Some range and approval voting poll results

This page collects poll results indicating what (presumably) would have happened if various elections had been held using range voting or approval voting (or still other kinds of voting).

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American National Election Study "Feeling thermometer" 1968-2008

The American National Election Study has interviewed a large number (over 1000) of random Americans each presidential election year pre- and post-election – including a range-voting pseudo-election using an 0-to-100 score-range. They published the following ridiculously abbreviated "summary table" giving the results of those pseudo-elections. Note: this table omits data (which they also collected) about all the non-Democrat non-Republican candidates, and also totally discards all sorts of other interesting conclusions which could also have been drawn from their data had they not been incredibly lazy about it. It would be good if somebody were to re-examine their data. For example based on the thermometer data P.R.Abramson et al: Third-Party and Independent Candidates in American Politics: Wallace, Anderson, and Perot, Political Science Quarterly 110 (1995) 349-367 found that in the years 1968, 1980, and 1992 (and this also is true in 1996) where there were significant third-party candidacies, the official election winner always also was the "Condorcet winner," i.e. was preferred versus each rival pairwise by a voter majority. However, that arguably was not true in 2000: Barry Burden showed that the ANES thermometer data indicated that Ralph Nader was the Condorcet winner i.e. was preferred versus every rival X by a majority of the voters who scored both Nader and X. (Although a substantial number of voters did not provide a score for Nader, and so this conclusion depends how the Nader non-scores are treated.)

Anyway, for what little the ANES summary table is worth, note that it finds that in every case 1968-2008 the same president would have been elected with highest-average-score range voting as with ordinary plurality voting (popular vote), namely 1968=Nixon, 1972=Nixon, 1976=Carter, 1980=Reagan*, 1984=Reagan, 1988=Bush I, 1992=Clinton, 1996=Clinton, 2000=Gore (popular vote winner; Bush II only won thanks to Electoral College & Florida), 2004=Bush II, 2008=Obama...

*except that in 1980, the range voting data actually gave a tie between Reagan and Carter, at least after rounding their average scores to whole numbers. The range voting assessment also found that Reagan's VP George H.W.Bush was slightly preferred by the electorate using range voting versus Carter's running mate Walter Mondale.

1980 US Presidential Election

Official plurality results: Ronald Reagan won with 50.7% of the popular vote, beating Jimmy Carter (41.0%), John Anderson (6.6%), Ed Clark (1.1%), and Barry Commoner (0.27%).

Approval & Condorcet voting: 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 in the official results, due to plurality-system distortions, than he deserved.

Range voting: ANES therometer data indicates Reagan & Carter would have finished in a near-tie.

1984 US Presidential Election

Reagan re-elected by "landslide" (58.8%) over Walter F. Mondale (40.6%). In third was David Bergland with 0.3%. We do not believe any reasonable election method would have changed that.

1988 US Presidential Election

Approval voting: NBC News/Wall Street Journal (they released this poll data on 18 November 1988) asked 1721 US citizens by telephone: "Do you have a favorable or an unfavorable opinion of Michael Dukakis?" The same question was asked also of other presidential candidates or people and also at other dates. Note: the Bentsen figures below, and those labeled CBSNYT, are instead from a CBS/New York Times poll 8-10 October 1988 of 1009 "likely voters." (There also was an ABC News/Washington Post Poll in September 1988 asking the same questions, but I do not have that data.) The results were:

Gallup asked 1232 registered voters by telephone on 21-23 October 1988: "Would Dukakis make a good president?" Results:

Dukakis: 36% yes,  31% no,  33% don't know / no-opin
Bush I:  48% yes,  28% no,  24% don't know / no-opin

Gallup asked 1007 people US-wide by telephone on 7-9 October 1988: "Is Dan Quayle qualified to be president?" Results:

Quayle:   46% yes,  42% no,  12% no-opin
Bentsen:  76% yes,  11% no,  13% no-opin

It appears from this data that Bush I would have won under approval as well as (as he did) under plurality voting, except that if Jesse Jackson had run (but in fact, Jackson dropped out of the race after losing the Democratic Party nomination to Dukakis) then it appears Jackson would have defeated Bush or come close. And definitely Jackson would have beaten Dukakis (based on this data) with approval voting. However Jackson lost to Dukakis among both Democrat voters and Republican pollees in the plurality-voting primaries and all Gallup polls when the full or anyhow a substantial set of Dem-party contenders were also present in that same primary or poll. So here we appear to have an example where the approval and plurality-voting winners (e.g. of the 1988 Democratic primary) differed. (Asterisk: since these polls were taken at different times that conclusion can be attacked.) Finally, Bentsen it seems would have won the whole ball of wax if he'd run under either range or approval voting.

Range Voting: Gallup asked 4089 registered voters by telephone on 3-6 November 1998: "Is your overall opinion of George Bush very favorable, mostly fav, mostly unfav, or very unfav?" (And same for other candidates.) Results ["Avg" computed using 3,2,1,0 scale]:

However the Jackson poll data in the above table was not got by Gallup on Nov 3-6 but instead is based on combining two Gallup polls of 1204 and 757 registered voters respectively taken on 21-23 April and 30-31 March. It thus is a good deal less legitimate for comparison purposes, indicated by using a different color for that row. It appears from the above data that the range-voting winner would have been (if he had been running for president instead of vice president) Lloyd Bentsen!

Official plurality election results:

1992 US Presidential Election: Range(1-7) poll, Approval poll, Plurality vote

Approval voting: We combine this New York Times telephone poll of 1854 US citizens (on 23 Oct. 1992) "Is your opinion of Ross Perot favorable, not favorable, undecided, or haven't you heard enough about him yet to have an opinion?" (same question also asked for Bush & Clinton) with the result of an independent Gallup telephone poll of 1579 US citizens (on 31 Oct. 1992) [almost identical question phrasing except "undecided" and "don't know" lumped into one]. The results (for all 3433 pollees; note some rows may not sum to exactly 100% due to integer twice-roundoff effects) are as follows:

Interestingly, note that no candidate got more "favorables" than "unfavorables." An academic paper by S.J.Brams and S.Merrill "Would Ross Perot have won the 1992 presidential election under approval voting?" PS: Political Science & Politics 27,1 (March 1994) 39-44 (pdf) also independently concluded, this time based on NES "thermometer" data, that Clinton would have won: they estimated Clinton 55%, Bush 49%, and Perot 42% approval.

Range(1-7) Voting: (Market Facts Inc. telephone poll of 1000 US citizens on 18 Oct. 1992) "First I'd like to know how you feel about some of the presidential candidates. Use a 7 point scale where 7 means that you have an 'extremely favorable' impression, 1 means 'extremely unfavorable' and 4 means 'neither favorable nor unfavorable.' Of course, you can use any number between 1 and 7. How do you feel about Ross Perot?"

And of course Clinton also won in the ANES thermometer range(0-100) voting pseudo-election with 56 (Bush=52, Perot less).

Plurality Voting: (Official US election nationwide popular vote results, 3 Nov. 1992)

An exit poll by "Voter Research and Surveys" (reported in NY Times 5 Nov. 1992) found that Perot drew 38% of his vote from Bush and 38% from Clinton, while the rest of his voters either would have stayed home or voted for somebody else had he not been on ballot. This indicates Clinton still would have won using "instant runoff voting" and also indicates Perot clearly did not play a "spoiler" role; his candidacy did not affect the election result.

It also indicates that at least 43.0+18.9×0.375=50.1% of the voters were "Clinton>Bush" voters (i.e. if they'd provided full preference orders as votes, at least 50.1% would have ordered Clinton above Bush). Does this mean that Clinton was a Condorcet winner? No, because it remains conceivable that, e.g. all Bush-voters preferred Perot>Clinton in which case Perot would have been preferred over Clinton by ≥56.3 of the voters. (Perot would have needed at least 86% of Bush voters to feel that way, to beat Clinton pairwise.) However, that didn't happen because NES "thermometer" data indicates Clinton indeed was a Condorcet winner. (To quote the analysis of that data from the Brams-Merrill paper: "Clinton is easily the Condorcet winner, beating Bush 953.5 to 687.5 and Perot 1038.5 to 585.5. Bush beats Perot in a relatively close race, 865.5 to 761.5." They also remark: "Borda totals for the three candidates are: Clinton 2,017.5; Bush 1,577.0; and Perot 1,379.5," where I presume they are artificially excluding candidates besides these three.)

1996 US Presidential Election

Approval voting: New York Times/CBS News telephone poll of 1919 US citizens (on 2 Nov. 1996) "Is your opinion of Ross Perot favorable, not favorable, undecided or haven't you heard enough about Ross Perot yet to have an opinion?":

Approval voting: CNN/USA Today/Gallup poll October 26-29:

Range(1-4) Voting: (Pew Research telephone poll of 1938 US citizens on 25 Oct. 1996) "Would you say your overall opinion of Bill Clinton is very favorable, mostly favorable, mostly unfavorable, or very unfavorable?" (Same also asked for Bob Dole, but unfortunately apparently not for H.Ross Perot. Higher ratings on 1-4 scale are better.)

Effect of Perot: CNN/Gallup polls were conducted of 866 registered voters in which pollees were given a 3-way choice {Clinton,Dole,Perot} and a 2-way forced choice {Clinton,Dole} via "If Bill Clinton and Bob Dole were the only candidates running for president in 1996, who would you vote for?" This allows us to enquire about Perot's effect – did he act as a "spoiler" and for whom? It appears that Perot, by running, hurt Dole (i.e. more Perot voters supported Dole than Clinton), based on the early polls (April). But in later polls (May & July) the situation reversed, and Perot by running seems instead to have hurt Clinton. So in 1996 just like in 1992, Perot was not a "spoiler" who ruined the election for Dole; instead if anything Perot's run hurt Clinton and helped Dole (relatively) albeit not by enough to alter the winner.

               3-way forced choice                         2-way forced choice
      Date     Clinton    Dole     Perot  Undec/Other   || Clinton   Dole  Depends/Neither/No-opin
 96 Nov          49        37        14                 ||
 96 July 18-21   50        33        12         5       ||   56        39         5 
 96 May 9-12     47        32        19         2       ||   58        38         4 
 96 Apr 9-10     49        35        15         1       ||   57        40         3    
 96 Mar 15-17    46        36        16         2       ||   54        42         4 
 96 Jan 12-15    43        39        16         2       ||   48        49         3
 95 Aug 4-7      39        35        23         3       ||   46        48         6
 95 Apr 17-19    40        37        18         5       ||   48        49         4    

Plurality Voting: (Official US election nationwide popular vote results, 5 Nov. 1996)

Again it seems virtually certain that Clinton also would have won using IRV and was a Condorcet winner.

2000 US Presidential Election

Range(0-100) Voting: A 7-state poll was done in 2000 by the University of Iowa with the following results (note, we give two "average scores" for each candidate, arising from two different calculation methods; fortunately both methods yield the same output-ordering of the 4 candidates; this poll was done before the primaries in those states; McCain did not actually run in the later general election after he lost in the Republican Party Primary):

The NES (national election study) conducted range-voting nationwide polls using ratings on an 0-to-100 score-range. (Their "feeling thermometer.")

Note that Nader data is based on 1221 responders (i.e. ignored many "don't knows") while the Gore and Bush data each are based on about 1770 responders.

Head-to-head matchups & Condorcet voting: A CNN/USA-Today/Gallup poll released 13 Dec. 1999 (phone interviews with 1037 adult Americans) found McCain would defeat Gore 52% to 44% in a hypothetical head-to-head race. Gallup also asked this again in late February 2000, finding a landslide win for McCain: 59% versus Gore's 35%. And of course, Gore beat Bush by a small margin in an effectively-2-way race – the official popular vote – although Gallup polls during this early period (Feb. 2000) predicted the opposite (53% to 44% win for Bush over Gore; sampling error ±5 %points). This poll also predicted both McCain and Bush would defeat Bradley head-to-head, although again McCain would beat him bigger. However, Bush easily defeated McCain in this poll among Republican voters only: 56% to 34% in a hypothetical 2-way matchup. (Later, McCain gained on Bush, but not by enough to win the Republican nomination.)

If it really is true that the US public as a whole (not just Republican primary voters) preferred Bush over McCain, then that demonstrates a Condorcet cycle

but if instead (which seems more likely) McCain would have defeated Bush USA-wide then McCain was the beats-all winner among these three.

From Burden's paper: "Examining the pre-election rankings (NES 'feeling theormometer' data), Nader beats Buchanan (659-240), Gore (527-500), and Bush (562-491), thus making him the Condorcet winner. Nearly every other [voting] method makes Gore the winner." But this is only if voters ranking Nader with "don't know" are excluded, or treated as midrange score (evidently the former). If these voters instead are regarded as rating Nader 0, then Gore is the Condorcet winner. The USA-wide popular-vote winner (in this case Gore) has been the Condorcet winner in every US presidential election studied by the NES under the latter convention. The reason Nader did so poorly in the official election (Burden found from the NES data) is that over 90% of people who rated Buchanan or Nader highest did not vote for them, i.e. the voting was dominated by strategic dishonesty!

But Gore wins based on the NES data using either "instant runoff," "range voting," or "Borda count."

Instant Runoff: This race, incidentally, is a good example of where IRV (instant runoff voting) would have failed America in a 3-way McCain vs Gore vs Bush race where we assume McCain would have continued running as a 3rd-party or independent candidate. McCain would have been the true-democratic winner in that race, based on our polls, range voting, approval voting, and the fact Bush voters tended to prefer McCain over Gore, and Gore voters tended to prefer McCain over Bush, making McCain the "Condorcet (beats-all) winner." (As the head-to-head polls agreed too.) However, with IRV, McCain presumably would have been "eliminated" and thus unable to benefit from "vote transfers" from either Gore or Bush. Thus IRV would, in this race, have behaved the same as plain plurality voting.

There also was a Gallup poll 14-16 July 2000 finding for Nader 42% favorable, 22% unfavorable, 36% other (e.g. "don't know"); for Gore 52-64% favorable and 30-46% unfavorable (fluctuated on poll dates during Jan-Nov 2000; Gallup's final Gore figures by election day were F=52, U=46); and for Bush about 55-66% favorability and 36-39% unfavorability (fluctuations during late 2000). This indicates Bush or Gore would have won (with the most "favorables") although Nader might well have been the winner in the sense of having the greatest F/U ratio (ignoring "don't knows"). But an ABC News/Washington Post poll of registered voters released 8 Sept. 2000 found only 31% favorable and 29% unfavorable for Nader, contradicting that.

Another approval-style poll by Time/CNN released 11 Nov. 2000 found:

albeit certainly this poll has insufficient precision to decide which of {Bush, Gore} would have won.

Plurality Voting: (Official US election nationwide popular vote results, 7 Nov. 2000; Note Bush won the election thanks to the Electoral College and Supreme Court, but lost to Gore in the nationwide popular vote tabulated here)

Over 90% of those rating Nader or Buchanan topmost in the NES pre-election poll, ultimately did not vote for them (according to NES post-election followup, see Table 1 of Burden's paper). This is a strong example of plurality system strategic voting distortions.

2002 French Presidential Election

See this. The winner Chirac would have stayed the same, but the second-place finisher Le Pen would have changed with approval voting to Jospin. The Chirac-vs-Le Pen runoff was a landslide 82-18 victory for Chirac, but a Jospin-vs-Chirac runoff would have been too close to call, albeit but the probabilities seem to give a slight edge to Jospin.

2004 US Presidential Election

Approval voting: A November 2004 CNN exit poll of 13660 voters nationwide found for BUSH and KERRY (but the NADER results are instead from a Mason-Dixon July 2004 poll which had Bush 46/40 fav/unfav and had Kerry about equally favored and disfavored, and National Annenberg Election Survey of 2436 adults interviewed 27 Sept. through 3 October 2004):

Range(-5 to +5) Voting: CNN/USA Today/Gallup Poll telephone poll of 1538 US citizens on 25 Oct. 2004) "Rate George W. Bush on a scale. If you have a favorable opinion of him, name a number between plus one and plus five - where a plus five is the highest position indicating you have a very favorable opinion of him. If you have an unfavorable opinion, name a number between minus one and minus five where minus five is the lowest position - indicating you have a very unfavorable opinion of him."

We also conducted our own exit poll range/approval voting study. (Fullest details in paper #82 here.) The main findings were: we did not find statistically significant evidence the winner (Bush) would have changed; but Nader would have gotten tremendously more votes (relative to Bush & Kerry) with either range or approval voting, and every third-party candidate would have gotten tremendously more votes with range voting (the "nursery effect"). At the same time, both range and especially approval voting decrease ballot spoilage rates.

Plurality Voting: (Official US election nationwide popular vote results, 2 Nov. 2004)

2007 French Presidential Election

See this this multi-voting-method summary (also some details on range-type substudy).

Sarkozy won (also would have won with IRV), but Bayrou would have won with score and approval voting. Bayrou was clearly the winner France preferred both at the time (e.g, beat every rival pairwise, said polls) and later, in hindsight, based on more polls.

2008 US Presidential Election

Approval voting: Real Clear Politics average of 5 polls totalling about 6000 people (and AP/Yahoo 27 Oct. poll for Nader, and USA Today/Gallup poll 21-23 Aug. for Barr of 1023 adults nationwide) found:

More approval poll data about USA 2008, 2012, and 2016 is on this page.

Range(1-4): ABC News/Washington Post asked 1108 people by telephone on August 19-22 2008 "Do you have a favorable or unfavorable impression of John McCain? Do you feel that way strongly or somewhat?" (Also Obama.) Meanwhile Associated Press/Yahoo asked the same thing of 1753 people US-wide online on October 17-27 about various other politicians. Here are the results (very favorable=4, somewhat favorable=3, somewhat unfavorable=2, very unfavorable=1; but the AP/yah poll used a different numerical scale):

It appears from the data here that Obama still would have been the winner with either Approval or Range.

Range(1-5): Zohopolls.com, a commercial polling site, ran a range(1-5) poll of numerous early candidates for the US president (including many political figures who eventually did not actually run, and even including one fictional person and several actors and comedians). The poll, created by rangevoting.org member Clay Shentrup, began in September 2006 and continued until February 2009. There were 5785 self selected voters. That is, anybody in the world with a net-browser who happened to browse to the zohopolls.com website and wanted to participate, could. (And if you clicked on any candidate name, you got a window with the wikipedia article about that candidate.) Voters could refuse to score candidates, in which case their scores only affected the averages for the subset of the candidates whom they did score. There were measures (which seem to have been successful; although sufficiently determined hackers probably could have defeated these measures, apparently they did not try) to prevent people from voting more than once. Unlike most polls, any voter could examine the results-so-far of the poll-so-far and could change any or all of her votes over time – but only the last change counted!

Here are the (Feb. 2009, but nobody's score moved more than ±0.02 since November 2008) results. We have put asterisks(*) next to "candidates" who in fact were not US politicians but instead were actors, commentators, fictional, or non-US citizens – but in the actual poll no such marks were present.

Range(0-100): Gallup's "feeling thermometer" asked 1001 American adults to rate presidential candidates (or whatever else) on an 0-to-100 "temperature" scale, 100=best, 0=worst.

Median "temperatures": Gallup did not provide medians, but from the partial data they published we can deduce (for this purpose we'll regard "no opinion" as equivalent to "0"):

Guiliani, Thompson, Clinton, Edwards, and McCain all had median "temperature" score exactly 50, with Romney slightly behind (median≈49?). Obama was the only candidate with median score above 50 (median≈53?).

Plurality Voting: (Official US election nationwide popular vote results, 4 Nov. 2004)

2009

The four most-important-to-the-USA elections of 2009 are examined here (and subpages 1, 2). In two of the first three cases democracy (based on plurality voting) severely malfunctioned; range or approval voting would have behaved reasonably but instant runoff voting (IRV) would not have. In the fourth case, the election was fraudulent and IRV would have made things even more of a mess.

2012 France Presidential Election

See this page. Hollande still would have won with several flavors of score voting and approval voting. But the second-place finisher probably would have changed.

2012 Egypt Presidential Election

See this page. The official system – plurality plus 2-man runoff – malfunctioned because both finalists Morsi and Shafik apparently won due to vote-splits among their rivals. It appears from poll data that the Condorcet and score-voting winner was either Moussa or Sabahi, neither of whom made it into the official final round. Morsi's approval ratings plunged while in office from about 75% to about 25% and then after only 1 year he was overthrown by a coup with wide popular support. However, Morsi's remaining supporters justifiably objected to his overthrow (since he was legitimately elected using the official rules) and as of 2013 the situation remains unclear with possible decay of Egypt into chaos, military dictatorship, or new rebooted democracy all possible.

2012 USA Presidential Election

See this study. Obama still would have won with either Approval or Range voting (versus all rivals we have those-kinds-of-voting data on), but the second place finisher might have been any of

among those candidates we have data for. (Also, we lack such data for Gary Johnson, Buddy Roemer, and Jill Stein.) The Republican Primary race featured crazy plurality-voting pathologies and disserved both that party and the USA as a whole.

Both Obama and Romney had about 50:50 approval:disapproval ratio (each), while Stein and Johnson each had about 33:66, which was less than O & R, but indicates their true support (undistorted by "fear of wasting vote") far exceeded that indicated by their official plurality voting totals (both below 1% each), in yet another all-too-typical enormous distortion of democracy.

2016 USA Presidential Election

See this study. Donald Trump won with the official procedure based on plurality voting with an electoral college. Sanders or Kasich would have won with score voting, and Sanders with approval voting. Under "popular vote," H.Clinton wins with approval voting restricted to the 4 finalists {Clinton, Trump, Johnson, Stein} as well as with plurality voting; with score voting restricted to these 4 it could have been any of {Clinton, Trump, Johnson}; too close to call which. Clinton was a "spoiler" but Johnson and Stein weren't.

For experimental relationship between approval voting and candidate-truthfulness, see this study.

For "fame-based failure" pathology of plurality voting which was the reason Trump won the Republican nomination (and therefore the presidency) see this.

Summary

In many of these elections, range or approval voting would not have changed the winner and the whole election would have come out approximately the same. However, in others, range or approval would have changed either the winner, the finish-order among the top few, or both. Also, in some elections the winner with range or approval would have been different if that candidate had run but thanks to the "to avoid wasting your vote, you must vote for one of the 'top two'" mindset of plurality voting that candidate was discouraged from running, did not run, and hence could not win. Specifically:

• In USA 1980 John Anderson would have done far better with Approval voting – finishing comparable or perhaps even ahead of Carter, although he could not have won. With Range Voting Carter would have been comparable to Reagan, not far behind.
• In USA 1988 our data is inadequate and these conclusions can be criticized, but anyhow as far as it goes it suggests Jesse Jackson (if he had continued to run) would have finished comparable with Bush and ahead of Dukakis with approval voting; and senator Lloyd Bentsen would have finished ahead of everybody if he had run for president instead of vice president and if range or approval voting had been used.
• In USA 1992, H.Ross Perot could not have won, but would have done far better (comparably to Bush) with either range or approval voting.
• In USA 2000, Ralph Nader would have done far better with approval voting (exceeding Bush) and John McCain would have done even better still (if he had continued to run) exceeding both Bush, Gore, and Nader to win the presidency with either range, approval, or Condorcet (but not IRV) voting! Gore would also have defeated Bush in Florida with either range or approval voting, so that Bush would not have won.
• In France 2002, Le Pen would have done far worse under approval voting, and Jospin and Chirac would have finished comparably, perhaps altering the winner or perhaps it would still be Chirac.
• In USA 2004, Ralph Nader would have done far better with range or approval voting – not enough to boost him out of third place, but enough to finish in the same vote-total "ballpark" as Bush and Kerry. Also with range voting, every third-party candidate would have gotten far more votes (usually a factor of 10 or even 1000 times more) relative to Bush & Kerry. This would have represented far more accurately what the electorate actually wanted.
• In France 2007, range voting (either median- or average-based) would have changed the winner from Sarkozy to Bayrou, at least based on the 1752 Orsay range-voters who were studied. And clearly Bayrou would have done far better than he did with plurality+top2-runoff (where he came third). This switch probably would have been an improvement since nationwide polls indicated Bayrou would have beaten every rival in a head-to-head race with that rival.
• In 2009, two of the three most-watched elections in the USA malfunctioned severely under plurality voting, ranking the most-probable winner with range, approval, or Condorcet voting far-last. (All three candidates were near-equal under either range or approval voting.) The same huge distortion would also have occurred using instant runoff voting (IRV).

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