Improved voting systems in France 2000-

France's Presidential elections occur in April & May of years ending in 2 and 7, and are done with plurality voting with separate top-2 runoff (if nobody got over 50% in the first round). We call that the T2R (top-2-runoff) system for short. But there have also been many studies of other possible voting systems, conducted by academics, with government funding and cooperation, as pseudo-election exit polls. As of the year 2018 these studies provide us with perhaps the best available simulation/understanding of what would have happened with those alternative voting systems. In the table below, the percentages shown in the "official winner" and "second placer" columns are for the valid 2nd round votes, and for approval voting are approval percentages. Do not confuse Marine Le Pen (daughter) with her father Jean-Marie Le Pen. Click on the YEAR to reach a page with deeper discussion of that year's election vis-a-vis the various systems.

Year Official Winner Second Placer Alternative systems
2002 J.Chirac (82.2%) J-M. Le Pen (17.8%) Approval: Chirac(37%) wins, L.Jospin(33%) second.
In hindsight: France still thought Chirac was the right choice (enjoying 76% approval 2.5 years after leaving office) and regards Le Pen's second place finish as a mistake which far overstated his true popularity.
2007 N.Sarkozy (53.1%) S.Royal (46.9%) Approval, Coombs, honest-Condorcet: F.Bayrou(50%) wins, Sarkozy(45%) 2nd.
Score, Pseudo-Borda: Bayrou wins, Royal 2nd.
IRV, Plurality, T2R: Sarkozy wins, Royal 2nd.
Balinski-Laraki "Majority-Judgment": Sarkozy wins, Bayrou 2nd.
In hindsight: Retrospective polls say France later wished Bayrou had won. (Royal also in hindsight was more popular than Sarkozy, although less so than Bayrou.)
2012 F.Hollande (51.6%) N.Sarkozy (48.4%) Approval, T2R, Plurality: Hollande(49%) wins, Sarkozy(40%) 2nd.
Score, honest-Condorcet: Hollande wins, Bayrou or Melenchon 2nd.
Asset voting: Hollande wins.
In hindsight: Retrospective polls say France later wished Melenchon or Bayrou had won; Hollande's approval rating had dropped to 36%, 18%, and 4% in three polls near the end of his term.
2017 E.Macron (66.1%) M.Le Pen (33.9%) honest-Condorcet: Macron wins, Melenchon 2nd.
Approval & Score: All score and approval systems seem to agree that the top two were {Melenchon, Macron} in some order, with B.Hamon in third place. The question of who wins, Melenchon or Macron, is unclear and seems to depend on the precise details of the system. But Macron would, at least in April, have won a M-versus-M runoff.
In hindsight: Macron's approval fell swiftly during the first few months of his term (e.g. reaching 40% in both late August 2017 and late March 2018), and Melenchon's also fell to about 30%. Nevertheless even at that reduced level Macron still seems to have more approval than his election rivals, suggesting that, at least up to April 2018, France still considers him to have been the best choice. In any case it is clear that M.Le Pen's second place finish far overstated her true popularity and was an artifact of "vote splitting" among her rivals.

Some people have attempted to criticize approval voting by claiming (with little or no evidence) that approval voters would simply vote in "plurality style" i.e. approving exactly one candidate. (If so, approval voting would effectively be plurality voting.) At least in these French elections, that criticism is incorrect:

Year #CandidatesMean #Approved%Plur.Style %approving>31%%using RTH%approving≥3
2002 163.1511%17%17%65%
2007122.23 or 2.3326%13%33%37%
2012 102.57 or 2.7221%24%79%52%
2017 112.42 or 2.48 19%18%46%46%
(all 4)12.252.6 or 2.719%18%44%50%

Slightly more than 50% of the voters adopted the strategy of approving 3 (or more) candidates, while only 19% adopted the "approve exactly one" strategy.

A different strategy is to approve the top fraction-F of the candidates. The "%approving>31%" column of the table shows that that strategy was adopted for F>31%, by slightly over 18% of the voters. I.e. this strategy was almost as popular as the "approve one" strategy. (With F=31%, this strategy coincides with plurality when the number C of candidates obeys C≤3, but differs when C≥4.)

Indeed, the closely related strategy of (in a C-candidate election, C≥2) approving the top max(1,⌊C/2-(C/2)1/2⌋) of the candidates (or more) was adopted by 44% of the voters, making that strategy over twice as popular as plurality-style voting. Call that the "reduced top half" (RTH) strategy. (The RTH and plurality strategies happen to be identical if C≤7 but if C≥8 then RTH voters always approve at least 2, if C≥11 at least 3, and if C≥14 at least 4, candidates.)

(The reason the "mean #approved" column contains entries such as "2.23 or 2.33" is that one figure pertains to the raw data set and the other to an extrapolation to all of France.)

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