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ADRES

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

Author(s): Antoinette Baujard, Herrade Igersheim and Thomas Senné

Source: Annals of Economics and Statistics / Annales d'Économie et de Statistique, No.

101/102, SOCIAL CHOICE AND VOTING (JANUARY/JUNE 2011), pp. 149-186 Published by: L'INSEE / GENES on behalf of ADRES

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The Political Supply in the 2007

French Presidential Elections: An

Analysis Based on Experimental Data

Antoinette Baujard Herrade Igersheim

crem, University of Caen Basse-Normandie cnrs and beta, University of Strasbourg Thomas Senné

crem, University of Caen Basse-Normandie

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.*

I. Introduction

The aim of conducting experimental tests of alternative voting rules is threefold. First, we learn more about each voting rule itself, such as what outcome it is more likely to induce (see Behue [2004]). 1 Second, it is the only way to investigate voters' actual rationality as regards participation (see GÜTH & Weck-Hannemann [1997]; Dittmann et al. [2007]) or strategic voting (see Fiorina & Plott [1978]; Guarnaschelli et al. [2000]; Kube & Puppe [2009]).2 Third, data gathered from field experiments dramatically enrich our information about voters' preferences and about the structure of political supply (see Laslier [2006]). 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 &

Igersheim [201 la]). 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 1. Such 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 & Igersheim [2007a].

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

*JEL: D71, C93 / KEY WORDS: Voting, Framed-Field Experiment, Approval Voting,

Evaluation Voting, Political Supply, MCA. 149

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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 & IGERSHEIM [2007a, 2009]) 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 Studies). 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], since AV and EV are plurinominal and give very rich information on voters' opinions, such an analysis 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], Aldrich & McKelvey [1977], Enelow & Hinich [1989], Endersby & Hinich [1992], Dow [2001]). 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 II presents the experimental design; Section III gives the global results of the experiment; Sections IV and V provide a classification of the political supply and an interpretation of each political position; Section VI concludes the paper.

II. 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. Furthermore, they are likely to substantially 3. For more details about AV and EV, including the criteria both voting methods satisfy, see Sections II and HI.

150 © ANNALS OF ECONOMICS AND STATISTICS - NUMBER 101/102, JANUARY/JUNE 201 1

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enrich the knowledge derived from theories and controlled experiments, and they are robust to most criticisms expressed regarding standard experiments in economics (see HARRISON &

List [2004]). 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 & van der Straeten [2004;2008]), 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 & Laraki [2007a,b]), and one by Farvaque, Jayet, and Ragot on single transferable voting (Farvaque et al. [2009]). 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 & van der Straeten peonóos]) in which approval voting was tested. The major differences 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 & IGERSHEIM [2010]). 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 exclude 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 reproducible 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 & Igersheim [2007c]) 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 4. In 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.

© ANNALS OF ECONOMICS AND STATISTICS - NUMBER 101/102, JANUARY/JUNE 201 1 151

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for instance Perrineau & Ysmal [2003], and С autres & Mayer [2004]).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 & Lepelley [1999]; Laslier [2004]), 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]; Satterthwaite [1975]), 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 matrix A with as many rows as there are voters and as many columns as there are candidates, with AyìC = 1 if voter v has approved candidate с and AVjC = 0 if she has not. The amount of support for candidate с is the column sum Lvev^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 in http://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 matrix N with as many rows as there are voters and as many columns as there are candidates, with NV)C = gii voter v has given the value g to candidate c. The score for candidate с is the column sum LvevM>,c- Under EV, the winning candidate is the one who obtains the highest score.7 From among the large range of EV rules that are possible, we chose to test a rule based on the (0,+l,+2) scale. It appeared to be the most simple, and would avoid major problems of interpersonal comparisons of scores while preventing any problem of confusion between being indifferent and disliking a given candidate (see Baujard & Igersheim [2007a] 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 5. Let 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] and Baujard & Igersheim [2011b]).

6. For an extensive presentation of AV, see for example Brams & Fishburn [1983;2005]. See also Laslier &

Sanver [2010] for an updated analysis.

7. E v is also called range voting or the utilitarian rule. For a theoretical presentation of EV, see HiLLlNGER[2004a,b,c;2005]; Felsenthal [1989]; Smaoui [2007]. A 10-point EV was tested in a pilot experi- ment conducted at Sciences Po Paris in 2002. See BALINSKI et al. [2002].

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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 & Igersheim [2007b, c]). 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

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.

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

© ANNALS OF ECONOMICS AND STATISTICS - NUMBER 101/102, JANUARY/JUNE 201 1 153

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Table I. - 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 III. 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 I 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 BAUJARD

& IGERSHEIM [2009]).

Table II 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 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 Is (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 Is for EV"

are independent. 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 about these voters' political opinion - most likely some disillusionment regarding political parties.

We found that the level of understanding of the two voting rules was very satisfactory, which confirms results already established by Laslier & van der Straeten [2008] regarding AV in 2002. There was a notably low number of null ballots. Further, most voters said they 154 © ANNALS OF ECONOMICS AND STATISTICS - NUMBER 101/102, JANUARY/JUNE 201 1

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Table II. - 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

Table III. - Number of Approved Candidates

Approvals 1 2 3 4 56789 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

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 answered the questionnaire declared themselves satisfied to have participated in the experiment (for further analysis of the questionnaires, see Baujard & IGERSHEIM [2007a]).

The satisfaction expressed by the voters throughout 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 acceptable level of un- derstanding 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 III 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 E V. 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.

9. A 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 questionnaire after their experimental vote.

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Grade 0 12 Total Number of ballots 20,901 7,357 4,598 32,856

% of ballots 63.61 22.39 13.99 100

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

The average total sum of grades for a ballot is equal to 6.05 (with 6.05 = (7357 + 2 x 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

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

10. Note that this point could be questioned. Indeed, for some participants in the experiment 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 m 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 1 1,955 grades 1 and 2 with EV).

156 © ANNALS OF ECONOMICS AND STATISTICS - NUMBER 101/102, JANUARY/JUNE 201 1 Figure 1. - Number of Approved Candidates

Table IV. - Distribution of Grades

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Table V. - Number of Grades per Ballot, for 2,738 Valid Ballots

Number 0 1 23456789 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 Table V 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 Is (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 Is: on average, the voters give 1.68 grade 2s and 2.69 grade Is 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 E v (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 some other candidates a grade 1.

Analysis of the results under approval voting and evaluation voting The results of the experi- ment are given in Table VI.

As we quickly observe from Table VI, 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 & Igersheim [2007a]) 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 VII).

Thus, even if voters logically give fewer grade 0s than "no approval" since the possibilities of evaluation are wider under E v (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 V 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.

© ANNALS OF ECONOMICS AND STATISTICS - NUMBER 101/102, JANUARY/JUNE 201 1 157

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