The Political Supply in the 2007 French Presidential Elections: An Analysis Based on Experimental Data

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The Political Supply in the 2007 French Presidential Elections:

An Analysis Based on Experimental Data

Baujard A.^∗, Igersheim H.^†, Senné T.^‡§

February 22, 2011

Abstract

The aim of this paper is to propose a picture of French political supply in 2007 as perceived by voters, with no a priori ideas regarding the relevant political dimensions. Our study is based on experimental data collected during the French presidential elections on April 22nd, 2007. Two alternative voting methods were tested: the approval voting rule and the evaluation voting (2,1,0) rule. We provide an extensive analysis of the political supply in terms of simple political characteristics, derived from an MCA on the ballot data: groups of candidates are associated with diﬀerent political positions with no a priori conjectures about political programs, societal trends, or candidates’ valence.

Classification JEL: D71, C93.

Keywords: Voting, Framed-field Experiment, Approval Voting, Eval- uation Voting, Political Supply, MCA.

1 Introduction

The aim of conducting experimental tests of alternative voting rules is three- fold. First, we learn more about each voting rule itself, such as what outcome

∗Corresponding author: Antoinette Baujard, Associate Professor, University of Caen Basse-Normandie, UFR Sciences Économiques et de Gestion & CREM – 19, rue Claude Bloch, 14 000 Caen – Tel.: (33) 02 31 56 57 94 – E-mail: antoinette.baujard@unicaen.fr.

†CNRS Research Fellow, BETA, University of Strasbourg.

‡PhD Student, CREM, University of Caen Basse-Normandie.

§The research on which this paper reports was funded by the Centre d’Analyse Stratégique (Convention 1048), and by two CNRS laboratories: CREM, University of Caen, and BETA, University of Strasbourg. We are grateful to Jean-François Laslier for valuable advice, as well as to the numerous participants in the experiment who made the research possible. We thank Jacques Drèze, François Maniquet, Vincent Merlin, Pierre Pestieau, and two anonymous referees for comments which have contributed to improving the paper. All errors and views expressed in this paper remain ours.

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it is more likely to induce (see Forsythe, Myerson, Rietz, and Weber 1993[24], 1996[25]; Behue 2004[12]).¹ Second, it is the only way to investigate voters’

actual rationality as regards participation (see Güth and Weck-Hannemann 1997[27]; Dittmann, Kubler, Maug, and Mechtenberg 2007[17]) or strategic voting (see Fiorina and Plott 1978[23]; Guarnaschelli, McKelvey, and Pal- frey 2000[28]; Kube and Puppe 2009[35]).² Third, data gathered from field experiments dramatically enrich our information about voters’ preferences and about the structure of political supply (see Laslier 2006[37]). Indeed, national elections provide an occasion to carry out some of the most important and influential studies of the political life of a nation: yet, for obvious reasons, single name ballots provide poor information about the nuances of each voter’s opinion, thus producing results which are marred by significant hesitation, assumptions, and unanswered questions (see Baujard and Iger- sheim 2011[11]). A much richer picture could be obtained if the voting rule used required voters to express their opinion about all candidates rather than just picking one of them. In this respect, plurinominal voting rules, such as the approval voting rule (henceforth AV) and the evaluation voting (2,1,0) rule (henceforth EV),³ allow voters to express more information about their political preferences than mere plurality rules, whether one- or two-round.

The large-scale experiment run by Baujard and Igersheim (see Baujard and Igersheim 2007[6], 2009[9]) on AV and EV that took place during the first round of the French presidential elections on April 22nd, 2007, provided an opportunity to thoroughly study French political supply at that moment.

Using electoral data to study voters’ perceptions of political supply can be difficult when the number of candidates is high. The standard method used in political science is based on questions to voters (see, for instance, the “feeling thermometers” used by the American National Election Stud- ies). Building the corresponding questionnaires logically requires an a priori assessment of the relevant dimensions which structure political opinions or political parties: yet the officially announced programs and values of the parties may differ from reality, as well as from the way citizens perceive them.

Besides this, the inescapable influence of the researcher’s personal feelings about what is more or less important regarding the design of questionnaires leads to problems of legitimacy. Here, however, we aim to propose an analysis of political supply which does not rely on a priori ideas about political programs: we claim that such an analysis can be run on the basis of our raw experimental data. Following Laslier (2006[37]), since AV and EV are plurinominal and give very rich information on voters’ opinions, such an analysis

1Such an analysis is not the aim of the present article, although it is likely that relevant results could be derived from our data. See, for example, Baujard and Igersheim (2007[6]).

2Again, this is not the aim of the present article, although the data gathered could be relevant to such a study.

3For more details about AV and EV, including the criteria both voting methods satisfy, see Sections 2 and 3.

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becomes possible: this, then, constitutes a major originality of our paper compared to studies based on data provided by national organizations (see among many others Rabinowitz 1973[43], Aldrich and McKelvey 1977[1], Enelow and Hinich 1989[20]), Endersby and Hinich 1992[19], Dow 2001[18]).

The classification of the candidates we propose here is thus derived from the plurinominal ballot papers: it reveals the relevant dimensions of the political structure of the moment, and the perception of the candidates by voters.

The analysis of the experimental data collected hence allows us to investigate several intuitions regarding French politics, with no a priori ideas about political program. As well as this, it also contributes to the empirical spatial theory of voting since it sheds light on the relationship between the two-round system and the possible spatial strategies of the candidates/parties. In order to classify candidates we first use agreement matrices to determine the groups of candidates. Second, we apply a Multiple Correspondence Analysis (henceforth MCA) to the data set out in the agreement matrices.

The remainder of the paper is organized as follows: Section 2 presents the experimental design; Section 3 gives the global results of the experiment; Sections 4 and 5 provide a classification of the political supply and an interpretation of each political position; Section 6 concludes the paper.

2 Experimental design

This paper is based on analysis of a framed-field experiment. In the field, individual preferences are not controlled by the protocol but are taken as they are. In framed-field experiments individuals know they are participating in an experiment; they may learn the experimental results but they also know that their lives will not be influenced by them. It is now well established that field experiments are not only complementary to laboratory experiments, but that they also produce results of similar quality. Further- more, they are likely to substantially enrich the knowledge derived from theories and controlled experiments, and they are robust to most criticisms expressed regarding standard experiments in economics (see Harrison and List 2004[29]). More specifically, the experiment we describe in this paper belongs to a new French stream of large-scale experiments in politics (on the scope of experiments in politics, see Laslier and Van der Straten 2004[39], 2008[40]), as illustrated by the numerous other experiments that also took place in parallel with the 2007 French presidential elections: one by Balinski and Laraki on “majority judgment” (Balinski and Laraki 2007[3], 2010[2]), and one by Farvaque, Jayet, and Ragot on single transferable voting (Far- vaque, Jayet, and Ragot 2009[21]). All three experiments are based on a similar protocol which was introduced by the seminal experiment conducted by Balinski, Laraki, Laslier, and Van der Straeten during the first round of the French presidential elections in 2002 (Laslier and Van der Straeten

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2004[39]; 2008[40]) in which approval voting was tested. The major dif- ferences between the four protocols lie in the voting rules tested and some corresponding specific improvements.

Let us briefly present our protocol (for an extended presentation of the protocol, see Baujard and Igersheim 2010[10]). On April 22nd, 2007, we ran a field experiment during the first round of the French presidential elections in six polling stations located in three diﬀerent towns of three regions: Illkirch- Graﬀenstaden (Alsace), Louvigny (Basse-Normandie), and Cigné (Pays de Loire). These towns belong to a wide range of political patterns in terms of their respective electorate, social and economic class, size and rural/urban characteristics.

The selection of the two voting rules tested was based on three criteria:

capacity for expression of one’s political opinion, transparency, and simplicity. The two latter criteria would be necessary for any voting rule which was likely to be accepted in actual political elections, especially at the national level. Taken together, they not only imply that the process of voting should be simple and quick whatever the number of candidates (and thus they ex- clude any full ranking rule, such as the Borda rule), but they also require that the computation of the electoral outcome should seem obvious and be repro- ducible by any voter, which implies two conditions: first, any voter should be able to reproduce it whatever his mathematical background – which excludes majority judgment, as it relies on the median, which is not an obvious concept for all citizens; second, it should not rely on machines – which excludes any rule based on long or complex calculations of the outcome,⁴ which rules out single transferable vote since this voting method involves a very complex outcome computation and thus militates in favor of electronic voting. Observations made during the field experiment itself as well as various field testimonies (see Baujard and Igersheim 2007[8]) have underlined, on the one hand, the problem of handicaps which hamper the exercise of the right to vote for too many citizens (blindness or motor handicaps among others), and on the other hand, citizens’ and technicians’ reservations as regards electronic voting; these observations reinforced our view that these two criteria were unavoidable. The first criterion, however – the capacity for expression of one’s political opinion – is probably the most urgent matter in the public debate as well as in the community of voting theorists. On the one hand, in the public debate, many voters are frustrated by the two- round plurality rule. This frustration has been clearly expressed in France, for example, since 2002 (see for instance Perrineau and Ysmal 2003[42], and

4In answers to our 2007 questionnaires, a recurrent remark was that rules which were too complicated would feed arguments in favor of electronic voting or counting. Hence, if one wants a voting rule which satisfies transparency and thus excludes electronic voting, one has logically to refuse overly complex voting rules and/or rules requiring long or computer-based counts.

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Cautres and Mayer 2004[16]).⁵ While citizens are very willing to take this unique moment of democratic expression to express their political opinion, there are two main problems: first, the plurality rule markedly reduces their scope for expression, ruling out hesitation or nuance; second, the two-round plurality rule encourages them to resort to strategic voting. Results in voting theory confirm that these impressions have a theoretical basis: as well as other flaws (see Merlin and Lepelley 1999[41]; Laslier 2004[36]), the current rule violates the Condorcet criterion, monotonicity, consistency, separability, is very sensitive to strategic voting, incites non-participation, and generates very diﬀerent results on the basis of such minimal changes as the introduction of clone-candidates. As established by the Gibbard-Satterthwaite theorem (Gibbard 1973[26]; Satterthwaite 1975[45]), no voting rule is strategy-proof:

yet some rules do better than the two-round plurality vote. As well as this, it seems that any plurinominal rule would allow for a wider scope of expression than the plurality rule, and hence any ranking rule – such as Borda – or evaluating rule would be an improvement. Thus approval voting or some simple evaluating rule would correspond to all three criteria: capacity for expression of one’s political opinion, transparency, and simplicity.

Under these rules, each voter votes for all candidates. With approval voting (AV), either she approves that candidate or she does not. The outcome of an election can be represented by a matrixA with as many rows as there are voters and as many columns as there are candidates, with A_v,c = 1 if voter v has approved candidate c and A_v,c = 0 if she has not. The amount of support for candidate c is the column sum ^�v∈V A_v,c. Under AV, the winning candidate is the one who obtains the most support. ⁶ With evaluating rules (EV), voters assess all candidates by giving them a grade g on a pre-defined scale – for instance, integers from 0 up to 99 (as inhttp://rangevoting.org/), from 0 to 20 (as in French school marks), or from -2 up to +2 (as in http://votedevaleur.info/), and so on. Hence the outcome of an election can be represented by a matrixN with as many rows as there are voters and as many columns as there are candidates, with N_v,c=g if voter v has given the value g to candidatec. The score for can- didatecis the column sum^�v∈V Nv,c. Under EV, the winning candidate is the one who obtains the highest score.⁷ From among the large range of EV

5Let us recall that the results of the first round of the 2002 French presidential elections shocked a large part of the population: J. Chirac, the sitting president, and J.M. Le Pen, the famous candidate of the extreme Right, were selected for the second round, while L.

Jospin, the candidate of the traditional Left only reached the third position. For many French citizens, these results underscored the flaws of the two-round plurality rule and raised the issue of strategic voting (for a discussion of the importance and the form of strategic voting in France in 2002 and in 2007, see for example Blais 2004[13] and Baujard and Igersheim 2011[34]).

6For an extensive presentation of AV, see for example Brams and Fishburn 1983[14], 2005[15]. See also Laslier and Sanver 2010[38] for an updated analysis.

7For a theoretical presentation of EV, see Hillinger 2004[32, 30, 31], 2005[33]; Felsenthal

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rules that are possible, we chose to test a rule based on the (0,+1,+2) scale.

It appeared to be the most simple, and would avoid major problems of in- terpersonal comparisons of scores while preventing any problem of confusion between being indiﬀerent and disliking a given candidate (see Baujard and Igersheim 2007[6] for the arguments in favor of this option). Though the results of experimental ballots under AV or EV should not be confused with actual individual preferences, they provide useful information about individual political opinions since they are likely to express more nuances about each voter’s ranking (especially with EV) and do not generate as much strategic behavior (especially with AV) than the current two-round plurality vote.

But it must of course be noted that the supplementary information provided by these two alternative voting methods is influenced by our experimental protocol (i.e., how the voting methods were physically made available to the participants, whether in the same experimental ballot, one after the other, or etc). This point is developed below.

After the 2002 experiment, the experimental design adapted for AV and EV was tested and confirmed through a pilot experiment conducted on March 20th, 2007 in the University of Caen with over 400 participants, and this led to a few improvements (see Baujard and Igersheim 2007[8, 7]). For the actual experiment, all voters were aware of the experiment before the day of the ballot: first, they had received a personal information letter by post; second, they had been invited to information meetings in their town;

third, local newspapers, radio, and television had taken up the event. Once registered, voters voted in the official polling station with the official voting rule, and then they were invited to vote in an experimental polling station set up to mimic the conditions of the official one. The test of the voting rules reproduced the modus operandi of the real elections: we respected a similar rhythm (with similar opening hours and waiting times), similar staff (with a president of the polling station and assessors), similar voting equipment (with envelopes, ballot papers, polling booth, ballot box), and the same rules to guarantee anonymity conditions (with the first voter of the day checking the empty box, locking the box, opening the box at closing time in front of voters, and checking for silence in the polling station). These conditions were intended to promote the acceptance of the one essential point of difference, i.e., the different voting rules. Further, it must be stressed that the two ballots (one for AV, the other for EV) were registered on the same sheet of paper: on the left of the sheet participants were requested to vote according to EV, and on the right according to AV. This is a key feature of our protocol since one of our objectives was to examine the behavior of the same individual facing different voting methods.⁸

1989[22]; Smaoui 2007[46]. A 10-point EV was tested in a pilot experiment conducted at Sciences Po Paris in 2002. See Balinski, Laslier, and Van der Straeten 2002[5].

8Of course, one can argue that participants’ votes for AV might be influenced by their votes for EV and vice versa, or even that participants could have strategically used a voting

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It is fair to say that the field experiment in itself was a success on all levels.

First, no organizational problems were encountered and the town councils of the three towns declared themselves happy and indeed proud to host the experiment. Second, most citizens expressed delight in being part of such an experiment and thereby contributing to the public debate about voting rules, either on the day of the vote or through their responses to the questionnaire that was sent to each of them after the ballot; for example, seventy four voters spontaneously declared in open questions that they appreciated the organization of the experiment. Third, the size of the experiment (2,836 participants), the experiment participation rate (61.60% of the 4,604 oﬃcial voters), and the return rate for the questionnaire (1,267 responses) were all satisfactory. Having established that the protocol in itself was robust, we can now present the participation features and the global statistics; these should testify that the data collected are reliable and relevant for the analysis of the voters’ perceptions of the structure of the political supply.

3 Global statistics and results by candidate

Participation. The experimental design was such that only voters who participated in the oﬃcial vote could take part in the experiment. The participation rate in the experiment is therefore defined as the ratio of the number of participants over the number of oﬃcial voters. Table 1 presents the participation rates for the three towns. We expected to find a higher rate for Cigné, which is a small village, than in the two other towns (for further analysis, see Igersheim and Baujard 2009[9]).

Table 2 presents the expression rates for each test. Under AV or EV, a ballot paper is null when there were annotations that were not in accordance with the rules. Under AV, it is blank when it is entirely blank; under EV, when it is entirely blank or contains zeros only. It is striking that the rate of expression is higher under EV than for AV, where the blanks are more numerous. One can say that a relatively significant number of participants (i.e., 120) favored EV over AV since they opted for EV only. Diﬀerent ways of explaining this are open to us. First, some voters may have decided to focus on one test rather than two, whether because of error, irritation, or lack of time. To support this first hypothesis, let us recall that the EV ballot was on the left of the experimental sheet. Second, the questionnaires

method to modify the other. With respect to the latter point, it must not be forgotten that the participants clearly understood that they were taking part in an experiment and that its results had no influence on the oﬃcial election. Thus, the participants had no incentive to vote strategically, and one can hence allow that the percentage of strategic voters would be marginal at best. Concerning the former point, it can be shown that the influence between the two voting methods was actually very weak, except for those participants who voted for one test voting method only. We will return to this issue in Section 3.

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Table 1: Participation rates per polling station

Cigné Louvigny Illkirch Total

1 2 2 8 10

Oﬃcial vote

Registered electors 378 940 1,008 1,160 1,291 760 5,537

Votes cast 318 859 901 929 1,022 575 4,604

Experimental Vote

Participants 233 516 547 606 584 350 2,836

Participation rate (%) 73.27 60.07 60.71 65.23 57.14 60.87 61.60

Table 2: Expression rate under AV and EV

Cigné Louvigny Illkirch Total

Participants 233 1,063 1,540 2,836

AV

Spoiled (blank/null) 18 (17/1) 75 (63/12) 50 (40/10) 143 (120/23)

Votes cast 215 988 1,490 2,693

Votes cast (%) 92.27 92.94 96.75 94.96

EV

Spoiled (Blank/null) 6 (0/6) 41 (24/17) 51 (21/30) 98 (45/53)

Votes cast 227 1,022 1,489 2,738

Votes cast (%) 97.42 96.14 96.69 96.54

confirm that voters preferred EV over AV: this could explain the fact that many participants decided to vote for EV only and thus that the percentage of AV blank ballots is higher. Third, a comparison of AV blank ballots with those for EV shows that on the one hand, an important percentage of AV blank ballots correspond to EV spoiled ballots (13 over 120, that is 10.83%;

and 98 over 2836, that is 3.46%). On the other hand, a high number of AV blank ballots correspond to unenthusiastic EV ballots, with no grade 2s and a low number of grade 1s (23 over 120, that is 19.17%; and 149 over 2836, that is 5.25%). According to a simple Chi-square test, neither the outcomes

“voting blank for AV” and “voting null or blank for EV,” nor “voting blank for AV” and “giving only grade 1s for EV” are dependent. This obviously shows that there is an link between EV and AV, at least with respect to those who voted blank for AV. Besides this, the latter dependency is noticeable since it proves that voters who approve of no candidate under AV do not give strong support (i.e. a grade 2) to any candidate either. Hence, we believe that this does reveal something aboutthese voters’ political opinion – most likely some disillusionment regarding political parties.

We found that the level of understanding of the two voting rules was

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Table 3: Number of approved candidates

Approvals 1 2 3 4 5 6 7 8 9 10 11 12

Ballots 736 905 673 264 75 23 13 1 1 1 0 1

% of ballots 27 34 25 10 3 1 0 0 0 0 0 0

very satisfactory, which confirms results already established by Laslier and Van der Straeten 2008[40] regarding AV in 2002. There was a notably low number of null ballots. Further, most voters said they understood the voting rules well (89.17% for EV and 83.55% for AV).⁹ Notably, voters who said they understood the experimental voting rules were also strongly inclined to defend the idea that these rules could be used in “real life” in place of the oﬃcial ballot system (84.02% of voters who said they well-understood AV and 92.62% for EV made this claim). Furthermore, 96.10% of those who an- swered the questionnaire declared themselves satisfied to have participated in the experiment (for further analysis of the questionnaires, see Baujard and Igersheim 2007[6]). The satisfaction expressed by the voters through- out the experiment confirms that they mostly took the experimental ballots very seriously, which undoubtedly raises the confidence we may have in the experimental data.

Overall, then, the design of the experiment, accompanied by the accept- able level of understanding of the two tested voting rules expressed by the participants, suggests that the data obtained are representative and reliable.

Global statistics. The global statistics of the two voting systems under test show that the voters really did use their experimental ballot to express their preferences on the twelve candidates more precisely. The first example of this fact is given in Table 3 and Figure 1. Each voter approves 2.33 candidates on average.

However, even though they could give their opinion on several candidates, about one-quarter of the voters (27.33% or 736 participants) support one candidate only, just as if they were participating in the oﬃcial two-round vote.

This conformism to the uninominal voting rule is nevertheless less marked in EV. Indeed, only 6.56% or 175 voters gave one grade 2 to a candidate only and 0 to the others, which would be equivalent to the two-round voting method. Therefore, the voters seem to be more willing to change their political expression behavior under EV than with AV, as confirmed in the analysis of the questionnaires. We now consider the distribution of grades

9A referee has stressed that the participants who aﬃrmed that they understood the two voting rules could have favored one voting rule over the other and/or could have voted strategically. Unfortunately, this important remark cannot be confirmed or disconfirmed on the basis of our data since both experimental ballots and questionnaires are anonymous and were not gathered at the exactly same time. Participants were requested to fill in the questionnaireafter their experimental vote.

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Figure 1: Number of approved candidates

Table 4: Distribution of grades

Grade 0 1 2 Total

Number of ballots 20,901 7,357 4,598 32,856

% of ballots 63.61 22.39 13.99 100

under EV. 2,738 participants (restricted here to valid ballots) gave 32,856 grades (32856 = 12×2738), which are distributed into grades 0, 1, or 2 as shown in Table 4.

The average total sum of grades for a ballot is equal to 6.05 (with6.05 = (7357 + 2×4598)/2738)). Therefore, if a voter does not give a grade 0 to a candidate, she grants her a grade 1 in 61.5% of cases and a grade 2 in 38.5% of cases. This corresponds to the intuition that giving a grade 2 to a candidate is rarer and more exceptional than any other grade or approval.

If we compare the statistics for AV (2.33 approvals on average per valid ballot) with those for EV (6.05 as the average total sum of grades per valid ballot), it is confirmed that the participants did not vote the same way for both systems. Specifically, they did not simply translate their approval for a candidate into a grade 2 for the same candidate under EV. Thus, the message enclosed in a grade is not the same as the one in an approval.¹⁰

10 Note that this point could be questioned. Indeed, for some participants in the ex-

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Table 5: Number of grades per ballot, for 2,738 valid ballots

Number 0 1 2 3 4 5 6 7 8 9 10 11 12

Grade 2 149 1,345 728 335 124 32 10 4 1 0 0 0 0

Grade 1 306 528 550 496 379 268 135 48 17 8 2 1 0

Grade 0 2 5 27 57 121 270 360 367 483 448 366 232 0

The following analysis permits us to go into greater detail about the latter issue.

Table 5 can be read as follows: 149 ballots include no grade 2, 1,345 include it once, 728 twice, and so on. 306 ballots include no grade 1, 528 include it once, and so on. We easily observe that it is most common for voters to give only one grade 2 (1,345 cases out of 2,738, or 49.12%), and two grade 1s (550 cases out of 2,738, or 20.1%). Furthermore, although very few ballots give more than 6 positive grades of either kind, the distribution of grade 2s is much more concentrated than that of grade 1s: on average, the voters give 1.68 grade 2s and 2.69 grade 1s per ballot, with variances of 0.6 and 5.30 respectively. The average number of grade 2s per ballot is lower than the average number of approvals per ballot (1.68 against 2.33): again, this shows that voters have not systematically translated their approval into a grade 2, but have also used grade 1 to express moderate support for a given candidate.

To sum up, these statistics show that participants in general do use the plurinominal property of AV and EV to express their preferences about the set of candidates more fully than with the two-round plurality voting system.

Although these voting methods enable them to evaluate the candidates more precisely, the voters only give 1.68 candidates the maximum grade under EV (against 2.33 under AV), while this kind of support is restricted to one candidate in 50% of the cases (against 27% under AV). Therefore, even though the voters who show high similarity to the oﬃcial ballot in the way they vote are in the minority, a significant number of voters are not so distant from its logic: they express their greatest support (grade 2) for one candidate, but avoid the frustrating nature of the oﬃcial ballot by giving

periment it seems that giving grade 0 to a candidate is more serious than not supporting him/her under the AV rule, since grade 0 could be seen as an actual punishment. To answer this argument, two remarks must be made. First, we do not really observe this kind of behavior in our data. In fact, Table 3 shows that over the 32,316 assessments given with AV (“no approval” and “approval”), there are 26,052 “no approvals” and 6,264 “approvals” (against 20,901 grade 0s and 11,955 grades 1 and 2 with EV). Thus, even if voters logically give fewer grade 0s than “no approval” since the possibilities of evaluation are wider under EV (3 possibilities: 0, 1, or 2) than with AV (2 possibilities only: “approval”

and “no approval”), a very large percentage of grade 0s (63.61%) still remains. Second, even if some participants were actually reluctant to give grade 0, they nevertheless did give it for the candidates they really disliked, as Table 5 clearly shows, while they decided to give a grade 1 to the candidates they liked or disliked in moderation. In any case, the same conclusion holds: the messages included in AV and EV ballots are not the same.

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some other candidates a grade 1.

Analysis of the results under approval voting and evaluation voting The results of the experiment are given in Table 6.

As we quickly observe from Table 6, the final rankings of the candidates under AV and EV are significantly different from those obtained by the official vote. These broad features should not be compared directly, however, since there is a participation bias in comparing experimental to official data in the tested towns, and a sampling bias in comparing them with national official data. Yet, contrary to what we had expected, our analysis of the participation bias (see Baujard and Igersheim (2007[6]) has shown that N.

Sarkozy’s voters were over-represented and F. Bayrou under-represented in our data; thus the trends we find with corrected data are similar and indeed even more definite. Putting this on one side, however, since the same number of voters participated in the experiment with respect to AV and EV, these two systems can be compared as they are (see Table 7).

Let us comment on these results. For both voting systems in the experiment, F. Bayrou obtains first position, while N. Sarkozy, S. Royal, O. Besan- cenot, and D. Voynet are respectively 2nd, 3rd, 4th, and 5th. Though rankings are steady for these five first candidates, thereafter they diﬀer greatly:

J.-M. Le Pen is in 6th position under AV but falls to 10th under EV, with A. Laguiller, J. Bové, M.-G. Buﬀet, and P. de Villiers in front of him. Let us first discuss the three highest candidates. The distance between N. Sarkozy and S. Royal, very significant in the oﬃcial ballot (34.11% against 23.6%), is greatly reduced under AV (19.41% against 18.77%) and becomes almost insignificant under EV (15.96% against 15.57%).¹¹ Under EV, S. Royal man- ages to catch up with N. Sarkozy by attracting a larger proportion of the electorate which gives her grade 1: though while her number of grade 1s is higher (29.93% against 20.61%), she receives fewer grade 2s (70.07% against 79.39%). Comparing the figures for AV and EV, we see that 80% of N.

Sarkozy’s voters translate their approval into a grade 2, while this proportion falls to 72% for S. Royal. Conversely, 29% of voters who did not approve S. Royal give her a grade 1, while this proportion comes to only 21% for N.

Sarkozy.¹² We can conclude that S. Royal enjoys broad support which is not particularly intense, while N. Sarkozy, on the contrary, has quite limited but very strong support. These two facts show that distinct groups of voters

11As a matter of fact, with some plausible assumptions regarding extrapolated and corrected data, S. Royal could equal or even overtake N. Sarkozy under AV. See Baujard and Igersheim (2007[6]).

12As stressed in footnote 10, some voters could have been reluctant to give grade 0.

This is one of the reasons why S. Royal’s score is higher under EV than AV. But it must be recalled that this is precisely a major purpose of this experiment: to show that voters do not vote the same way – whatever their reasoning or inclinations – when confronted with distinct voting methods.

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Table 6: AV and EV results (2,693 valid AV ballots, 2,738 valid EV ballots)

ApprovalVoting(AV)Evaluationvoting(EV)Oﬃcialballot

Num ber of app rov als

%o fb allo ts

%o fa ppr ova ls

Nbo fgr ade2

Nbof grade 1

Sco re

%o fs cores

Aver age gra de

Num ber of vot es

%o fb allo ts

N.Sarkozy1,21645.1519.411,0495442,64215.960.961,55134.11 S.Royal1,17643.6718.779037712,57715.570.941,07323.60 F.Bayrou1,34049.7621.399799872,94517.791.081,04522.98 J.-M.LePen31211.594.982053457554.560.283467.61 O.Besancenot63723.6510.174178211,65510.000.601844.05 P.deVilliers2428.993.861654337634.610.28771.69 M.-G.Buﬀet1987.353.161226508945.400.33370.81 D.Voynet45616.937.282809091,4698.870.54972.13 A.Laguiller2509.283.992026951,0996.640.40461.01 J.Bové30911.474.931886781,0556.370.39501.10 F.Nihous913.381.45582964242.560.15290.64 G.Schivardi381.410.61242272751.660.10120.26 Total6,265233.641004,5987,35716,5531006.054,547100

Nb: In Tables 6 to 8 the candidates are ranked according to the oﬃcial results of the 2007 French presidential elections.

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Table 7: Comparing AV and EV

AV EV

Total Total grade 2 grade 1 EV / AV

score score (%) (%)

N. Sarkozy 1,216 2,642 79.39 20.61 2.17

S. Royal 1,176 2,577 70.07 29.93 2.19

F. Bayrou 1,340 2,945 66.50 33.50 2.20

J.-M. Le Pen 312 755 54.39 45.61 2.42

O. Besancenot 637 1,655 50.40 49.60 2.60

P. de Villiers 242 763 43.17 56.83 3.15

M.-G. Buﬀet 198 894 27.22 72.78 4.52

D. Voynet 456 1,469 38.11 61.89 3.22

A. Laguiller 250 1,099 36.75 63.25 4.40

J. Bové 309 1,055 35.64 64.21 3.41

F. Nihous 91 424 27.34 69.92 4.66

G. Schivardi 38 275 17.47 82.53 7.24

Total 6,265 16,553 55.55 44.45 2.64

exist. The scores of the three main candidates are practically multiplied by two between AV and EV: if they receive an approval from a voter, the probability of obtaining grade 2 is high while the probability of receiving a strictly positive grade from voters who support another of the three main candidates is simultaneously low. The scores of the other candidates are multiplied by three or four (seven for G. Schivardi, a candidate of the alternative Left).

Hence, some voters give these candidates a grade 1 even where they do not approve them under AV.

Secondly, some political parties receive numerous approvals, and thus are much more strongly represented under AV than in the oﬃcial vote where they are almost nonexistent. For example, O. Besancenot and D. Voynet are respectively ranked 4th and 5th with high scores, whereas they are respectively ranked 5th and 8th in the oﬃcial result with 4.05% and 2.13% of the vote. They both receive support (especially grade 1s) from voters who do not vote for them or even approve them. The gap between these two candidates and the three highest ranked ones (N. Sarkozy, S. Royal, F. Bayrou) is greatly reduced under the plurinominal voting systems. This observation reflects the fact that even if voters agree with these two candidates and are willing to give them approval, they are not prepared to vote for them in the two-round vote.

Lastly, O. Besancenot and D. Voynet beat J.-M. Le Pen, while they remain substantially behind him in the oﬃcial ballot (respectively 4.05% and 2.13% against 7.61%). J.-M. Le Pen’s diﬀering rank is particularly important under EV, where he is only 10th (compared with 6th for AV). Among the voters who do not approve a given candidate, many nevertheless give them grade 1, thereby showing a convergence of view. J.-M. Le Pen does

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benefit from this kind of support, but relatively less so than his competitors (excepting G. Schivardi and F. Nihous). In other words, J.-M. Le Pen is diﬀerent from the other candidates because most voters chose not to support him when they could, thereby showing explicit disagreement with his position.

Hence, the analysis of the official ballot could have led to misinterpretation of the voters’ interest in the candidates. The experimental results enable us to see how the official voting system itself is responsible for this misinterpretation. Furthermore, it must be stressed that our data allow us to confirm that AV and EV satisfy the three criteria mentioned in Section 2 (capacity for expression of one’s political opinion, transparency, and simplicity). Regarding the capacity for expression, the global statistics show, first, that the participants actually used the experimental ballots to give their opinion on each candidate; second, the fact that the winner under AV and EV is different than the one designated by the two-round vote clearly proves that the voters expressed different views in the official and the experimental votes. As for transparency and simplicity, the high rates of participation and of expression, plus the analysis of the questionnaires, demonstrate that a very large majority of participants understood and welcomed the alternative voting methods we tested (for more details on these points, see Baujard and Igersheim 2010[10]). Further, our data provide information about how close to or distant from each candidate voters feel themselves to be, and therefore how close the candidates are perceived as being with respect to each other.

The results of the experiments with AV and EV are therefore particularly relevant to a study of voters’ perceptions of political supply.

4 Classification of the political supply: Diﬀerenti- ation of Candidates

Key aspects of the voting rules tested in the April 22nd, 2007 experiment are the capacity for voters to support several candidates, and, in the EV case, the ability to qualify this support. Apart from the assessment of each candidate, the ballots reveal an even richer body of information: correlations between candidates. In other words, these data enable us to determine the degree of similarity between candidates as perceived by voters. In the rest of this paper, we aim to provide a classification of candidates into diﬀerent groups, and to set out a relevant partition of the political supply according to the voters’ assessments. Any ordering on a left–right ideological axis, even the most standard and uncontroversial one, is ad hoc. As shown elsewhere (see for example Weisberg 1980[47]), a unidimensional analysis cannot represent the candidates’ locations as perceived by voters; for this, one needs to conduct a multidimensional analysis. Further, following Laslier (2006[37], p. 163), we attempt here “to provide spatial candidate representation in a

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Table 8: Average number of approvals for other candidates - AV Candidate Average number of approvals

N. Sarkozy 1.33

S. Royal 1.79

F. Bayrou 1.63

J.-M. Le Pen 1.89

O. Besancenot 2.33

P. de Villiers 2.02

M.-G. Buﬀet 3.01

D. Voynet 2.46

A. Laguiller 2.86

J. Bové 2.72

F. Nihous 2.69

G. Schivardi 3.11

purely endogenous way, that is, without reference to an a priori specified set of issues; it thus contrasts with methods, such as the directional theory of voting, that take as their starting point a set of issues (Rabinowitz and Mac- Donald 1989[44]...).” Thus, the first step of our analysis is the presentation of groups of candidates via agreement matrices; each group corresponds to a similar segment of the political supply according to voter perception. The following step is characterization of the groups using MCA (see Section 5).

We will then give an a posteriori interpretation of the diﬀerent segments of the political supply. Note that such a study is particularly interesting in the case of the 2007 French presidential elections. Notably, it calls into question the positioning of F. Bayrou, the so-called centrist candidate, who obtains the highest score with AV and EV but only came third in the oﬃcial vote.

Average numbers of approvals. Before presenting the agreement matrix, let us consider Table 8, which gives the average numbers of approvals for other candidates. More precisely, for each candidate, the average number of approvals for other candidates corresponds to the average number of approvals on the ballots in which the considered candidate is approved (the approval of the considered candidate being excepted). Hence, for instance, the voters who approve of N. Sarkozy support on average 1.33 other candidates.

The average of the average number of approvals for one ballot paper is 2.33. This value separates the 12 candidates in two categories. With values under 2.33, the first category comprises five candidates, among whom are the three “main” ones (F. Bayrou, N. Sarkozy, and S. Royal) and the two candidates of the so-called nationalist Right-wing (J-M. Le Pen, P. de

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Villiers).¹³ Symmetrically, the second category comprises the five other Left- wing candidates, as well as the two remaining candidates, F. Nihous and G.

Schivardi, whom we will show are atypical. This observation is the starting point of the analysis of the political supply. Unlike the approvals for the members of the first category, the approvals for the members of the latter seem quite scattered. This allows us to classify candidates into groups according to how they are perceived by voters, in the first instance by using agreement matrices.

Agreement matrix and graphs for AV. For an election with 12 candidates, the agreement matrices for AV have 144 values: each candidate meets all the others. Table 9 gives the percentage of voters who support a particular candidate (by column) and simultaneously another one (by row).

Henceforth the diagonal is always equal to 100% but, contrary to a corre- lation matrix, the agreement matrix is not symmetric: the proportion of voters for J.-M. Le Pen (312 approvals) who also supported N. Sarkozy is 71%, while the proportion of voters for N. Sarkozy (1,216 approvals) who also supported J.-M. Le Pen is only 18%; the diﬀerence makes sense since we do not consider the same set of voters in computing the percentage. This property of asymmetry induces diﬀerent lessons depending on whether rows or columns are considered. In the columns we see the propensity of voters of a particular candidate to support another candidate; in the rows we see the propensity of voters of other candidates to support the candidate in question.

In order to compare candidates, we have represented the information contained in Table 9 with curves. In Figures 2 and 3 we have ordered the candidates to make for easier reading according to our results: we basically intended to obtain nice curves, single-peaked or single-curved as far as possible. After several attempts, including discussion about the relative position of the various Left-wing candidates, this eventually generated an ordering which is close to the standard ideological axis from Left-wing to Right-wing.

By construction, the graphs – representing either columns or rows – are characterized for each curve by a 100% mode, corresponding to the diagonal features of the agreement matrix.

Figures 2 and 3 present curves for each candidate. Visually, some curves correspond to like trends, and others to significantly diﬀerent trends: a first glance hence permits us to build four groups of candidates. As we can see, analyses in columns or rows do coincide in this regard. The first group is characterized by candidates who possess numerous approvals from voters who simultaneously approve another candidate too: this group corresponds to the three main candidates. It is in fact equivalent to three diﬀerent sub-

13Let us recall that we will propose a posteriori interpretations of the political supply in Section 5.

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Figure 2: Representation of columns of agreement matrix - AV

(a) The three main candidates (b) The alternative Left-wing candidates

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Figure 3: Representation of rows of agreement matrix - AV

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Table 9: Agreement Matrix - AV

Schivardi Laguiller Besancenot Bové Buﬀet Royal Voynet Bayrou Nihous Sarkozy deVilliers LePen

Schivardi 100 3 3 5 4 1 2 1 10 1 2 2

Laguiller 18 100 23 22 34 13 16 6 18 5 7 8

Besancenot 50 59 100 55 57 33 35 20 31 10 10 14

Bové 39 28 27 100 30 17 26 9 15 4 5 5

Buﬀet 21 27 18 19 100 13 20 5 10 2 1 2

Royal 29 59 61 63 76 100 66 43 30 19 14 13

Voynet 18 30 25 38 46 26 100 17 15 8 6 6

Bayrou 37 35 43 39 33 49 49 100 47 48 39 32

Nihous 24 6 4 5 5 2 3 3 100 4 7 5

Sarkozy 37 22 18 17 12 20 22 44 58 100 70 71

de Villiers 24 7 4 4 2 3 3 7 18 14 100 30

Le Pen 13 10 7 6 3 3 4 8 18 18 39 100

Nb: as stated in Section 4, the order of the candidates has now been changed in order to obtain clear curves in Figures 2 and 3 and to bring out the structure of the political supply.

groups, i.e. to three diﬀerent political supplies. The other so-called Left-wing and Right-wing candidates are characterized by similarity between ability of candidates to receive supports from voters for another candidate and the propensity of voters for a particular candidate to support another candidate (i.e., the degree of similarity between curves). Finally, the two other candidates are special cases. This primary analysis induces the following classification of candidates: (1) N. Sarkozy matches Right-wing voters; (2) S. Royal matches voters of the traditional Left-wing; (3) F. Bayrou matches voters refusing bipolarization; (4) P. de Villiers and J.-M. Le Pen match voters of the nationalist Right-wing; (5) D. Voynet, O. Besancenot, J. Bové, M.-G. Buﬀet, and A. Laguiller match voters of the traditional and alternative Left-wing. The last two candidates, F. Nihous and G. Schivardi, are special cases who attract very little support; for this reason, we claim they do not really represent a homogeneous segment of the political supply.

Agreement matrix and graphs for EV. For EV, we focus on the agreement matrix between the grade 2s. This restriction to grade 2s is induced by the diﬀerentiation between an approval for a candidate (AV) and a maximal grade to a candidate (here, grade 2). The corresponding agreement matrix is given by Table 10. Following the previous AV study, we obtain Figures 4 and 5 representing the corresponding graphs. Reading Table 10 and Figures 4 and 5 leads to similar conclusions as in the case of AV. The reading of Table 10 is as follows: the value 67 indicates that 67% of voters who give

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Table 10: Agreement Table - EV - Between grade 2s

Schivardi Laguiller Besancenot Bové Buﬀet Royal Voynet Bayrou Nihous Sarkozy deVilliers LePen

Schivardi 100 3 4 7 5 0 0 1 6 0 2 1

Laguiller 29 100 27 27 37 10 18 6 16 3 9 7

Besancenot 67 56 100 56 53 20 29 12 22 6 10 11

Bové 54 25 25 100 24 9 22 5 19 25 6 4

Buﬀet 25 22 16 15 100 7 16 2 5 19 2 2

Royal 17 44 44 43 50 100 51 29 25 12 8 10

Voynet 4 25 20 34 38 16 100 9 12 4 4 6

Bayrou 25 28 27 28 17 32 32 100 28 30 27 20

Nihous 17 5 3 6 2 2 3 2 100 2 5 7

Sarkozy 8 17 15 12 9 14 13 32 39 100 55 54

de Villiers 17 7 4 5 2 2 2 5 14 9 100 29

Le Pen 8 7 5 5 3 2 4 4 22 10 36 100

grade 2 to G. Schivardi simultaneously give grade 2 to O. Besancenot.

These results are confirmed, interpreted, and improved with the use of the MCA in Section 5. One final remark, though, should be added here:

the curves based on agreement matrices we obtained in this section can be understood as a contradiction of the single-peakedness hypothesis. Indeed, the correlations between candidates as expressed by voters’ opinion on every candidate can be seen as a way of capturing a part of voters’ actual preferences. Inspection of Figures 2 to 5 shows clearly that it is impossible to order the candidates according to a similar axis so that all curves would be single-peaked. All the more reason, then, to conduct a multidimensional analysis as in the next section.

5 Interpretation of the political supplies: A multi- ple correspondence analysis

The previous analyses, based on voters’ assessments of each candidate, have highlighted diﬀerent groups of candidates; yet this provides no interpretation on a political level. For this, we must use a more powerful data-mining tool, the multiple correspondence analysis (MCA). The aim of this section is thus to provide an a posteriori positioning for these five groups as perceived by the voters.

Presentation of the method. Multiple Correspondence Analysis (MCA) is a descriptive and exploratory technique designed to analyze multi-way tables containing some measures of correspondence between the rows and

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Figure 4: Representation of columns of agreement matrix - EV

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Figure 5: Representation of rows of agreement matrix - EV

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columns. As such, it is an extension of simple correspondence analysis, which applies to two-way tables.

The MCA of electoral data resulting from the experiment on AV and EV will provide an analysis of the similarities and diﬀerences between the variables (candidates). As a principal components analysis but for nominal variables, MCA is a tool used to reduce multidimensional data sets to lower dimensions for analysis.¹⁴ Technically, an MCA is obtained by using a standard correspondence analysis on an indicator matrix (i.e., a matrix whose entries are 0 and 1).

Interpreting an axis with MCA consists in stressing what is similar between all levels situated to the right of the origin on the one hand, and between all levels situated to its left on the other. Further, on the graphs, whenever two levels of the same variable (candidate) are close, then voters who exhibit one or the other of these two levels are similar from other variables’ point of view. Further, whenever the levels of two candidates are close, this means that the same set of voters tends to support both of them.

Results with AV data. The graphs obtained with MCA for AV are given by Figures 6, 7, and 8.¹⁵ Each level is proportionally represented according to its contribution to the inertia of the two considered axes.

The first step of the analysis of Figures 6, 7, and 8 is the a posteriori interpretation of the main axes. We shall consider the first three axes for AV. The first axis is, by construction, the most explanatory axis. Here it explains 23.64% of inertia (88.40% according to Benzécri’s correction formula).

As in Dow (2001[18]) and Laslier’s (2006[37]) use of PCA, the first axis in political MCA stands for the standard “Left–Right” distinction (on this, see for example Endersby and Hinich 1992[19]). Table 11 indicates the levels whose contributions to the formation of the first axis are particularly high:

it corroborates this standard Left–Right interpretation in every respect.

The very high contributions to the first axis of attributions of support to O. Besancenot, M.-G. Buﬀet, J. Bové, and A. Laguiller (called Besan- cenot=1, Buﬀet=1, Bové=1, Laguiller=1), all of them candidates of the alternative Left-wing, must be stressed. On the other side of the axis, J.- M. Le Pen (Le Pen=1), the candidate of the nationalist Right-wing, and N.

Sarkozy (Sarkozy=1), the candidate of the traditional Right-wing, play the major roles. Yet any conclusion should be nuanced as, for Buﬀet=1 and Villiers=1 in particular, the distance to the axes and their contributions to the first and second axes might be essentially explained by their relatively low numbers of voters as compared to the other candidates.

14With our data, note that a Principal Component Analysis (henceforth PCA) could be used as well. But the Chi-square metric enables us to avoid some of the drawbacks of PCA, such as mass eﬀects.

15Note that the two last candidates, F. Nihous and G. Schivardi, are not included in the AV analysis nor in the EV analysis since their impact on the results is not significant.

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We further observe how close are the levels Sarkozy=1 and Royal=0 on the one side and the levels Sarkozy=0 and Royal=1 on the other, i.e., how similar are the voters who exhibit both levels. If we add the respective contributions of these two groups of levels we obtain the highest contributions for both sides (16.5% and 16.83% respectively). The strong opposition N.

Sarkozy vs. S. Royal is thus in itself just as meaningful as the Left vs. Right opposition.

The interpretation of the second axis, which here explains 13.66% of the inertia (10.72% with Benzécri’s correction formula), is more delicate. One can observe its main characteristics in Figure 7 and Table 11. According to Endersby and Hinich (1992[19], p. 72), “the second dimension is commonly said to measure positions on social issues.” For older French features, Dow (2001[18]) has talked about positions over the European Union, international trade, and so on. Using AV experimental data from the 2002 French presidential elections, Laslier (2006[37]) refers to issues of authoritarianism or positions on racism. Here, two issues seem to render consistent the ranking presented from the Left to the Right of the second axis in Figure 7: first, as in Laslier (2006[37]), less-to-more authoritarian means of eﬀecting change;

second, as for Dow (2001[18]), issues about liberalism vs. protectionism, and, relatedly, from accepting the E.U. to rejecting the E.U. In fact, according to voters’ opinions, candidates such as P. de Villiers, J.-M. Le Pen, A. Laguiller, M.-G. Buﬀet, J. Bové, and O. Besancenot share a similar set of features: they tend to be more authoritarian in their governance and to adopt a suspicious attitude towards Europe. On the contrary, F. Bayrou and S. Royal are perceived as more open to Europe and more accepting of public debate as to how to conduct reforms.

The analyses of the first and second axes are suﬃcient since they explain more than 99% of the inertia with Benzécri’s correction. The third axis (see Figure 8 and Table 11), however, also oﬀers relevant lessons, manifesting an interesting – albeit marginal – characteristic of the 2007 French political supply. First, the levels Bayrou=0 and Bayrou=1 make up more than 50%

of the inertia of this axis, followed by Voynet=1 and Villiers=1. The positive part of the third axis can thus be interpreted as the support for values which many voters share, such as the vision of Right and Left reconciled carried by F. Bayrou (the centrist candidate), the importance of ecological issues for D. Voynet (the Green candidate), or of chauvinism for P. de Villiers (one of the candidates of the extreme Right-wing).

We can check that the five groups highlighted in Section 4 are reflected in Figures 6, 7, and 8, hence that these figures characterize the segments of the political supply as it is perceived by voters; thus for each group we

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Figure 6: Multiple Correspondence Analysis - AV - Axes 1 and 2

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Table 11: Contribution to the axes - AV

- +

First axis

Sarkozy=1 (9,79%) Besancenot=1 (11,34%) Royal=0 (6,71%) Buﬀet=1 (10,95%) Le Pen=1 (5,18%) Royal=1 (9,48%) Villiers=1 (4,77%) Bové=1 (9,46%)

Voynet=1 (8,72%) Laguiller=1 (7,42%)

Sarkozy=0 (7,35%) Second axis

Bayrou=1 (9,14%) Le Pen=1 (22,94%) Villiers=1 (18,34%) Laguiller=1 (12,77%)

Bayrou=0 (8,19%) Buﬀet=1 (5,40%)

Bové=1 (4,45%) Third axis

Bayrou=0 (24,67%) Bayrou=1 (27,54)%) Voynet=1 (21,48%) Villiers=1 (11,90%)

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can propose a description of their positions based on the interpretations of the three axes: (1) F. Bayrou, the centrist candidate, best represents the rejection of bipolarization (axes 1 and 3) and open-mindness to Europe (axis 2);¹⁶ (2) S. Royal is the candidate who best represents Left-wing opinions (axis 1), and her position is also opposed to authoritarianism (axis 2); (3) N. Sarkozy is the candidate who is most opposed to S. Royal (axis 1), hence representing the opposite segment of the political supply (notice, for every axis, the significant proximity between Sarkozy=0 and Royal=1 on the one hand and Sarkozy=1 and Royal=0 on the other hand); (4) J.-M. Le Pen and P. de Villiers are very close, representing a Right-wing and radical segment of the political supply (axes 1 and 2); (5) M.-G. Buﬀet, J. Bové, O. Besancenot, and A. Laguiller represent a Left-wing segment of the political supply (axis 1) which is more or less radical (axis 2), and we can add that if D. Voynet is separated from the four other candidates of the last group according to the second and the third axes, she is very close to them according to the first axis; (6) Finally, F. Nihous and G. Schivardi are not included in the analysis since their level “=1” is not significant.

In a nutshell, the ACM on AV has provided three distinct lessons. First, there is an uncontroversial proximity between the Left and extreme-Left candidates according to the first axis (as far as voters express it through their approval). Such a proximity can also be seen between the nationalist and traditional Right-wing candidates. Second, there is a relatively large distance between S. Royal and the extreme-Left candidates along the second axis, as there is between N. Sarkozy and the two nationalist candidates. In other words, what explains the distance of the extreme candidates of the Left from S. Royal, or respectively from the Right for N. Sarkozy, would be explained exclusively by the second axis, and not by the first. Third, F. Bayrou seems to be the exception on the graph. Indeed, according to voter perception he is exactly the converse of the two big Left and Right candidates (S. Royal and N. Sarkozy). He would correspond to the Rightist first axis (as N. Sarkozy) and the Leftist second axis (as S. Royal): F. Bayrou is therefore in exact opposition to any extreme position. The third axis also corroborates this reading. If we accept the interpretation we have given to the axes, F. Bayrou is rightist-centrist, pro-European, and anti-protectionist, and a proponent of democratic rather than authoritarian change. Further, for the voters he represents a possibility of a reconciliation between Right and the Left. We then understand why voters for F. Bayrou are said to come 50% from the Left, and 50% from the Right: they appreciate distinct

16It must be stressed that both Farvaque, Jayet, and Ragot (2009[21]), who tested the single transferable vote, and Balinski and Laraki (2010[4]), who experimented with majority judgement, showed that F. Bayrou was the Condorcet-winner of the 2007 French presidential elections. Further, for Farvaque et al. (2009[21]) he is the winner of the experiment with the Coombs method. This means that F. Bayrou is the most consensual candidate since he collected the lowest score of rejections.