R with 48.25%). However, Blaine would have won if he had carried New York state, which he lost by 1047 votes thanks to the spoiler effect of the Prohibition Party candidate J.P.St.John, who got 24999 New York votes and 1.5% nationally. (The Democrats quietly funded St.John to increase his spoiler effect even though the Republicans were clearly the major party that was most anti-alcohol; thus the result of St.John's anti-alcohol candidacy was – exactly what he did not want – the election of Cleveland, "the ally of the saloon.") Depends... we have no doubt St.John's big New York vote swung the election. But if you regard the electoral college as illegitimate, then it is a lot less clear what would have happened to the national popular vote (especially when we also consider the effect of B.F.Butler's Greenback/Anti-Monopoly-party candidacy).
USA 1876 Presidential There is little debate nowadays that Samuel Tilden(R) was the true winner, while the official winner Rutherford B. Hayes(D), who "won" by one electoral vote, got there due to massive fraud. (Also, even the fraudulent official totals gave the popular vote victory to Tilden 51.0% to 47.9%.) But this election really does not belong in this list because this was not caused by the mathematical flaws in the voting system, but was just a matter of out-and-out fraud. E.g. see Roy Morris Jr: Fraud Of The Century: Rutherford B. Hayes, Samuel Tilden and the Stolen Election of 1876, Simon & Schuster NY 2003. But... just to justify the presence of this election, we note that if the number of electoral votes had been got from the states' populations using Hamilton's apportionment method, then Tilden would have won. Congress had added 9 new seats in 1872 without using Hamilton's method – which was the method they'd supposedly adopted in 1852 – nor, for that matter, did they use any other specified method.
USA 1860 Presidential Abraham Lincoln won with 39.8% of the popular vote when his opponents S.A.Douglas (29.5%), J.C.Breckinridge(18.1%), and John Bell(12.6%) split the vote. Despite Douglas coming clear second in the popular vote, he was far last in the electoral college vote because of an unfortunate-for-him geographic distribution of his supporters. Lincoln was the only antislavery candidate (albeit only in a rather lukewarm way) and only Republican. The Democrats were split between the Northern wing (Douglas), the Southern wing (Breckinridge), and in between (Bell). After Lincoln won, the South seceded and shelled Fort Sumter, causing the US Civil War, huge devastation, and the eventual abolition of slavery. Douglas would have won a nationwide popular-vote election under either IRV or Plurality with separate top-2 runoff, since the Breckinridge and Bell supporters undoubtably preferred Douglas over Lincoln by large margins. It is unclear who would have won with range, approval, or Condorcet voting, but my top guess would be Douglas. But (Richard Winger points out) even if 100% of the Breckinridge and Bell votes shifted to Douglas, giving him an enormous 60.2% to 39.8% popular-vote victory over Lincoln (equivalent to the third-biggest "landslide" in US history up to 2005), then still Lincoln would have won the presidency by at least 173-to-130 electoral votes, due to the electoral college system and the geographic distribution of the voters!
Note: A.Tabarrok & L.Spector: Would the Borda Count Have Avoided the Civil War? J. of Theoretical Politics 11,2 (April 1999) 261-286 also examined this and concluded Lincoln was a wrong-winner and Douglas a right-winner: "By comparing the outcome under plurality rule to the outcomes which would have occurred under other voting systems, we conclude that Stephen Douglas, not Lincoln, was plausibly the candidate who best represented the preferences of the voters." That quote is wrong in the sense that Lincoln's victory cannot be questioned unless you question the legitimacy of the electoral college. Just winning the North alone was enough electoral votes for the presidency. Lincoln wrote off the South as a lost cause, in some Southern states neglecting even to print ballots (at that time, campaigns printed and distributed their candidate's ballots)! However, in all this it should be noted that if slaves had had the right to vote, the numbers would have changed substantially.
USA 1848 Presidential General Zachary Taylor(Whig) won. His opposition was split between Lewis Cass(Dem) and Martin Van Buren (former Dem president who did not get their nomination and therefore ran on the Free Soil more-antislavery ticket). Taylor died 16 months after his election and was supplanted by his vice-president Millard Fillmore. Van Buren's vote count was 2.1 times larger than the Taylor-over-Cass margin, and probably most of his voters would have preferred Cass over Taylor. (Taylor was a malleable non-politician who'd never held elected office, nor even voted, before. He'd gotten good press in the Mexican war and had the right relatives.) However, due to the distributions of voters with respect to the electoral college, having a voting system immune to vote splitting probably still would have failed to elect Cass. If the USA had had both a good voting system and straight popular vote for president (i.e. no electoral college), then it becomes at least plausible Taylor would have lost (a 74-26 split of the Van Buren voters for Cass over Taylor would have sufficed).
USA 1844 Presidential James Polk(Dem) won with 49.54% of the popular vote, beating Henry Clay(Whig)'s 48.08%. But Clay would have won if he had gotten New York's 36 electoral votes, but did not thanks to the Liberty Party's "spoiler" antislavery candidate James Birney (2.30%). The antislavery candidate thus managed to get Polk (a slave-owner) elected. Clay lost New York by 5106 votes while Birney got 15812 New York votes. It is plausible the Birney voters predominantly would have considered Clay the lesser of two evils since he was slightly less pro-slavery than Polk (e.g. did not recommend admitting Texas as a slave state). If that happened in at least a 2:1 ratio (which is at least plausible) then Clay would have won if New York had used IRV, Plurality with separate top-2 runoff, range, approval, or Condorcet. S.E.Morison: Oxford History of the American People 1965, p.557: "...the expansionists trotted out the first `dark horse' in American history. His name, new to most of the country, was James K. Polk... Clay... received the Whig nomination by acclamation... but... enough antislavery Whigs voted for Birney, the abolitionist candidate in New York, to give Polk a slight edge..."
USA 1824 Presidential J.Q.Adams won with 30.9% of the popular vote, beating Andrew Jackson (41.3%), Henry Clay (13.0%), and W.H.Crawford (11.2%) thanks to deals in the US House of Representatives, into which the election fell after nobody got a clear majority. (Re these numbers: yes, Adams apparently did win with fewer votes; but since about a quarter of the states did not use popular vote at the time, this is not completely clear. Only two states did not use popular vote in 1828, which thus is the first year in which "popular vote" had a reasonably clear meaning. The two holdouts were Delaware and S.Carolina, which converted to popular in 1832 and after the Civil War, respectively.) Unclear. In elections of this nature, a top-2 runoff would have yielded a hard-to-dispute winner, but was never conducted so we shall never know. Jackson recontested Adams in 1828 and won by a large margin, so it is plausible it should have been Jackson.

Conclusions

These "direct effects" (i.e. wrong election winners) are only the tip of the iceberg of the enormous damage caused by the flawed plurality voting system. There is also enormous "indirect damage" caused by candidates who don't even run because they are afraid of causing a spoiler pathology (like these), or because of 2-party or 1-party domination (a bad voter-choice-denying side effect of the plurality voting system) causing their chances to be minuscule. You can see the enormous distortions caused by the Plurality system in these numbers.

It seems clear from the above that adding a delayed runoff round to the single-round plurality system yields an improvement: There are at least a dozen (and maybe over 20 or even 30) national presidential elections where it would have yielded (or did yield) a more-preferred winner. The instant runoff (IRV) system has been touted as an even-further improvement because it supposedly yields the same result, but in only one round (saving time and money). However, that is not true: it can fail to yield the same result as a consequence of strategic voting (and on balance, in those cases we would expect IRV's winner to be worse than delayed runoff's), and it is in some ways more expensive and error prone (because simple voting machines can be used for plurality but not for IRV elections) and definitely yields a far higher risk of crisis-inducing near-tie nightmares. And there is one clear empirical difference – noted by Duverger – while plurality-with-delayed-runoff leads to multiparty democracy, IRV leads to 2-party domination.

But the delayed and instant runoff systems are not perfect; there are three clear cases (France 2007, Peru 2006, and Chile 1970) where these systems still yielded the wrong winner, plus three further cases (France 2002, Slovakia 2004, Cyprus 1988) where in each there seems about 50% chance delayed-runoff gave the wrong winner (and also runoff might have delivered wrong winners in Mexico 2006 and/or Iran 2005). Also one could find innumerably more examples if one considered races lower-level than presidential. For example Brams & Fishburn analyse the 1970 race for New York State's senatorship, which J.Buckley won with 39% over R.Ottinger (37%) and C.Goodell (24%). Their analysis claims Goodell was the Condorcet winner and probably also the approval-voting winner, but instant (or ordinary) runoff would not have elected Goodell (and both probably would have elected Buckley just like the plurality system).

We also have examples in Portugal 1986 of the failure of the Approval system and in Kiribati 1991 of the failure of the Borda system (and this failure was so massive and common-seeming it led to Borda's abandonment) .

It seems at least plausible (although there is no way to prove it) that range voting would have given the correct winner in every case tabulated, plus it can be run in a single round on simple voting machines while reducing tie-risk, thus getting the best of all worlds.

It is also fairly clear that the USA's electoral college system is a very bad idea. It pointlessly greatly increases the risk of crisis-inducing near-ties. It causes presidents to cater only to the interests of a very small number of "swing states" and to almost completely ignore all the other states. And it can lead to very crazy results such as Douglas placing far-last in 1860. It would be far better either to elect the president by straight nationwide popular vote (and preferably using range voting!) or, if we insist on giving the low-population states greater power, then use a weighted nationwide popular vote with the weights chosen to reflect that state's number of electoral college members.

Main sources

Adam Carr's Psephos election &c database; Election World; Binghamton Election Results Archive;

S.J.Brams & P.Fishburn: Approval Voting, Birkhauser 1983.

Ian Gorvin (ed.): Elections since 1945 a worldwide reference compendium, Longman international reference 1989.

William R. Keech & Donald R. Matthews: The Party's Choice, Brookings Institution, Washington DC 1977 with an epilogue concerning the 1976 nominations. Also available electronically for money through the Questia online library.)

Thomas T. Mackie & Richard Rose: The international almanac of electoral history (third revised ed.), Macmillan 1991.

Benjamin Reilly: Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries, International Political Science Review 23,4 (2002) 355-372.

Political handbook of the world, (ed. Arthur S. Banks, recently), published annually since 1928 by various publishers including the Center for Social Analysis.


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