Balinski & Laraki's Orsay Range Voting experiment

M.Balinski & R.Laraki, with French government funding and cooperation, carried out a range voting experiment in the town of Orsay in the April 2007 French Presidential election. [Our own, local, French→English translation of that page is here.] It confirmed that

1. range voting had smaller "ballot spoilage" rates than plurality voting, and
2. elected a different winner, apparently in greater consonance with what the French people actually wanted.

Official results (using plurality + later top-2-runoff voting)

In that election, the official nationwide winner was Sarkozy, who defeated Royal in the second (runoff) round. And the official nationwide totals in the first (plurality) round were Sarkozy 31.2%, Royal 25.9%, Bayrou 18.6%, and Le Pen 10.4% in that order (the other 8 candidates all did worse). But restricted just to the three precincts of Orsay, not nationwide, the official winner (at least of the first round) was Royal with 29.9%, beating Sarkozy's 29.0%, Bayrou's 25.5%, and Le Pen with 5.9%.

In retrospect a year later, the French appear to have been sorry their election system elected Sarkozy (e.g. Alasdair Sandford: "French voters deliver stinging verdict on Sarkozy's first year; President's party suffers losses in local elections," The Guardian 17 March 2008; and later Sarkozy's poll ratings declined even further).

Range Voting Result (preview)

Bayrou won.

What (polls said) the French voters really wanted

According to a nationwide IPSOS poll ending 21 April, Bayrou would have beaten Sarkozy in a head-to-head (i.e. potential second-round) election by 52.5% to 47.5%, and this conclusion was true no matter what time the poll was taken from early March until late April. According to a CSA poll ending 20 April, a head-to-head Sarkozy v. Royal matchup – which in fact happened – would be a tossup (50%-50%), while the IFOP poll (also ending 20 April) gave a 51-49 edge to Sarkozy. The IFOP poll also indicated Bayrou would have beaten Sarkozy 55-45 head to head, and Bayrou would have beaten Royal 58-42 head-to-head. At least 9 other polls also examined a possible Bayrou-Sarkozy runoff and all also concluded Bayrou would win it.

From these polls we clearly conclude that Bayrou would have beaten either major opponent in a head to head contest and thus was the "Condorcet winner." However, Bayrou was eliminated in the first round, in a clear failure of France's plurality+top2runoff system. The same pathology would also have happened with "instant runoff" at least if we restrict attention to the (31.2+25.9+18.6=75.7)% of the electorate who voted for these three only (because in a 3-candidate election with self-consistent voters, plurality+top2runoff and IRV are the same thing).

If we do not thus-restrict our attention, then it is possible (although it seems unlikely) that IRV would have permitted Bayrou to win if the fallback choices of the remaining 24.3% of the voters were pro-Bayrou enough. [This possibility, if real, presumably would represent an advantage for the instant runoff system versus the 2-round runoff system France actually used.] Indeed those 24.3% could (at least in theory, mathematically speaking) have made any of the top 3 win.

As we shall see, if the French had been using range voting then this failure of democracy either would not have occurred, or at least would have been closer to not occurring.

Range Voting results

In the unofficial Balinski & Laraki election conducted, essentially, as an exit poll, voters were asked to rate every candidate on a 6-point scale (in English, "Excellent," "Very good," "Good," "Acceptable," "Poor," "Reject"; or they provided no rating for a candidate). We have regarded these ratings as 5,4,3,2,1,0, and NO SCORE.

Note that line 8 was NO SCORE, not NO OPINION. Contrary to our recommendations, the Orsay voters were clearly informed that NO SCORE would be counted the same as "To Reject." Therefore, they counted NO SCORE as a 0 rating. However, if it had been counted as NO OPINION, then we would have gotten the alternative range-scores in the "Range Voting (NS=X)" line, which would not have changed anything (the lesser-known candidates would have gotten slightly higher range scores, but not enough to alter the top three; Bayrou still would have won, indeed by a slightly greater margin).

Here is the table of Balinski & Laraki's results. They got 1752 voters (which was 74% of the 2360 official voters in those precincts, a remarkably high rate of participation in the study), but 19 of them cast ballots deemed invalid, so the results below include only 1733 range-votes. For each candidate you can see the entire distribution of the scores he/she received, in rows 2-8. The average, i.e. "range score," is in row 10. Bayrou would have won (at least in Orsay) if the election had been conducted with range voting. Balinski & Laraki were actually interested in their own, more complicated, range voting variant (they call it the "majority judgement") based on medians not averaging. That is in the "Majority Judgement" line. Bayrou also won Orsay under that voting method. (However, Balinski & Laraki do not consider it clear that Bayrou would have won all France if all France had used this method; they think perhaps Sarkozy might still have been able to win. In contrast we have evidence Bayrou really would have won all France using either {0,1,2} range voting or approval voting, and was the Condorcet winner.) In this election, the median-based and average-based procedures both output compatible orderings of the top 12 candidates (although the last 4 were in different orders if you carry out the B&L tiebreaking procedure to the bitter end; the candidates are listed in order of finish according to B&L's method). Note that Le Pen did far worse with range voting than with the official French plurality voting system.

Table by Jan Kok.

Ballot spoilage rates

With 19 out of 1752 range ballots deemed invalid, the ballot-spoilage rate was 1.1%. We contrast that with

• The 0.4% spoilage rate in the previous French election's approval voting study,
• The official (plurality voting) spoilage rates of 3.4% of the registered voters in round #1 and 5.4% in the second and final round, in the 2002 French presidential election (but some claim these figures are not to be entirely due to voter error but to French notions of "protest voting")
• The official (plurality voting) spoilage rates of 1.44% of the registered voters in round #1 and 4.20% in the second and final round, in this 2007 French presidential election
• The official nationwide spoilage rate of 1.8% in the 2000 USA and 2.2% in the Mexico 2006 presidential elections;
• The Australia 1993 spoilage rate of 2.5% using rank-order voting (and in 2004 it was 3.4% to 6.1% depending on region).

Range voting (Finish order: Bayrou, Royal, Sarkozy)	Official Plurality (Finish order: Sarkozy, Royal, Bayrou)

German approval-voting studies
French approval-voting study
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