Donald Trump exploits plurality voting system flaws to try to become US president

By Warren D. Smith, July 2015. Please notify warren.wds AT of any errors/comments. Executive summary.

Abstract. Plurality voting can suffer a severe pathology we call "fame-based failure." Whenever a famous, media-philic candidate X runs against a large number of lesser-known and comparatively-similar rivals, with care X is almost assured victory almost regardless of what the voters think of the rivals' versus his quality. We explain why that happens, and give three important recent elections in which it did happen: Arnold Schwarzenegger 2003, Hamid Karzai 2009, and Donald Trump (ongoing) 2015 Republican primary (July polls). We then demonstrate how in the first and last of these three examples, approval or score voting would have cured the disease. ("Demonstrate" means "based on poll data.") Finally we consider the proposal by Sam Wang that IRV – Instant Runoff Voting/polling – would be another cure, and demonstrate that idea is dubious at best, and disproven at worst. IRV is highly unsuited for use by pollsters in elections with many candidates.

Fame-based failure

A circumstance in which plurality voting tends to fail even more spectacularly than it usually does, is when one famous, media-philic, and perhaps controversial candidate X runs versus a large number of lesser-known and comparatively-similar rivals. In that situation X can almost guarantee victory, whether voters like him or not!

Why? Because if some voter wants to vote against X, he/she must decide who to vote for. Even if (say) 90% of voters agree X is the single worst candidate, and they all agree every single rival is hugely superior – they still could split their anti-X votes among the (say) 15 rivals, causing X to be elected by 10% versus 6,6,6,..,6% each. Paradoxically, it can easily happen that the more spectacularly horrible X is, the more famous he therefore gets, and the more rivals are motivated to run against him, causing more vote splitting among the great number of excellent alternatives – causing X to win even bigger!

Of course, in real life the numbers usually aren't quite as dramatic as in that hypothetical 15 rivals/90% example we used to explain the phenomenon – which only makes our point more valid. The source of the problem is that the plurality system refuses to permit voters to say that they think X is the worst. It only allows them to say one name, the one they supposedly think is best, and then forces them to shut up and say nothing about all the others, i.e. absolutely zero about how much they like or dislike any of them.

These problems are then amplified by "strategic voting" effects. Voters recognize the problem and try to compensate by intentionally lying in their vote, pretending Y is their favorite even though truly it is Z. They do so because they think Y has a better chance to win than Z, and they do not want to "waste their vote." The problem with that is: it then is not about "who voters think is best," and not about "finding out how much voters like/dislike each candidate." It instead is primarily about "who convinces voters he has among the top 2 chances of winning"! Voters who do not want to waste their vote, are forced to (likely dishonestly) vote for one of those top 2. Anybody who starts out famous automatically is among the top 2 leaders on day one, simply because, on day one, many voters have only heard of the famous guy, and "never heard of him" does not count as a vote. Afterwards, voters if (and because) they follow the strategic imperative of always voting (in polls) for one of the top 2 leaders, almost always will keep X in the leading 2 slots, regardless of whether they like him. Once X is top-two poll leader, strategic voters "must" vote for either him or his top rival. So with a modicum of care it is almost impossible for X to stop being one of the top two. Similarly money donors are "strategically forced" to donate to a leader, who then uses the money for advertising, increasing his perceived-top-two status, reinforcing the situation. Again, that all happens regardless of whether voters like X or not.

Voila, X is guaranteed to finish first or second (barring some huge disaster) simply because he was the most famous on day 1. And if X can by design or luck keep enough of his large set of rivals all seeming to have similar chances to each other, then X is virtually guaranteed to win! All this has almost nothing to do with how good or bad voters think X is, and almost nothing to do with how good or bad voters think the rivals are in comparison.

Arnold Schwarzenegger 2003

was a rich and famous movie star, in large part due to him having spectacular muscles acquired with the aid of anabolic steroids. (Won Mr. Universe and Mr. Olympia pro body building titles multiple times 1967-1980 as well as several national weightlifting championships. Although he admitted steroid use, A.S. never faced any legal repercussions for it, unlike such athletes as Lance Armstrong, Marion Jones, and Barry Bonds.) He'd never held any government office, had only a high school education, and seemed to be one of the world's greatest narcissists. Sixteen women came forward to the press claiming Schwarzenegger had sexually molested them. Running against him in 2003 for the governorship of California were 134 opponents. (Sample ballot.) None were as rich as him. None were as famous as him. None had as many women complaining of unwanted sexual "grope-gate" to the press, as him. Many, however, had more education, more government experience, and/or were more willing to participate in debates.

Schwarzenegger got lots of publicity despite generally keeping his policy stances extremely vague, and refused to participate in debates with his rivals until the very last one (which had the "advantage" for him that it made all his main rivals look "similar" as debators, while he was "different" – remember, with the plurality system, clones lose).

Result: Schwarzenegger won the governorship easily with 48.6% of the vote. (See tables below.)

Unfortunately "The Governator" did not work out well for California. When he left office at the end of his legal term limit at the end of 2010, Schwarzenegger had the lowest approval rating (19% in July 2010, with 71% disapproval) of any CA governor ever. By contrast, Gray Davis enjoyed 32/44 approve/disapprove rating in July 2010 – suggesting that in hindsight California's voters regretted kicking Davis out in 2003 given that they'd had to suffer 7 years of Schwarzenegger as a result.

This report by CREW found he'd committed numerous corrupt ethical violations, making him one of the worst governors in the country in that respect, by their reckoning. It was revealed he'd secretly fathered a child with the maid he and his wife had hired to clean their house (this revelation probably played a role in causing his wife to divorce him). On his last day as his last act in office as governor he commuted the 16-year jail sentence of Esteban Nunez for manslaughter (pled guilty), down to 7 years. By an amazing coincidence, Esteban was the son of Fabian Nunez, CA's Assembly Speaker during most of Schwarzenegger's terms, whom the press claimed had become a great personal friend of Schwarzenegger. Meanwhile Schwarzenegger made the opposite move by (in the year 2009 alone) overturning decisions by the state's parole board to free 285 long-serving inmates. (Despite the fact this parole board had been appointed by his own office.) Of those, 29 did the same crime under the same circumstance as Nunez's, and of those 11 had no previous criminal record, also the same as Nunez. Among the reasons Schwarzenegger frequently gave for reversing the parole board, was that he was offended by the victim having been killed over something "trivial," and/or that the crime showed "callous disregard for human suffering," often by fleeing the scene and leaving the victim to die. Which was exactly was Nunez did after he and a friend stabbed two strangers when denied entrance to a fraternity party. Sadly for those 285, none had a parent who happened to be Schwarzenegger's buddy. He ordered the Nunez commutation without any consultation with either the stabbing victim's family or prosecutors. Schwarzenegger then refused to answer any press enquiries about it.

As of 2009, California's schools were ranked 47th out of 50 in the nation. At the start of summer 2009 the CA state government was so deep in debt that it began issuing IOUs instead of wages. In 2010 CA's state debt per capita was $4008, exceeded only by the notoriously corrupt states New York ($6694) and Illinois ($4790) within the 10 largest-population states. However, since CA's central government effectively downloaded a lot of debt to localities, really those figures understated the problem. CA's debt obligations including both state and local were estimated as $10900 per resident when Schwarzenegger left office, a figure larger per capita than every other large state in the USA besides New York. California's Moody's credit rating was tied only with Louisiana for the status of "worst state in the USA," meaning it had to pay the largest interest rates on any further debt. Its unemployment rate during 2009 and 2010 soared to 12.4%, the highest in 70 years.

Was all that the result of CA's foolish use of the plurality voting system? It looks that way. Here are the official plurality election results, approval-style pre-election poll results (favorable/unfavorable percentages), and score-style pre-election poll results using 3 score levels which I have regarded numerically as (0,1,2) for purposes of computing the average rating. For example "(19,25,47)⇒1.31" means 19% of pollees rated McClintock "VeryPoor/Poor," 25% rated him "Fair," and 47% rated him "Excellent/Good" in response to "What kind of job would McClintock do as Governor over the next three years?". (The remaining 9% refused to answer or said "Don't know.") This corresponds to an average score of (19×0+25×1+47×2)/(19+25+47)≈1.31.

A.Schwarzenegger48.58%52/41(31,21,41)⇒1.11,   (8,10,33,33,7)‡
Gray Davis†44.61%†41/52†(48,21,28)⇒0.79,   (29,30,17,1)‡
Cruz Bustamante31.47%34/56(40,23,31)⇒0.90
Tom McClintock13.41%53/34(19,25,47)⇒1.31
Peter M. Camejo2.80%24/38?
Arianna Huffington*0.55%22/54*?
Peter Ueberroth*0.29%37/34*?
Larry Flynt0.20%??
Gary Coleman0.16%??
George B. Schwartzman0.14%??
Mary E. Cook/Carey0.13%??
Bruce M. Margolin0.11%??
Bill Simon Jr.*0.10%*30/39*?
Others (combined)2.05%??
"In general, do you think it would be a good thing or a bad thing for this country if more famous people without any political experience like Arnold Schwarzenegger got involved in politics at the national level, such as running for president or the U.S. Congress?" [Princeton Survey Research Associates/Newsweek Poll, 9-10 October 2003 for Newsweek; 1004 interviews with adults nationwide]
25% Good thing
56% Bad thing
13% Neither/Mixed views (Volunteered)
6% Don't know

Details: (†) Davis asked on separate question. Specifically, the official ballots asked voters whether to recall the sitting governor Davis. They did by 55.39% to 44.61%. Then they were asked who should replace him.
(*) Simon withdrew from race 23 August, Ueberroth on 9 September, then Huffington on 30 September, but nevertheless received votes perhaps from voters unaware they'd withdrawn. (This official sample ballot dated 7 Oct. still has Ueberroth and Simon on ballot.) Consequently their approval fav/unfav (and score) ratings had to be taken from polls earlier than the telephone poll (field date 25 sep-1 oct, release date 3 oct) of 894 "likely voters" by the Field Institute that was the basis for our other approval and score ratings.
(‡) For added amusement we also have included this 12-17 August 2003 Harris poll result: "Based on what you may have seen, read, or heard about, how would you rate the job Governor Gray Davis is doing as governor – excellent, pretty good, only fair, or poor?" (1011 adults interviewed nationwide, not just in CA)

1% Excellent, 17% Pretty good, 30% Only fair, 29% Poor, 23% Unsure/Refused.
and this 3-4 Sept 2003 Harris poll result (1003 adults interviewed nationwide): "If elected, do you think Arnold Schwarzenegger will be a great governor (of California), good, average, poor, or terrible?"
7% Great, 33% good, 33% average, 10% poor, 8% terrible, 9% unsure/refused.

Simon said the reason he was dropping out was that "There are too many Republicans in this race and the people of our state simply cannot risk a continuation of the Gray Davis legacy (via a 'spoiler' scenario)." In other words, Simon fully agreed with us this race was about the distortions to democracy caused by the Plurality voting system, and they impressed him so much that he actually dropped out of the race to try to diminish them! If Simon, Ueberroth, and Huffington had not dropped out, undoubtably the "vote-splitting" would have been greater, and presumably Schwarzenegger would then have enjoyed an even greater victory margin. In terms of life background and qualifications, it seems hard to identify any logical reason why Mary Carey should have been any less qualified than Schwarzenegger, but she got only 1/370 of his vote count.

Tom McClintock, the official 3rd (or 4th) place finisher, would have won using either approval or score voting. McClintock had previously served in the CA assembly 1982-1992 & 1996-2000, and CA senate 2000-2008, and later became a U.S. congressman for CA (2008 up to at least 2016). The table shows McClintock was the only candidate with more approval than disapproval and with over twice as many "Excellent/Good" ratings as "VeryPoor/Poor."

Other candidate backgrounds included: Camejo (also ran for Gov. 2002 and 2006; helped found CA's Green party, CEO of financial firm), Huffington (columnist and later co-founder of The Huffington Post), Ueberroth (baseball commissioner, organizer of 1984 summer olympics, and former airline executive), Flynt (publisher of pornography and 1st amendment activist, slogan "smut peddler who cares"), Coleman (former child actor), Schwartzman (little-known businessman), Cook (pornographic actress who usually worked under the name "Mary Carey"; also film director & ran for Lt.Gov. in 2006), Margolin (criminal defense attorney and advocate of marijuana legalization), Simon (the GOP candidate for CA governor who'd been defeated by Davis in 2002 by 47.26% to 42.40%, with Camejo getting 5.26%).

More data: The academic paper R. Michael Alvarez & D. Roderick Kiewiet: Rationality and Rationalistic Choice in the California Recall, British Journal of Political Science 39 (2009) 267-290 [originally written 2005] describes a survey of 1500 voters in this CA 2003 election; preference orderings were solicited from the voters within the (small) candidate-subset {Schwarzenegger, McClintock, Davis, Bustamante}. Only 50.7% of those surveyed agreed to give a full preference ordering among these 4. The 6 pairwise preferences (in net) all were compatible with the ordering S>M>D>B. Of the 6 pair preferences, only Schwarzenegger vs. McClintock was in doubt, statistically speaking; i.e. really the ordering should be written "S≈M>D>B" because S vs. M was a statistical tie. Specifically, of the 1244 voters who expressed a preference about this pair, 30 more preferred Schwarzenegger. This was smaller than the ±2σ statistical error √1244≈35.3. Meanwhile McClintock was found to be more-preferred vs. Bustamante and vs. Davis, than Schwarzenegger was, further indicating "tie." Concerning the strategic imperative to lie in your vote to "support" one of the top two leaders that we mentioned in our first section, they also report "Schwarzenegger's vote share was boosted significantly by strategic voters, and over two-thirds of Bustamante's votes came from those whose (honest) first choice was for another candidate." Obviously the plurality-caused distortion was enormous as you can see by comparing the S≈M finding of the Alvarez-Kiewiet poll, with the S=48.58% vs. M=13.41% finding of the official election.

Afghanistan 2009

Another classic failure of this ilk was the absurd and highly corrupt presidential election in Afghanistan 2009 "won" by Hamid Karzai (the USA's attempt to install a puppet, and the brother of one of the biggest opium dealers in the country) versus 40 rivals.

Donald Trump 2015

is currently (I am writing this in July 2015) either intentionally or by luck, imitating Schwarzenegger's strategy, but now running for the US presidency rather than governor of its largest state. Trump also is a famous and rich ultra-narcissist playboy and braggart. He is currently estimated to have somewhere between $1 and $12 billion in wealth (albeit you are warned that Trump has a record of greatly exaggarerating his wealth) despite 3 marriages (all to beautiful models and actresses) – acquired by being born the son of a New York real estate mogul, then continuing to become an even bigger real-estate mogul, plus owning gambling casinos. Trump later experienced several gigantic bankruptcies, becoming on paper perhaps the poorest man in the world in the sense his wealth was an enormous negative number. Those also made him ultra-famous. They however did not end his career (it was pointed out that if you are in debt for $5000, you are just broke; but if in debt for $200,000,000 that is the bank's problem, not your problem). He presently is diversified into owning hundreds of businesses in many areas, e.g. one of his largest recent income sources was advertising mattresses. "The Donald" also became very famous by becoming a bombastic television celebrity and game-show host with an unusually impressive hairdo, by writing numerous books (mostly of the "get rich" business-advice type and actually written by ghost-writers), and by constantly making well-publicized outrageous controversial statements, such as his theory that President Obama faked his birth. Trump however had never held (or run for) any government office, his web site was unique among all the 17 Republian contenders in that it had no "issues" section (at least as of mid-August 2015; Update: still none at the end of Sept. 2015) and his main qualification for the presidency apparently was simply that he had acquired great wealth and fame.

Nevertheless, I happen to think Trump is more qualified (or perhaps a better phrase is "less unqualified") for high government office than his apparent role-model Schwarzenegger was. (E.g, Trump did have a college education.)

None of Trump's 16 major Republican rivals were anywhere near as rich as him, few if any had as much fame, television exposure, or as many wives... but most had far greater government experience (e.g. served as governor, senator, congressman). Trump adopted a strategy of making numerous well publicized entertaining/controversial/insulting style statements, while delivering very few details about what he'd do. For example, Trump explained he had a secret plan, which he would not divulge, which would virtually instantaneously defeat the ISIS militant/religious group that had taken over most of Iraq and a large chunk of Syria! Trump generally would not provide any specific stances or proposals in answer to press enquiries, instead answering with some brag or at best a vague hint. (E.g. what would Trump do about women's issues? "I'd be excellent for women. I love women and women love me." Oh.) He also stated that "the worst elements in Mexico are being pushed into the United States by the Mexican government. The largest suppliers of heroin, cocaine and other illicit drugs are Mexican cartels that arrange to have Mexican immigrants trying to cross the borders and smuggle in the drugs. The Border Patrol knows this. Likewise, tremendous infectious disease is pouring across the border. The United States has become a dumping ground for Mexico and, in fact, for many other parts of the world... The Mexican Government is forcing their most unwanted people into the United States. They are, in many cases, criminals, drug dealers, rapists, etc."

Polls – with different voting methods

By August 2015, Trump's flavor of the Schwarzenegger-imitation strategy had worked superbly. All major nationwide plurality-voting-style polls during July 2015 agreed that Trump led all Republican candidates for the US presidency. (Because the 17th major Republican candidate, former VA governor Jim Gilmore, waited until 30 July to announce his candidacy, he was not included in the polls tabulated below. But if he had been, he would lie at or near the bottom with <1%. We have employed such abbreviations as Huckabee→Huckb, Christie→Chrst, Santorum→Santm, Kasich→Kasch, Fiorina→Fiorn. Update: Trump continued to lead every nationwide plurality poll up until the end of Sept. 2015.)

July PollDateTrumpWalkr BushRubioHuckbCarsnPaulCruzKasch ChrstPerryJindlSantmFiorn PatkiSpread
Quinnipiac23-2820131066665 5322111Trump +7
Rasmussen26-27261410575375222211Trump +12
CNN/ORC22-25181015654674432211Trump +3
ABC/Wash Post16-19241312786642342101Trump +11
PPP (D)20-2119171210810443311140Trump +2
FOX News13-15181514746842310210Trump +3

Meanwhile, Hillary Clinton enjoyed an even more enormous lead in all major July plurality-voting-style polls during July 2015 for the Democratic party's nomination. This was certainly due, in part, to the same "famous person versus lesser knowns" phenomenon. Everybody in the USA had heard of (former first lady and later Senator and secretary of state; also had run for US president in 2008) Hillary Clinton. But her rivals Bernie Sanders, Jim Webb, Lincoln Chafee (sitting or former senators from small states) and Martin O'Malley (former gov. of the small state of Maryland) were much lesser known, in fact probably most US citizens had never heard of them. It could be argued that Clinton's fame was "legitimate" in that everything she was famous for, prepared her for the presidency (as contrasted with Schwarzenegger's and Trump's reasons for fame, which seemed less relevant job preparation). But regardless of whether their fame was "legitimate" or not, it triggered the same mathematical plurality voting phenomenon/flaw. Clinton easily led the polls versus these rivals, despite a news report by the NY Times that she might be under investigation for criminal evasion of laws about official emails, including criminally negligent handling of state secrets, while secretary of state. (Asterisk *: Biden was included in 4 of these polls despite not having announced candidacy & never ran. L.Lessig entered the race too late to be included in the polls below and his numbers would have been below 1%.)

July PollDateSampleClinton SandersBiden*J.WebbO'MalleyChafeeSpread
Quinnipiac23-28681 RV551713110Clinton +38
CNN/ORC22-25392 RV561915100Clinton +37
PPP (D)20-21496 RV5722523Clinton +35
ABC News/Wash Post16-19RV631412210Clinton +49
FOX News13-15382 RV59198111Clinton +40

Approval- and Score-style polls

Meanwhile, approval-style and score-voting style polls were also conducted. These two voting systems enjoy far better (arguably complete) immunity to the "cloning" and "vote splitting" problems, and allow voters to express positive or negative opinions about every candidate, not just one. These undistorted polls told a very much different story!

PPP1a: Public Policy Polling survey of 524 Republican primary voters nationwide, 20-21 July 2015. 80% of participants via telephone, 20% over the internet.

ARSC: Anderson Robbins Research (D) / Shaw & Company Research (R) poll of 1005 registered voters (654 landline, 351 cell phone) 21-23 June 2015 for Fox News. This poll asked about head-to-head races between Republican X versus Hillary Clinton. (If the pollee votes for Republican X, that can be regarded as "approving" him; but if votes for Hillary, that's "disapproving" him.) [Also asked: "Do you approve or disapprove of the job Barack Obama is doing as president?" finding 44% approve, 50% disapprove; "Do you consider Donald Trump a serious presidential candidate or a side show?" finding serious 18%, sideshow 77%.]

PPPh: Same PPP poll 20-21 July, but now asking about a Republican X versus Hillary Clinton head-to-head race, and using 1087 voters nationally (note not just Republicans).

PPPs: Same as PPPh, but now asking about a Republican X versus Bernie Sanders head-to-head race.

HartPOSsys: Hart/Public Opinion Strategies score-style poll (for Wall St. Journal & NBC news) 22 June asking 236 Republican Primary voters, for each candidate, one at a time, whether "you could see yourself supporting that person for the Republican nominee for president in 2016." (Yes or no.) This is a kind of approval.

McCMar: McClatchy News Serice/Marist telephone poll of 1249 adults nationwide, 22-28 July 2015, including 964 registered voters. We have only employed their results within the 964-RV subset. "If the 2016 presidential election were held today, whom would you support if the candidates were X(repub) versus Hillary Clinton(dem)?"

HartPOSscore: Hart/Public Opinion Strategies score-style poll (for Wall St. Journal & NBC news) 22 June (asterisked *) and 17-21 July 2015 (unstarred). each by telephone to 1000 adults nationwide (note not just Republicans). "Now I'm going to read you the names of several public figures... and I'd like you to rate your feelings toward each one"; the scale used was (very negative, somewhat negative, neutral, somewhat positive, very positive) which I have regarded as (0,1,2,3,4) for purposes of computing average scores. Also polled, although not candidates:

John Boehner: (18,18,24,15,3)⇒1.58; George W. Bush: (25,14,22,25,13)⇒1.87.

The candidates have been sorted in decreasing order of their fav/unfav ratio in the PPP1a column.
CandidateFav/UnfavYes/NoYes/NoYes/No Yes/NoYes/No Score%s⇒Avg
Scott Walker58/1541/4741/4640/39 57/1941/48
Marco Rubio54/1944/4541/4641/36 74/1542/47(12,12,24,16,7)⇒1.92
Ben Carson53/1941/4639/4739/49
Bobby Jindal43/1736/28
Rick Santorum48/1949/40
Rick Perry50/2053/3140/47
Ted Cruz51/2142/4840/4851/3140/49
John Kasich29/1525/3039/49
Carly Fiorina38/2237/4731/29(6,7,14,11,4)⇒2.00*
Mike Huckabee49/3040/4665/3241/50(14,14,26,18,8)⇒1.90*
Rand Paul42/3042/4642/4549/4543/48
Donald Trump48/3934/5137/5037/4732/6638/54
Jeb Bush41/3543/4341/4644/3775/2243/49(20,16,29,21,6)⇒1.75*
Lindsey Graham21/3327/49
Chris Christie25/5638/4636/5540/50
George Pataki12/2913/44
Jim Gilmore4/14

These prove that Trump's "top" ranking by a large margin in plurality-style polls (above) was a massive distortion. Trump is actually bottom (among Republican candidates surveyed) in terms of his head-to-head comparison versus Hillary Clinton (twice), and his head-to-head comparison versus Bernie Sanders, and his "could you see yourself supporting" score among Republican primary voters. In case you are wondering, a distortion between far and away in first place versus bottom place is "massive."

It also is interesting that Carly Fiorina was the top scorer (among Republican candidates and noncandidates surveyed) in the US-wide score-style poll. (All the pundits had dismissed her as though she were nothing.)

PPP1b: Public Policy Polling survey of 426 Democratic primary voters nationwide, 20-21 July 2015. 80% of participants via telephone, 20% over the internet.

HartPOSscore: Hart/Public Opinion Strategies score-style poll (for Wall St. Journal & NBC news) 22 June (with *) and 17-21 July 2015 (unstarred). each by telephone to 1000 adults nationwide (note not just Democrats). "Now I'm going to read you the names of several public figures... and I'd like you to rate your feelings toward each one"; the scale used was (very negative, somewhat negative, neutral, somewhat positive, very positive) which I have regarded as (0,1,2,3,4) for purposes of computing average scores. Also polled, although not candidates:

Barack Obama: (27,14,13,20,25)⇒2.02* and (26,14,12,20,28)⇒2.10 (mean 2.06); John Kerry: (14,15,24,28,10)⇒2.05*;
Joe Biden: (20,15,21,21,17)⇒2.00; Andrew Cuomo: (6,9,24,11,5)⇒2.00.

Hillary Clinton69/22(29,11,15,23,21)⇒1.96*
Bernie Sanders42/26(7,6,22,8,8)⇒2.08*
Jim Webb12/33
Martin O'Malley13/36(3,2,14,5,2)⇒2.04
Lincoln Chafee9/32

It is interesting that Sanders is top (among Democratic candidates – and Democratic noncandidates, and Republican candidates and noncandidates too!) in the score-style poll of a USA-wide sample, even though Clinton is top using either plurality or fav/unfav polling using Democrat-only samples.

Instant Runoff Voting – a different cure for this problem? Dubious.

As we have just seen, in the Schwarzenegger and Trump cases, we have clear evidence that approval and score voting would have cured the problem. Pollsters, and the Democratic & Republican primaries, and the general election, all should switch to these polling methods, as far as we are concerned. And that is not only because it would help the USA and the world. It also would help the Republican party alone. Note that Trump was far and away leading all July plurality-style polls among Republican voters, but, if nominated, he would provide Republicans with by far their worst election chances versus either Clinton or Sanders! Sixty-six percent of Republicans "could not see themselves supporting" Trump!! That proves the Republican party is suicidally stupid to use plurality voting to produce their nominee. Do they have a death wish?

But Sam Wang (Princeton neurobiology professor) instead recommended a different cure – that pollsters should switch to Instant runoff voting (IRV). This was in his article Donald Trump Is Not the Frontrunner. Smarter Polls Would Prove It, published in the New Republic 20 July 2015.

Unfortunately, I know of zero direct evidence for Wang's stance. Using IRV as a polling method in an effort to avoid the fame-based failure pathology seems dubious for these reasons:

  1. Concerning the "fame-based failure" pathology in general: although thousands of IRV elections have happened – mostly for Australian House seats – as of July 2015 I am unaware of any instance in world history, in which one famous candidate has (a) run under IRV versus a large set of lesser known rivals, none of whom were particularly pre-eminent, and (b) lost.
  2. There is no direct evidence IRV would have cured the Trump and Schwarzenegger problems, because no IRV-based poll was ever run for these contests. Incidentally, it nowadays is very common that pollsters run approval- and score-style polls, but exceedingly rare that they ever run an IRV-style poll... indeed I am unaware of any pro pollster ever conducting an IRV poll (or any poll soliciting a full preference ordering) in any election with more than 10 candidates, in the history of the world... and there are good reasons for that:
  3. It would have been pretty absurd to use IRV for a poll. To do so, pollsters would have needed to ask pollees to rank all 17 major Republican candidates in order of preference (Trump) or all 135 (Schwarzenegger). That would have been too much to ask! Very few would have been willing to do so. Indeed, the average person is not capable of even remembering an ordering of more than 7±2 items. That would make it impossible to do a preference-ordering, e.g. IRV, poll over the telephone; it would only be possible with paper and pencil. Since pollsters regard telephone polls as the best compromise between cost, speed, and accuracy, that would be a major problem. With score and approval voting pollsters can simply ask for a score (or approval yes/no decision) on each candidate one at a time and no insuperable mental challenge occurs.
        One could try countering that there is a flavor of IRV implemented in some places (but not in most of Australia) in which it is not mandatory to rank all candidates. Pollees using that IRV variant could only rank some of the candidates. I would expect, in fact, that most pollees only would rank a few. (Indeed, in the PPP 2nd-choice polls discussed below, 20% of Republican voters, and 49% of Democratic voters, refused to provide anything beyond just their first choice! In the Alvarez-Kiewiet poll above only 51% could/would rank-order merely 4 candidates.) Unfortunately, with that IRV-variant, the numerous unranked candidates are automatically and inherently regarded as all ranked coequal-bottommost. That would provide an extremely – near-maximally – distorted notion of voter preferences. (With score voting, voters can leave candidates unscored and then that will not affect those candidates' average scores. With favorable/unfavorable approval-style polling, voters who choose not to score a candidate, again do not affect his fav/unfav ratio. These two methods, therefore, do not suffer that kind of large distortion.)
  4. Even if pollsters did manage (perhaps via a monetary incentive), to convince all pollees to state full preference orderings, then the 2nd (and all succeeding) choices of the Trump-voters still would be ignored by the IRV process – a rather absurd waste of hard-earned polling data! (Also, many other stated preferences, in fact the majority of them, also would be ignored by the IRV process.) Pollsters do not like flushing data down the toilet, especially hard-to-obtain and expensive data.
  5. For Schwarzenegger's 2003 election, IRV would not have cured the problem, because the Alvarez-Kiewiet poll showed McClintock statistically tied with Schwarzenegger, but IRV would have eliminated McClintock early, preventing him from ever entering the IRV final round. Therefore IRV would have elected Schwarzenegger. This fact contradicts Wang's hypothesis IRV would cure the "fame-based failure" problem. (The CA 2003 election also probably contradicts the hypothesis "Bucklin voting" would have cured the problem. Sam Wang told me privately he now prefers Bucklin over IRV, but did not deign to mention that in his New Republic article.)
  6. A "second choice" poll was conducted for the Trump-dominated Republican primary, see below. ("Who would be your second choice for the GOP candidate for President in 2016?" Asked of 524 Republican primary voters nationwide, 20-21 July 2015, by PPP.) To explain the table format by example: Mike Huckabee (MH) got 8% of the vote. Among Huckabee voters, 12% would pick Ted Cruz as their 2nd choice.
percent1210 3 4 4 0 0 8 1 3 0 4 110 11917(100)
Jeb Bush *2 1212 2 2322 13 21232828 7 9|   9
Ben Carson 3 *132238100 18 9 8 7 9 10 5|   9
Chris Christie13 3 * 2 1 21 2 1 8 1|   4
Ted Cruz 3 9 *10 12 7 3 2 8 9 6|   6
Carly Fiorina 4 834 2 * 1 3 2 2 3 9|   1
Jim Gilmore 3 * 8 |   5
Lindsey Graham 1 2 * 1 |   0
Mike Huckabee 513 4 * 6 4 4 3|   4
Bobby Jindal 3 54 2 * 7 4 5|   2
John Kasich 5 3 23 *79 2 4 9|   4
George Pataki 1 * 1 1|   0
Rand Paul 4 5 4 3 * 7 6 1|   3
Rick Perry 1 3 4 9 12 * 1 2 5|   3
Marco Rubio 11 9 3 6 7 3 715 17 *36 812|   8
Rick Santorum 4 1 5 * 2 2|   2
Donald Trump 510 1612 820 3 823 611 *12|   7
Scott Walker 220 32 7 23027 53927 20 *|   12

Does this poll support Wang's "use IRV" idea? Not much. Trump is the winner (with 19%) in this poll using first choices only (and a bigger winner in other plurality polls, see above). His top four rivals are Walker (17%), Bush (12%), Carson (10%), and Rubio (10%). Now as a second choice, the top five are the exact same set of candidates, except it now is Walker 12%, Bush 9, Carson 9, Rubio 8, Trump 7. The summed (first+second) popularity scores therefore are Walker 29, Trump 26, Bush 21, Carson 19, Rubio 18. If the IRV process were used to eliminate everybody besides Trump and Walker, then the final head-to-head round would be Walker 25 versus Trump 24 which would be a slight victory for Walker, albeit well below the margin of statistical error. (Assumption underlying this: as each candidate is eliminated, his votes transfer to his second choice in the proportions tabulated. Note that if, say, X is eliminated with some votes transferring to Trump and some to Y, then Y is eliminated, some of Y's votes may transfer to Trump, which indirectly causes some more X votes to transfer to Trump.) And if we attempt to correct for the fact that this particular poll happened to feature atypically small Trump and atypically large Walker support (versus the other polls tabulated above) probably really Trump would have been the IRV victor. (Update: Walker dropped out of the race, or at least "suspended his campaign," in Sept. 2015.)

In short, we have evidence that IRV would not have been a cure, but approval and score would. That would flat out contradict Wang. It also would demonstrate the continued suicidal/death-wish nature of the idea of switching to IRV, from the standpoint of the Republican Party. If on the other hand we really do believe Walker would have won with IRV, then that would mildly support Wang. But only mildly, since demotion of Trump to 2nd place by a statistically insignificant margin is not exactly a dramatic cure for the massive "fame-based failure" distortion suffered by plain plurality voting.

Incidentally, PPP simultaneously conducted the same kind of "2nd choice" poll for the Democratic primary, finding using 1st-choices only that Clinton won with 57% over her closest rival Sanders with 22%; these same two also were the most popular as 2nd choices (Sanders 20%, Clinton 13%). If the IRV process had been used to eliminate everybody besides Clinton and Sanders, then Clinton would have won by 60-24 over Sanders.

Jack Lessenberry detects fame-based failure probably about to happen in Michigan, but draws wrong conclusion from that

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