USA 2012 presidential election viewed through prism of voting method reform

By Warren D. Smith, April 2013 (also with some contributions from Jameson Quinn)


We shall review the 2012 USA presidential election contrasting what happened with the official plurality-based voting system, with what would have happened using approval or score voting. To do this we take advantage of the fact that about 100 nationwide polls were conducted using these alternative systems.

The General election and Democratic party primary would still have come out the same. The Republican party primary would have changed substantially and probably for the better if changed to use score or approval voting and merged into the whole general election (so that the whole populace voted on all these candidates); a substantially different set of candidates would have performed well; there would have been less "wild variability" and "randomness"; and there would have been a better chance that a Republican could defeat Obama (i.e. the Republican party itself would have been better off switching voting systems). Approval voting tends to have a "pro-centrist bias," versus plurality's and IRV's pro-extremist biases, and that might also have happened in this election provided we regard Cain, Bachmann, Perry, Santorum as more "extreme" and "strange" as opposed to regarding Huntsman & Pawlenty as more "centrist."

Also, as usual, the official system tremendously distorted the level of support for third-party candidates, making it appear they had almost none whereas in fact it was substantial.

The General Election

The general election, since essentially a 2-man race between Obama & Romney, was boring from the standpoint of voting method theory.

Official popular vote totals for 6 Nov. 2012 election.
Barack Obama(D)51.07
Mitt Romney(R)47.21
Gary Johnson(L)0.99
Jill Stein(G)0.36
Virgil Goode(C)0.09
0-100 range voting (16-18 Oct. 2012, Democracy Corps, Greenberg Quinlan Rosner Research Inc; 1001 likely voters; online). "Warm" means score>50, "cold" means score<50.
Candidatemean score%warm%cold
{+2, +1, -1, -2} score voting. 31Oct-2Nov. 2102, ABC News/Washington Post, sample 1485 by telephone using verbal scale {strongly favorable, somewhat fav'ble, somewhat unfav, strongly unfav}.
Approval Voting. Based on's combined assessment of many approval-voting-style polls leading up to election day 2012; Reason/Rupe Sept. 2012 poll (question 6) for Johnson; PPP poll of MA only June 2012 (hence asterisk *) for Stein; PPP poll of VA only released 7 Oct. for Goode (question 7).
G.Johnson 7%14%
Jill Stein*12%23%
Virgil Goode*13%29%

Note MA and VA were Stein's and Goode's home states, respectively. In the rightmost score-voting table, the "means" were calculated via

mean for Obama = (38×2+16×1-11×1-34×2)/(38+16+11+34) = 0.1313
mean for Romney = (30×2+23×1-14×1-31×2)/(30+23+14+31) = 0.0714

If however we instead calculated them via

mean for Obama = (38Y+16X-11X-34Y)/(38+16+11+34) = (4Y+5X)/99
mean for Romney = (30Y+23X-14X-31Y)/(30+23+14+31) = (9X-Y)/98

for any scores X,Y with 0≤X<Y (not necessarily Y=2 and X=1, for example Jameson Quinn prefers X=1, Y=3 yielding equispaced scores), then we'd still always conclude "Obama defeats Romney" so this conclusion is robust.

The two score voting polls' question wordings were

Democracy Corps ABC/WashPost
Please rate your feelings toward some people and organizations, with 100 meaning a very warm, favorable feeling; 0 meaning a very cold, unfavorable feeling; and 50 meaning not particularly warm or cold. You can use any number from 0 to 100, the higher the number the more favorable your feelings are toward that person or organization. If you have never heard of that person or organization or have no opinion about them, please enter 101. Barack Obama.   Overall, do you have a favorable or unfavorable view of Barack Obama? Do you feel that way strongly or somewhat? (Same wording for Mitt Romney, of course.)

I also found a Reuters/Ipsos poll (3-7 Sept 2012, 1434 likely voters) using {+3,+2,+1,-1,-2,-3} score voting using the verbal scale
   {Very favorable, Somewhat favorable, Lean towards favorable, Lean towards unfavorable, Somewhat unfavorable, Very unfavorable}
and a NBC/WSJ poll (1475 likely voters interviewed, 1-3 Nov 2012) using {+2,+1,0,-1,-2} verbal scale
   {Very positive, Somewhat positive, Neutral, Somewhat negative, Very negative}:
Candidate+3+2+1-1-2-3 mean
Obama2917811629% 0.19
Romney191815151023% 0.04
NBC/WSJ 17-20 Oct
Candidate+2+10-1-2 mean
NBC/WSJ 1-3 Nov
Candidate+2+10-1-2 mean

The only development of much interest was statistician Nate Silver (whose "FiveThirtyEight" forecasts and models are often published in the New York Times) successfully predicting not only Obama's 2012 victory, but indeed Silver's model correctly called all 50 US states plus the district of Columbia.

We therefore focus on the primary elections.

The Primaries

The Democratic Party primary was even less interesting: President Obama easily won their (re)nomination with almost no opposition, winning every state by a massive margin.

The Republican Party primary, however, was a prolonged and massive joke. Or perhaps better phrases are "national embarrassment" and "slow moving political train wreck." The Republicans (and entire country) would certainly not have been worse off, and might have been far better off, if they had used score voting for their primary.

, Plurality tracking polls: RCP average 2012

Why? With plurality voting, what tends to happen is that two candidates, via luck, or past history, or a big dose of advertising money, appear temporarily to be "the two most likely to win." Then they shoot up hugely in the polls since nobody wants to "waste their vote" on anybody who is not a contender. This in turn causes them to get money donations (nobody wants to donate to non-contenders) causing them to appear more convincingly to be "one of the top two" etc. So largely by random chance, two candidates get selected and for the rest of Time, the race is just between those two. That's unfortunately what usually happens and it is ridiculous – the Republican Party and USA both deserve better than "most wanted among two randoms."

However, in this race, that did not happen. It kept trying to happen, though. A random, often incredibly asinine, candidate would appear, somehow create the impression he/she was one of the Top Two, then shoot up in polls and votes. As you can see from Real Clear Politics' graphical attempt to track and average plurality-style polls of the GOP contenders throughout the Republican primary, first Bachmann shot up to top in the polls (actually RCP seems to have missed the 15-17 July nationwide poll showing that, which we've added); then fell to low numbers (she eventually dropped out). Then Perry shot up to top, then fell, even more dramatically. Then Cain. Then Gingrich. Finally Santorum. Eventually, Romney, who'd managed to stay "one of the top two" throughout, emerged on top simply by dint of staying power even though widely disliked; and note he too then experienced a great rise in the polls at the end. (Romney's only previous elected office was as 1-term Massachusetts governor; he did not run again since it seemed clear that if he tried he could not be re-elected. Romney mainly distinguished himself in this race by probably the greatest number of major "flip flops" ever seen from a major US presidential contender.) At that point, one might have expected Huntsman (or Paul?) to shoot to the top just to continue the roller-coaster pattern, but by that time Romney had accumulated so many votes that it was fairly clear that Huntsman could not credibly claim to be "likely to win" (nor even "second most likely to win") even if he too could hitch a Random Rocket Ride. Therefore, voters and donors abandoned him and that did not happen.

All those sudden amazing rises were not at all logical in the sense that the rocketing candidate suddenly got to be a lot better in any objective sense. No: it always was a fad, caused by the strategic imperatives of the stupid Plurality Voting System. [Perhaps the fact that in this race, for the first time in a long time, unlimited money by corporations and rich donors was allowed, was one reason things were so volatile.] After said incredo-rise, the candidate would usually fall flat on his (or her) face by revealing his/her massive asininity in the most public and clear possible manner, causing him/her no longer to be reckoned "top two most likely to win" producing an equally dramatic fall. This kept happening. Romney's eventual final rise also was not caused by any great improvement in perceptions of him independent of the GOP race: his favorable:unfavorable rating started out in late 2010 and early 2011 as 36:29 and 40:30, in January 2012 was 39:37, dipped to a low of 37:47 in early April, in late June 2012 had recovered to 43:43, and by the time of the Nov. 2012 election it was 49:45. The net change actually was a drop!

You have to realize than many of the candidates were ludicrous. For example Cain had never held any elected office and made a living as a "motivational speaker" talking about how he had in earlier days been appointed head of the "Godfather pizza" restaurant chain (after still earlier managerial experience in "Burger King") which I guess was supposed to inspire other people to also become pizza chain managers. Perry famously announced during a nationally televised debate that he was going to trump all his wimp rivals at budget cutting, by totally eliminating 3-5 departments of the Federal government. But then, a minute later, he could not remember how many and which ones! Bachmann earned the sobriquet "batshit crazy" for her continual propensity to utter the most absurd notions of what was going on in the world. Gingrich was the former speaker of the USA house, who'd resigned as the result of an ethics scandal (not exactly a strong qualification) and he'd played a leading role in the failed impeachment of President W.J.Clinton over his philandering (oh sorry, Gingrich's stance was it was because Clinton lied about doing it, not because he did it), which also was unlikely to impress the bulk of the public, especially since Gingrich himself had such a long history of repeated embarrassing marital failures/imbroglios that it actually made Clinton look good by comparison.

Eventually after many such amazing rises and falls of candidates revealed as embarrassments... Romney, who had lots of money and managed mostly to avoid the highest levels of stupidity, won even though widely disliked.

The net result was that the Republicans nominated a contender (Romney) unable to beat Obama. But Jon Huntsman, as former Utah Governor (two terms, won re-election with over 78% of the vote and had very high approval ratings among Utahans, e.g. over 80% at end of second term and sometimes 90% during terms) Ambassador to China, and wealthy businessman, on paper seemed the most qualified. Utah was named the "best managed state" by the Pew Center on the States during his terms. And Nate Silver's model suggested Huntsman was the most electable versus Obama (indeed some models predicted he was the only Republican able to defeat Obama), see graphic below. However... Huntsman got nowhere!

Silver model predicts Huntsman the most electable
From "Choose Obama's Re-Election Adventure," New York Times 3 Nov. 2011. Silver's "Obama versus X" model
regards Gingrich and Santorum as nearly equivalent to Perry, but makes no forecast about Ron Paul.

Similar remarks could be made about (two term MN Governor, approval:disapproval ratings of 46:40, 49:49, 42:52 among Minnesotans during and after terms) Tim Pawlenty, also a highly qualified and perhaps comparatively electable Republican. Pawlenty dropped out of the US presidential race in August 2011 – I repeat, August, before even a single vote had been cast – an apparent victim of plurality voting pathologies (he did not believe he could "catch a rocket ride" because he'd used up his early pool of money without succeeding in creating the impression he was one of The Top Two Most Likely To Win, thus judged himself unlikely to be able to attract a huge pool of further money, etc).

That was just absurd. Why should the most qualified and electable candidates feel/be unable to run just because they couldn't reach top-two poll status before the game even began?

This early nationwide score voting poll by Quinnipiac University (21-28 Feb 2011; note it also includes many – here italicized – "contenders" who actually made no attempt to run for 2012 president; they unfortunately omitted Perry but based on data we shall present later Perry would have done poorly with score voting) indicated that actually Pawlenty and Huntsman both initially enjoyed better mean assessments than every Romney-rival (Bachmann, Santorum, Gingrich, Paul) all of whom, mainly due to the "random rocket ride" phenomenon, far out-primaried them both:

Quinnipiac 21-28 Feb 2011 score-voting style poll
1887 registered voters, split sample, names were rotated, each respondent
asked 15 names, rating each on 0-100 "temperature" scale ("margin of error ±2.3"). 
Mean scores and the percent who said they did not know enough about the people 
to rate them were:
Michelle Obama                  60.1 degrees      4 percent
President Clinton               59.2              2
Christopher Christie            57                55
President Obama                 56.5              0
Rudolph Giuliani                52.3              13
Mike Huckabee                   51.8              22
John Boehner                    51.1              41
Mitt Romney                     50.4              23
Tim Pawlenty                    48.2              67
Jon Huntsman                    47.9              84
Ron Paul                        46.3              34
Michael Bloomberg               46                35
Michele Bachmann                45.6              55
Mitch McConnell                 45.2              48
Mitch Daniels                   45.1              78
Donald Trump                    45                5
Rick Santorum                   43.9              63
President George W. Bush        43.9              0
Haley Barbour                   43.5              65
Newt Gingrich                   42.7              17
Sarah Palin                     38.2              4
Harry Reid                      34.8              37
Nancy Pelosi                    32.9              15

This suggests the Republican party would have been better off, providing the USA with a better debate, among more-impressive and logical candidates, yielding them a greater chance of winning, if they had instead employed score voting.

{-2, -1, +1 +2}-score voting: a closer look

Other score voting style polls using allowed-score-set {+2, +1, -1, -2} were conducted by ABC News/Washington Post, and independently by AP News/GfK, and Reuters/Ipsos at numerous dates (in addition to the final ABC/WashPost one using a larger sample we gave at the top of this page). Unfortunately for our purposes, these pollsters included (and omitted) different sets of candidates in their polls at different dates. You can seek fairer comparisons among pairs of candidates by examining their mean ratings at the same (or nearly same) polling dates.

Tarrance/Lake19-22 Sep 2010 Romney16%291314+0.2778
Tarrance/Lake19-22 Sep 2010 Pawlenty5%964+0.2083
Tarrance/Lake19-22 Sep 2010 B. Obama39%15837+0.1111
Tarrance/Lake19-22 Sep 2010 Gingrich17%221029-0.1538
Reuters/Ipsos3-6 Mar 2011 B. Obama24%301824+0.1250
Reuters/Ipsos3-6 Mar 2011 Pawlenty5%17127+0.0244
Reuters/Ipsos3-6 Mar 2011 Romney8%2820120.0000
Reuters/Ipsos3-6 Mar 2011 Gingrich10%251920-0.1892
Bloomberg News9-11 Sep 2011 Obama21%291928-0.0412
Bloomberg News9-11 Sep 2011 Cain7%151314-0.2449
Bloomberg News9-11 Sep 2011 Perry11%211625-0.3151
Bloomberg News9-11 Sep 2011 Huntsman3%141814-0.5306
Bloomberg News9-11 Sep 2011 Bachmann8%201929-0.5395
Bloomberg News9-11 Sep 2011 Gingrich7%212431-0.6145
Bloomberg News9-11 Sep 2011 Santorum4%131718-0.6154
Bloomberg News9-11 Sep 2011 Ron Paul8%242318-0.2603
Bloomberg News9-11 Sep 2011 Romney10%322315-0.0125
ABC/WashPost14-18 Sep 2011 Romney5%271614-0.1129
ABC/WashPostlate Sep 2011 Bachmann9%181318-0.2241
ABC/WashPost14-18 Sep 2011 Perry7%161219-0.3704
ABC/WashPost12-16 Oct 2011 H. Cain10%2014130.0000
AP/GfK13-17 Oct 2011 B. Obama30%241431+0.1651
AP/GfK13-17 Oct 2011 H. Cain16%271815+0.1447
AP/GfK13-17 Oct 2011 Romney13%362215+0.1163
AP/GfK13-17 Oct 2011 Ron Paul10%282114-0.0137
AP/GfK13-17 Oct 2011 Huntsman3%18207-0.2083
AP/GfK13-17 Oct 2011 R. Perry9%292124-0.2651
AP/GfK13-17 Oct 2011 Santorum5%201715-0.2982
AP/GfK13-17 Oct 2011 Bachmann8%271727-0.3544
AP/GfK13-17 Oct 2011 Gingrich9%262228-0.4000
ABC/WashPostlate Nov 2011 Romney9%292017-0.0933
ABC/WashPost9-13 Nov 2011 Gingrich10%212121-0.3014
ABC/WashPost9-13 Nov 2011 H. Cain11%182123-0.3699
ABC/WashPost9-13 Nov 2011 Perry6%182323-0.5571
AP/GfK22-27 Nov 2011 Romney9%292017-0.0933
AP/GfK22-27 Nov 2011 Ron Paul8%242015-0.1492
AP/GfK22-27 Nov 2011 Gingrich11%241824-0.2597
ABC/WashPost7-11 Dec 2011 B. Obama23%251633-0.1134
ABC/WashPost7-11 Dec 2011 Gingrich12%232127-0.3373
AP/GfK8-12 Dec 2011 Romney11%372217+0.0344
AP/GfK8-12 Dec 2011 Ron Paul9%292313-0.0270
AP/GfK8-12 Dec 2011 Huntsman4%22219-0.1607
AP/GfK8-12 Dec 2011 Gingrich12%272126-0.2558
AP/GfK8-12 Dec 2011 Santorum5%201714-0.2679
AP/GfK8-12 Dec 2011 Bachmann8%252124-0.3590
AP/GfK8-12 Dec 2011 Cain10%192331-0.5542
AP/GfK8-12 Dec 2011 Perry4%242326-0.5584
AP/GfK4-8 Jan 2012 Romney10%281816-0.0278
AP/GfK4-8 Jan 2012 Santorum7%201514-0.1607
AP/GfK4-8 Jan 2012 Ron Paul6%251919-0.2899
Pew Research Cntr11-16 Jan 2012 Romney7%241727-0.4400
ABC/WashPost18-22 Jan 2012 B. Obama27%251429+0.0737
ABC/WashPost18-22 Jan 2012 Romney6%252523-0.4304
ABC/WashPost18-22 Jan 2012 Gingrich8%202031-0.5823
Pew Research Cntr8-12 Feb 2012 Santorum10%231620-0.1884
Pew Research Cntr8-12 Feb 2012 Ron Paul7%241726-0.4189
Pew Research Cntr8-12 Feb 2012 Romney7%252029-0.4815
Pew Research Cntr8-12 Feb 2012 Gingrich6%192928-0.6585
AP/GfK16-20 Feb 2012 B. Obama33%241329+0.1919
AP/GfK16-20 Feb 2012 Ron Paul10%372416+0.0115
AP/GfK16-20 Feb 2012 Romney14%362221+0.0000
AP/GfK16-20 Feb 2012 Santorum15%292121-0.0465
AP/GfK16-20 Feb 2012 Gingrich9%252038-0.5761
GWU/Battleground19-22 Feb 2012 B. Obama37%17834+0.1562
GWU/Battleground19-22 Feb 2012 Santorum18%21926-0.0541
GWU/Battleground19-22 Feb 2012 Romney12%252428-0.3483
GWU/Battleground19-22 Feb 2012 Ron Paul7%242422-0.3896
GWU/Battleground19-22 Feb 2012 Gingrich7%192241-0.7978
ABC/WashPost29 Feb-6 Mar 2012 B. Obama31%231528+0.1443
ABC/WashPost29 Feb-6 Mar 2012 Ron Paul8%232515-0.2254
ABC/WashPost29 Feb-6 Mar 2012 Santorum10%221623-0.2817
ABC/WashPost29 Feb-6 Mar 2012 Romney9%262025-0.3250
ABC/WashPost29 Feb-6 Mar 2012 Gingrich6%172135-0.7848
Bloomberg/Selzer8-11 Mar 2012 B. Obama23%2915300.0000
Bloomberg/Selzer8-11 Mar 2012 Ron Paul11%272816-0.1341
Bloomberg/Selzer8-11 Mar 2012 Romney11%312622-0.1889
Bloomberg/Selzer8-11 Mar 2012 Santorum10%291925-0.2410
Bloomberg/Selzer8-11 Mar 2012 Gingrich7%232930-0.5843
ABC/WashPost21-25 Mar 2012 B. Obama31%231528+0.1433
ABC/WashPost21-25 Mar 2012 Santorum11%231624-0.2568
ABC/WashPost21-25 Mar 2012 Romney8%262525-0.3929
ABC/WashPost21-25 Mar 2012 Gingrich8%162433-0.7160
Rasmussen10-11 April 2012 Santorum17%241932-0.1471
NBC/WSJApril 2012 Obama*30%181326+0.1494
NBC/WSJApril 2012 Romney*10%231818-0.1594
ABC/WashPost23-27 May 2012 B. Obama29%231431+0.0515
ABC/WashPost23-27 May 2012 Romney15%262124-0.1512
ABC/WashPost1-5 Aug 2012 B. Obama24%12314+0.3256
ABC/WashPost8-10 Aug 2012 Pawlenty*6%161812-0.2692
ABC/WashPost1-5 Aug 2012 Romney16%231930-0.2727
Ninety {+2, +1, -1, -2} nationwide score voting polls. Each poll sampled usually slightly more than 1000 pollees (but occasionally substantially more) by telephone. ABC News/Washington Post polls and Tarrance/Lake (also called "Battleground") were very similar (see at top for wording). AP & Rasmussen used similar samples and wording but replacing "strongly" with "very"; Reuters/Ipsos & Pew used AP's wording but with "somewhat" unfavorable changed to "mostly" unfavorable. Asterisks (*): the wording for Pawlenty in this poll explicitly mentioned that he was a possible vice presidential pick, whereas all the other polls' wording just gave a name, mentioning no office. The NBC/WSJ polls used 5-point scale {very positive, somewhat positive, neutral, somewhat negative, very negative} where here we've discarded the neutral counts (Obama 13% and Romney 26%). We unfortunately have no poll data at all of this type for Gary Johnson, Buddy Roemer, Jill Stein, and Virgil Goode. (Indeed, yet another embarrassing commentary on US elections is that Ann Romney and Michelle Obama both were the subject of far more polls and press than these legitimate candidates.)

Note by Jameson Quinn about "Graduated Majority Judgment" system: GMJ is similar to average-based range voting except that

  1. it is based on median not average rating, and
  2. with a certain "tie-breaking scheme" added.

Quinn redid the above table computing, in addition,

  1. What would have happened using average-based ratings but based on {+3, +1, -1, -3} equipspaced scores (call this "AVG31"; in contrast AVG21 is based on {+2,+1,-1,-2})
  2. What would have happened if GMJ were then used.

Regarding each individual poll (mono-colored block) in the above table as an "election," Quinn found that GMJ and AVG31 completely agreed about the full ordering of the candidates except for the following differences:

Which pollCandidates affected AVG21 order AVG31 orderGMJ order
Tarrance/Lake Sep 2010Pawlenty, Obama2,32,33,2
AP/GfK Oct 2011Obama, Cain, Romney1,2,33,1,21,2,3
AP/GfK Dec 2011Ging, Sant, Bach, Cain, Perr4,5,6,7,84,5,6,7,85,4,6,8,7
AP/GfK Feb 2012RonPaul, Romney2,32,33,2
GWU/Battleground Feb 2012RonPaul, Romney4,34,33,4
(near tie)

The most important among these is obviously the AP/GfK Oct 2011 result. With AVG21 the average-based order agrees with GMJ's. The issue is that with {±3, ±1} score, Obama gets pulled down by his higher negatives, whereas with GMJ his net positive is all that matters. Quinn argues that GMJ is doing it right in this case. Smith would, however, argue that which is doing it "right" would depend on whether we really agree the correct numerical scores ought to be {±3, ±1} (the voters were not given numerical scores, they were merely given verbal descriptions such as "very favorable" and "somewhat unfavorable") and also on whether we believe those voters were being "honest" or "strategic." Pretending for the purposes of argument the voters had known the scores were {+3,+1,-1,-3}, then if those high-negatives for Obama were honest – i.e. the voters really did have bimodal opinions about him while having unimodal (single peaked) opinions about Romney & Cain – then Obama should come in last among these 3 candidates (agreeing AVG31), but if those high negatives instead were due to those voters 1-sidely strategically exaggerating in an effort to hurt Obama, then he should come in first (agreeing GMJ). This demonstrates how GMJ tends to correct for strategic "1-sided exaggeration" by voters better than average-based range voting. [End of GMJ note.]

Conclusions: Obama would have defeated all rivals with {+2,+1,-1,-2} score voting. But the second-place finisher is not clear: it might have been Pawlenty, Paul, Romney, or Santorum. (The statistical and temporal fluctuations are great enough that we cannot decide who, but the earlier-listed candidates perhaps seem a bit more likely than the later-listed.)

This all is restricted to the candidates polled this way; we do not know how Johnson, Roemer, Stein, and Goode would have performed since we have no data for them. Note that Ron Paul got greater mean ratings than Mitt Romney on 2 (later) occasions and less on 4 (earlier) occasions. [And Paul also outscored Romney in a {+2,+1,-1,-2}-score-style poll conducted online by Public Religion Research Institute 7-20 March 2012 among adults age 18-24 (not shown).] So one could claim it would have been Paul. Remember, the date that matters is 6 Nov. 2012, and more recent polls within our table have more relevance to that date. Santorum similarly outscored Romney in later (but not earlier) polls of this kind, but Paul in turn usually outscored Santorum. Also, Pawlenty outscored Romney in the two later out of the three such polls we are aware of that included him (but this matter is confused by the asterisk, and Pawlenty had a much greater fraction of voters who said they "did not know enough" to score him).

Approval Voting

Approval versus time

This graph shows "how approved" each candidate was at different times. The vertical axis is 1000F/(F+U) where F and U are the fraction of the population rating him "favorable" and "unfavorable" in some poll at that time. (Multipoll average used if more than one at same time.) The horizontal axis is (a somewhat distorted version of) time. (The underlying dataset.) There is a lot of "noise," some of it due to genuine changes in public opinion, but a goodly fraction is genuine statistical noise in those polls (which you can mentally remove by "smoothing" the curves). Most of the polls plotted sampled 1000 people, and if (say) half provided an opinion of that particular candidate while the other half refused, then that datapoint since based on only 500 respondents would have standard error ±32. [And that's pretty large: ±32 is a 64-wide interval which is 21% of the 300-wide range graphed, and two standard deviations worth of noise would be 43% of fill graphed range, and then there is additional noise due to slight methodological differences between different pollsters. Also note Obama as the most-well-known candidate seemed to have the least noise, as expected.]

It also is interesting that {Paul, Pawlenty, Huntsman} all did better reckoned by approval fraction than any of {Bachmann, Perry, Gingrich, Cain}, but almost exactly the opposite happened with the official method, plurality voting.

On Wild Variability

As we saw, the plurality-style poll numbers fluctuated wildly often changing by a factor exceeding 5 for a single candidate.

Example: Perry had about 5% in mid-June 2011, rose to 30% in mid-September, then dropped back to about 6% in mid-January 2012.

Also, some candidates had over 500 times fewer votes than others.

Meanwhile, the {+2,+1,-1,-2} score-voting means did not fluctuate nearly as much. The lowest-ever poll number for anybody was -0.78 and the greatest ever +0.33 on a -2 to +2 scale, which if we translated the scale to "0 to 4" to allow easy comparison with plurality polls, would be a 1.22 to 2.33 subrange, which is variability factor≤1.9, among all candidates and all times polled. I.e, with score voting the most popular candidate at peak had 1.9 times the support of the least-popular one (among those polled) at min.

That immediately tells you that score voting provides more realistic and less-crazily-varying "random" results than plurality voting. Plurality voting would have yielded 6 different Republican winners,

Bachmann, Cain, Gingrich, Perry, Romney, Santorum.

depending on the date, out of the 8 graphed candidates. Among the same 8 candidates, {+2,+1,-1,-2} score voting would have yielded only 4 winners (depending on date)

Cain, Paul, Romney, Santorum,

(which note are not a subset of the 6 – the underlined candidates are the set-difference) with Pawlenty becoming an additional 5th winner if included as a 9th candidate.

The greatest-ever approval-fraction in our graph was 617 (Paul in August 2012; second-greatest was 602 for Obama in March 2011) and the least-ever was 286 (Perry in late October 2011; second-least was Gingrich's 303 in early Feb. 2012). This is a total range of variation of a factor 617/286=2.13. The greatest variation seen for any single candidate was Perry who fell from 478 in late Aug. 2011 to 286, a factor 417/286=1.67. These again are far smaller than the variations under plurality-style voting.

Miscellaneous about Ron Paul – I. "most approved" on 8 August

A substantial fraction of this section is quoted almost verbatim from We warn the reader that the Pulse poll seems atypically pro-Paul; e.g. other pollsters at other dates found lower "favorable" percentages for Paul. Indeed, this poll represented the highest-ever approval fraction known to me, for any candidate during the whole campaign.

In a poll conducted by Pulse Opinion Research, released 8 August 2012, which matched up presidential candidates Barack Obama and Ron Paul, one thousand likely voters said that they have near-equal preference when given a choice between Obama and Ron Paul. Here are the results from the poll, when a randomly selected group (via phone) were asked the following question "Suppose in this year's Presidential Election you had a choice between Republican Ron Paul and Democrat Barack Obama. If the election were held today would you vote for Republican Ron Paul or Democrat Barack Obama?"

45% Ron Paul; 47% Barack Obama; 6% Some other candidate; 2% Not sure
Margin of sampling error ±3 percentage points with 95% confidence.

Meanwhile in an independent nationwide poll by CNN/Opinion Research Corp. held 5-7 August (sampled 1008 by phone) asked "If Barack Obama were the Democratic Party's candidate and Mitt Romney were the Republican Party's candidate, who would you be more likely to vote for – Obama, the Democrat, or Romney, the Republican?" The results were:

47% Mitt Romney; 49% Barack Obama; 4% Neither/Other; <0.5% No opinion

Also interesting were the favorability ratings found by the Pulse poll:

58% of those surveyed have a favorable view of Ron Paul, while just 36% have an unfavorable view.
Compare this to Mitt Romney (50% favorable, 45% unfavorable) and
Barack Obama (51% favorable, 48% unfavorable).

Evidently, at least at that time, Paul rose above Romney & Obama and presumably to the top in terms of approval voting. This contrasts with the fact Paul never got past third place (he may not have even reached third) using plurality voting, which seems a massive distortion of democracy.

Miscellaneous about Ron Paul – II. Vote splitting

The Pew Research Center in an 11-16 January 2012 poll (1207 registered voters sampled) asked voters whom they'd vote for in a 2012 election between Obama & Romney, and also under the supposition Ron Paul would run as a third-party candidate.

ObamaRomneyOther/don't know
ObamaRomneyRonPaulOther/don't know

Evidently, Paul thus-running would have assured a (clearer) Obama victory, because Paul would have extracted over twice as many votes from Romney as Obama. (As it was, Paul did not run.) Approval voting does not suffer from this unhealthy "vote splitting" phenomenon. Thus with the (unfortunately used) plurality system, Paul was discouraged from running; but with approval, at least if he believed in his above record high favorable:unfavorable rating, Paul would have been very encouraged to run.

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