France 2012 Presidential Election

By Warren D. Smith, May 2013.

In France 2012, the official winner was F.Hollande, who won both the first round plurality vote (10 candidates; 22 April) and then also the 6 May runoff against (the previous president) N.Sarkozy (who had placed second in that first round). We shall see Hollande also would have won using score and approval voting.

The approval tallies are from a exit poll study (2340 voters, about 54% of the real voters at the locations studied, participated, but some only partially), with post-adjustment to correct for sampling biases. [Because the official France-wide vote counts for each candidate, and the official vote-counts at the polling places involved in the study, and the claimed-official votes of most voters who participated in the study, all were known, it was possible to correct for the differences between the studied sample and the whole voter population of France.] The study (including the adjustment) was by Antoinette Baujard, Frederic Gavril, Herrade Igersheim, Jean-Francois Laslier, and Isabelle Lebon.

IPSOS also independently conducted a professional approval-voting-style France-wide poll 19 April 2012. (Apparently by telephone with about 956 respondents.)
Candidate Approve:Disapprove
 F.Hollande    61:33 %
 F.Bayrou      48:42
 N.Sarkozy     49:48
 J-L.Melenchon 45:46
 M.LePen       33:62
 E.Joly        30:61
Meanwhile OpinionWay (for Metro) did France-wide score-voting-style polls: "Are you very satisfied, somewhat satisfied, somewhat dissatisfied or very dissatisfied with the work of Nathalie Arthaud?" [7April telephone 1000; 4April telephone 1002].
    date    candidate     ts as am tm NSPP  31mean   21mean
7April-2012 Hollande      13 47 20 11  9    +0.363   +0.341
7April-2012 Arthaud        4 29 22 18 27    -0.479   -0.288
7April-2012 Melenchon     10 29 21 30 10    -0.578   -0.356
7April-2012 Bayrou         4 32 29 23 12    -0.614   -0.398
4April-2012 P. Poutou      3 19 22 15 41    -0.661   -0.458
7April-2012 Dupont-Aignan  2 21 21 17 39    -0.738   -0.491
4April-2012 Sarkozy        7 29 26 35  3    -0.835   -0.546
7April-2012 M. Le Pen      9 22 18 43  8    -1.065   -0.696
4April-2012 Eva Joly       4 23 29 33 11    -1.045   -0.719

ts=tres satisfait, as=assez satisfait, am=assez mecontent, tm=tres mecontent
31mean=(3*ts+as-am-3*tm)/(ts+as+am+tm),  21mean=(2*ts+as-am-2*tm)/(ts+as+am+tm)

Note the following differences between the official plurality vote and the approval vote:

  1. Plurality falsely makes it appear that the losingest candidates have almost zero support. Really, they have a substantial amount of support, about 3-6 times larger than plurality makes it appear.
  2. Similarly, plurality made Hollande's win and Sarkozy's second-place finish both seem more-overwhelming (versus the other 8 candidates) than they really should have been.
  3. With approval the second-place finisher might have been any of {Sarkozy, Melenchon, Bayrou}, we cannot tell which because the differences between them are below the statistical noise level. With plurality, the second place finisher was clearly Sarkozy. That "higher level of support" for Sarkozy was a distortion and illusion.
  4. With plurality, M. Le Pen came in 3rd and F.Bayrou 5th. But with approval, Le Pen and Bayrou swapped places (Le Pen 5th, Bayrou 3rd). Le Pen was an extreme rightist candidate. Bayrou was a centrist and indeed appears to have been the "Condorcet winner" in the preceding (2007) election (i.e. would have beaten any rival in a head-to-head forced-binary-choice vote). Either Hollande or Bayrou was Condorcet winner in this 2012 election – probably Hollande, but we have some difficulty telling which because the Bayrou-Hollande pairwise contest was close – but it seems clear they both defeated every other rival pairwise.
    Based on a different 2012 voting study (by Karine Van der Straeten, Jean-Francois Laslier, and Andre Blais), conducted on an internet web site created and advertised for this purpose rather than as an exit poll (hence probably with a biased sample; 8044 "voters"), in hypothetical head-to-head 2-man runoffs Bayrou won against every opponent (with 53% versus Hollande, 66% against Sarkozy, 65% against Melenchon, and 79% against Le Pen). However, this internet study seems to have had a biased sample that overestimated Bayrou's support and underestimated Hollande's versus the exit-poll study. It heavily overestimated Bayrou's and Melenchon's support – and underestimated Sarkozy's by a factor>3(!) – versus the official vote count. E.g. (as proof that this study's sample was biased pro-Bayrou) it found Bayrou would have placed second behind Hollande with approval voting: Hollande=46%, Bayrou=41%, Melenchon=Sarkozy=36%, Joly=33%, LePen=23%, Dupont-Aignan=15%, Poutou=11%, Cheminade=4% approval, total=254%, and would have placed top using {-2, -1, 0, +1, +2} score voting or GMJ. This bias was enough that probably Bayrou's 53% "win" over Hollande pairwise, really (i.e, with an unbiased sample of French voters) should have been a "loss." That hypothesis is supported by the unbiased pairwise polls below which found Hollande was Condorcet winner and that Bayrou was not top using score and GMJ voting. Nevertheless, the internet study's biases seem small enough to make it plausible that Bayrou probably really would have defeated every rival pairwise except Hollande. That is supported by the unbiased pairwise polls below. This internet study also found Hollande would have won using "instant runoff voting" (beating Sarkozy in the final round, with Melenchon 3rd, Le Pen 4th) which is interesting as yet another illustration of the fact that IRV can refuse to elect a candidate (namely, Bayrou according to the voters in that study) who was both a beats-all and score-voting (and GMJ) winner, indeed IRV regarded Bayrou as finishing far behind.
  5. Also swapped: N.Dupont-Aignan and Ph.Poutou.
  6. Approval also gives a less-distorted picture of support for the high-finishing candidates. E.g. Hollande achieved almost-majority-approval (49.44% approved) or majority-approval (≥61% by IPSOS's count) which was not at all apparent from the plurality-voting results.
Official votemean #approved
Le Pen2.412.61

The typical approval ballot approved 2.57 candidates (mean), but as you can see from the above histogram, some ballots (465, or 20.7%) approved only one, while 8 ballots (0.36%) approved all 10. As you can see from the table at right, the voters for the official 5 top candidates (yellow) tended to approve fewer (unweighted mean 2.61) and the voters for the 5 bottom candidates tended to approve more (unweighted mean 3.21) options. That suggests they had some appreciation of approval voting strategy – if your favorite has little chance of winning, it makes sense to also approve more options to increase the chance of your ballot having an impact.

Sarkozy and Le Pen had the "narrowest" support. That is, voters for them approved the fewest rivals, and conversely (the data also shows), voters for others rarely were willing to approve them. As the study-authors point out, approval voting tends to disfavor such narrowly-supported candidates (they call them "exclusive") favoring more "inclusive" candidates. A related and here hard-to-disentangle effect which we had discovered many years before using "Yee diagrams," is that approval voting tends to favor "centrists" while plurality and instant runoff tend to favor "extremists."

WhereVoting system#valid ballots receivedSpoilage rateTop four (ordered winner first)
Louvigny{-1, 0, +1}9190.54% blank, 0.65% spoiled Hollande, Bayrou, Melenchon, Poutou
St-Etienne{0, 1, 2}3741.3% blank, 2.1% spoiled Hollande, Melenchon, Le Pen, Sarkozy
Strasbourg{0, 1, 2, ..., 19, 20}9565.8% blank, 0.78% spoiled Hollande, Bayrou, Melenchon, Joly
All three above towns{0, 1}   (approval)22473.1% blank, 0.85% spoiled Hollande, Sarkozy, Bayrou, Melenchon (adjusted)
Hollande, Melenchon, Bayrou, Joly (raw)
All Franceofficial plurality 1st round (10 canddts)358832091.92% spoiled+blank Hollande, Sarkozy, Le Pen, Melenchon
All Franceofficial 2nd round (Hollande v. Sarkozy)348613535.82% spoiled+blank(Hollande 51.64%, Sarkozy 48.36%)

Their study also asked voters to vote using three kinds of score voting as seen in the first three rows of the table above. Since Hollande won under all voting systems (score, approval, and official), the main interest of these studies is not "who wins," but rather, insights into voter behavior in these systems more generally.

Most popular score is 0: This phenomenon, which I have seen many times before, was once-again observed:

Spoiled and blank: A ballot could be invalid either because it was not filled out (i.e. left blank) or because it was "spoiled" i.e. filled out in some other way incompatible with the rules of the voting system. The offical tally amalgamated both of these into a single count of spoiled-or-blank ballots, but the study counted the two failure modes separately.

It is quite surprising that the {-1, 0, +1} voters had a lower spoilage rate than the {0,1,2} voters. (One might have naively expected negative signs to cause more confusion.) However, keep in mind that the numbers of nonblank spoiled score-ballots at the three locations were 6, 8, and 8 respectively, meaning (since these were very small numbers) that the "noise" in these spoilage percentages is very large. So this "conclusion" might just be statistical noise.

The total blank-ballot rate for score-voting ballots (all three kinds combined) was 3.1%, and the spoilage rate for score-voting ballots was 0.98%. For approval-voting ballots: blank=3.1%, spoiled=0.85%, For the official plurality-style ballots: somewhere between 0%, 1.92%, and 5.82% were spoiled. The final-round ballot since simpler would be expected to have smaller spoilage rates than in round 1; hence presumably its greater spoiled+blank rates were caused by voters unsatisfied with the two candidates on offer (versus the original 10) who intentionally left it blank.

Voter lying: By contrasting the score-voting ballot with the official ballot, the study authors were able to show that at least 17%?? of the voters lied on their official ballot, i.e. voted for somebody different from their true favorite. They did this strategically to gain more impact for their vote. (I apologize – I had difficulty translating this part of the paper, hence the figure 17% might be wrong.) A more precise figure was obtained by the TNS-Sofres France-wide poll (22 April 2012) which asked 1515 voters about "les motivations de leur vote." It found that 20% of voters polled said they'd strategically lied in their official first round vote ("le vote utile"). This large lying rate seems a huge indictment of the plurality system.

"Majority Judgment:" The professional polling agency Opinion Way conducted a poll using (among other things) the median-based range-voting method sometimes called majority judgment. There were 1000 respondents. Each pollee was asked to rate each candidate on the 7-point scale

Excellent / Tres bien / Bien / Assez Bien / Passable / Insuffisant / a Rejeter

The bad news is that this poll occurred 6-7 April 2011, over a year before the real election (22 April 2012). Therefore the candidates were not the same set as those who actually ran...

The MJ winner (no tie-break needed) was (Socialist Party head) Martine Aubry. In the actual election, Aubry did not run, but Francois Hollande (also Socialist party) did run (beat Aubry 56-43 in a 2-person runoff in the Socialist Party primary), and then won the Presidency. [Asterisks (*) on candidates who did not actually later run; average scores computed using numerical 7-point scale 6,5,4,3,2,1,0.]

MJ-RankCandidate% rating above MJ"Majority Judgment"% rating below MJ Score-counts (best→worst) Average
1M. Aubry*38.0Assez Bien -49.382, 129, 170, 126, 196, 114, 1842.70
2J-L. Borloo*46.0Passable +34.422, 62, 153, 223, 196, 159, 1852.27
3D.d. Villepin*40.1Passable +39.320, 58, 119, 204, 207, 174, 2192.08
4F. Bayrou37.9Passable -35.912, 47, 128, 192, 261, 166, 1932.09
5E. Joly29.9Passable -49.832, 47, 74, 145, 203, 190, 3091.75
6N. Sarkozy46.9Insuffisant +41.341, 87, 111, 95, 135, 118, 4131.80
7JP.Chevenement*43.1Insuffisant +32.25, 11, 58, 129, 228, 247, 3221.41
8J-L. Melenchon36.8Insuffisant -41.813, 27, 50, 112, 165, 214, 4181.29
9O. Besancenot*35.4Insuffisant -44.28, 17, 69, 99, 161, 204, 4421.23
10N.Dupont-Aignan25.5Insuffisant -46.75, 14, 27, 70, 139, 277, 4670.97
11N. Arthaud25.8Insuffisant -48.01, 9, 34, 77, 137, 261, 4800.95
12M. Le Pen44.4A Rejeter -068, 65, 70, 72, 78, 93, 5561.48

Simply using average score gave pretty much the same election results as the more complicated median-based MJ system except for Le Pen, whom MJ ranked dead last while average claimed she finished 7th out of 12. You can read this Anti-MJ analysis of what went wrong in this poll. However, Le Pen's position under average-based range voting seems to have varied a great deal depending on the precise score-set used and the precise time the poll was taken (average sometimes also ranked her last!) so those anti-MJ conclusions may have been unjustified.

Pairwise Polls: Pollsters conducted various nationwide polls of the form "if it were a 2-man runoff between X and Y, then for whom would you vote?" (Actually Marine Le Pen is a woman; I used the word "man" generically.):

PairResult of poll(s)Pollster(s)
Hollande vs. SarkozyH. by 51.64% over S's 48.36%Official runoff
Sarkozy vs. Le PenS. by 63-74% over L's 26-37%OpinionWay, Ifop, LH2, Harris
Hollande vs. Le PenH. by 72-76% over L's 24-28%Ifop, LH2
Bayrou vs. Le PenB. by 68% over L's 25%OpinionWay/Lyon Capitale
Bayrou vs. SarkozyB. by 56% over S's 35%OpinionWay/Lyon Capitale
Hollande vs. BayrouH. by 46% over B's 45%OpinionWay/Lyon Capitale

Also, Hollande was forecast to defeat Bayrou in a hypothetical head-to-head 2nd round by 54-to-46% by a Logica Business Consulting-France Televisions-Radio France-Le Monde-Le Point poll on Sunday 22 April on a sample of 1090 people representative of the French population.

In view of these pairwise polls I believe Hollande was the "Condorcet winner" – not Bayrou – but only with about 96% confidence.

Asset voting: Bayrou publicly said he would vote for Hollande in the runoff. Surely Melenchon would also have preferred Hollande over Sarkozy. Le Pen publicly said she would cast a blank vote. In view of these plus the official plurality vote, it seems extremely likely Hollande would also have won with asset voting.

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