Gregory J Deangelo
email: gregory.deangelo@cgu.com

Dimitri Dubois
email: dim-itri.dubois@umontpellier.fr

Rustam Romaniuc
email: rustam.romaniuc@univ-catholille.fr

The perils of democracy *

In this work we examine a common social dilemma in experimental economics, the public goods game, to determine how voting impacts pro-social behavior. As noted in Markussen, Putterman & Tyran (2014, Review of Economic Studies), a democratic dividend exists.

Couching the public goods game in a phenomenon that is playing out in much of the world -drastic income inequality -we examine the decision of groups to share local public goods with groups that have, effectively, no endowment to contribute toward public nor private consumption. Our results show the perils of democracy in that subjects in the position to vote use their advantageous situation to reward the ingroups at the expense of the less endowed outgroup members.

Introduction

Much research in economics, law and political science studies the conditions under which people choose to implement efficient institutions (i.e. institutions that would lead to Pareto efficient outcomes). While some argue that the reduction of transaction costs is essential in reaching efficient institutional arrangements (North 1990), others stress the need to better understand the cognitive underpinnings of institutional lock-in (Kuran, 1995). In the last two decades, a different 1 yet complementary strand of literature emerged and is currently thriving in the experimental economics of cooperation in public goods games that shows that the way in which an institution is implemented matters. More specifically, the results of many laboratory experiments suggest that there is a "dividend of democracy" (Markussen et al., 2014): the opportunity of democratic choice leads to higher cooperation levels than when the same choice is made by a third-party.

We design a public goods experiment to study the "dividend of democracy" in a novel environment characterized by radical income-asymmetry between groups, a phenomenon that is receiving considerable recent interest in the scientific community (Atkinson et al., 2011) and in public policy circles. Indeed, a meta-analysis of the use of voting in experimental papers in the top 25 journals that publish experimental research finds that 133 papers utilize voting in the research. Of these manuscripts, only 21 of these papers examine voting as the object of interest in the research, with the remaining 112 papers simply utilizing voting to determine a state of the world. Thus, directly examining the role of voting in decision-making involving public funds merits further investigation. From a policy perspective, conflicts in the Middle East and North Africa pressed public authorities in many developed countries to develop different policy responses to face the growing concerns about how immigration in general, and the refugee crisis in particular, may affect social order. Solidarity with refugees may mean that the native population accepts to give access to various local public goods -congestible -to zero-income individuals who were not previously part of their community. This, in turn, is likely to affect their behavior in terms of how much they want to contribute to the provision of local public goods. If the majority of natives vote against welcoming refugees and therefore against letting them benefit from local public goods -such as hospitals, museums, or even sidewalks -the voting outcome could strengthen cooperation among the natives because refusing solidarity may express one's commitment to preserve local public goods for natives, or conversely it might communicate one's egoistic type, thereby destroying group cohesion. [START_REF] Alesina | Preferences for redistribution[END_REF] Obviously, the question of how voting on immigration issues affects local public goods provision is not confined to the current situation in the European Union.

One could think of many economic, political and social crises that pressed millions of people to cross the border and led governments to raise the question of whether and how local citizens should be consulted and how this will affect social cohesion. Mexican immigration in the United States of America is one bold example. More generally, Hatton (2016) shows how each year about 60 million people flee their home country and seek to cross into developed countries, thus urging the latter to develop different policy responses.

As such, in our main treatments of interest, we ask subjects in each group with a positive endowment to vote on whether they are willing to share the benefits from their group's account with one other group composed of subjects who, due to an exogenous shock, have zero endowment. The voting outcome is decided by simple majority. We then examine how the positive endowment subjects vote and how the voting outcome affects their post-voting contributions to the public account as compared to a setting where the same outcome is implemented without a vote. Our results show the perils of democracy in that subjects in the position to vote use their advantageous situation to reward the ingroups at the expense of the less endowed outgroup members.

To the best of our knowledge, this is the first experiment to study the effects on cooperation from introducing voting in an environment with income inequality between groups. But we are not the first to examine the impact on cooperation from voting in the context of the public goods game. Our work is closely related to Dal Bo et al. (2010) who experimentally showed that the effect of a policy on the level of cooperation is greater when it is chosen democratically by the subjects rather than when it is exogenously imposed. Also Feld and Tyran (2006) There are, however, important differences with the aforementioned works. First, we investigate the effect of voting on cooperation in the context of endowment inequalities between groups.

Second, our focus is on how ingroup cooperation is affected by the mere act of voting whether or not to share the benefits from the group's account with zero-income outgroups. [START_REF] Andreoni | Impure altruism and donations to public goods: a theory of warm-glow giving[END_REF] The second dimension that we manipulate in the experimental design is the costs and benefits of voting in favor (against) sharing the group account with one zero endowment group. While the first situation does not enable subjects endowed with zero funds to contribute to the shared [START_REF] Andreoni | Why free ride? Strategies and learning in public goods experiments[END_REF] Other studies on the benefits of voting in public goods games include Dal Bo (2010) and Kamei (2016a, 2016b). [START_REF] Andreoni | Impure altruism and donations to public goods: a theory of warm-glow giving[END_REF] We should note from the outset that, contrary to the literature on the minimal group paradigm (see Hargreaves Heap and Zizzo, 2009; Pan and Houser, 2013), we did not induce group identity other than the random formation of groups, as is common in standard public goods experiments. In this sense, ingroup identity is minimal in our experiment. Indeed, the only difference between ingroups and outgroups is that they belong to different groups that have been randomly formed. We do acknowledge that immigrants have a different identity from native populations. However, since this is the first laboratory experiment to test for the effect of inter-group solidarity on ingroup cooperation, we wanted to study this question in a neutral environment so as to provide a lower bound on how local public goods provision could be affected by the refusal to share the social benefits with "others". It is reasonable to expect that when people belong to different group identities then the probability that one group agrees to share the benefits from its public account with another group is lower than in the absence of identity differences. Experimental research found, indeed, that subjects tend to protect the interests of their ingroups (Klor and Shayo, 2010). public account, in a second treatment we implement a situation where the zero endowed subjects can work (put in effort in a real effort task) in the public interest. Thus, in case of a vote in favor of sharing, the efforts made by the zero endowed subjects would yield tokens placed automatically in the public account. This treatment intends to mimic a policy that would require incoming zero-endowed individuals to do public service work.

Our results confirm that a dividend from democracy exists in that subjects are inclined to increase their contributions to the public account in a voting environment. However, they are not inclined to share the public account with the zero endowment group that cannot work in the public interest. Alternatively, when the zero endowment group can work in the public interest, positively endowed subjects are now inclined to share but they significantly reduce their contributions after voting in favor of sharing. An analysis of individual behavior reveals that subjects voting in favor of sharing the public account reduce their post-voting contributions in the two scenarios, when the zero endowed subjects can and cannot work in the public interest, but the rationale is different. When subjects in favor of sharing are in the minority, they subsequently reduce their contributions because they treat the voting outcome as a signal about the prosocial type of the other group members. Indeed, when subjects in favor of sharing learned that the majority voted against, their contributions converged to the contribution level of the week freeriders who had voted against sharing. We conjecture that voting against helping a less endowed group was treated as a signal that the majority in the group has no (or very low) altruistic inclinations, feels little warm-glow from helping others, and does not care about high levels of inequality in income. Absent these three motives identified in the literature as the main drivers of prosocial behavior, conditional cooperators responded by substantially reducing their own contributions. [START_REF] Andreoni | Cooperation in public-goods experiments: Kindness or confusion?[END_REF] In the treatment where the zero endowed subjects can work, the subjects that vote in favor of sharing are in the majority but since the incentives to vote in favor are now different, those voting in favor of sharing are not necessarily prosocial (or inequity averse). The post-voting behavior in this treatment reflects the majority's intention to take advantage of the subjects in the zero endowment group that can work to contribute to the public account.

Thus, contrary to the extant literature that emphasizes the benefits of democratically chosen changes in the context of public goods games, we find that the implementation of voting has unintended negative consequences. This is, of course, not to say that democracy has a dark side. We have implemented a particular set-up to simulate voting in a laboratory context where communication -to mention but one important institutional aspect of democracy -was not allowed. The study of intergroup helping when there is radical income asymmetry should be pursued in more ecologically relevant contexts. Our experiment acts as a first attempt to isolate the effect of voting to (not) share public goods with less-endowed others on cooperation within the voting group.

The remainder of the paper is structured as follows: in the next Section, we review the literature on the behavioral effects of allowing people to choose a specific institution as compared to when people are assigned to the same institution, Section 3 presents the experimental design and the way the experiment was implemented, Section 4 discusses the results and Section 5 concludes.

The effect of democratic choice on cooperation

In this section we review the extensive experimental literature on the behavioral effects of allowing people to choose a specific environment in a social dilemma as compared to when people are assigned to the same environment. The bottom line is that there are a number of studies finding that the opportunity of collective choice leads to higher cooperation levels than when the same choice is made by an unaffected third-party. This seems to be a robust result.

The experimental literature on the freedom of choice in a social dilemma burgeoned with oftcited article "Achieving compliance when legal sanctions are non-deterrent" by Tyran and Feld (2006). The authors investigate whether the effect of a mild sanction depends on the sanction being exogenously imposed or endogenously enacted. They implement a public goods game with groups of 3 playing a one-shot game under different conditions. The experiment has two main design features. First, there are three sanction levels: (1) in the "no law" condition, the sanction for free-riding is zero, (2) in the "severe law" condition, the sanction is high enough to deter a subject who solely cares about his/her own monetary gains, and (3) in the "mild law" condition, the sanction is too law to deter rational and egoistic agents from free-riding. The second design feature concerns how the law is enacted: (i) it is either exogenously implemented -in which case the sanction is meted out by the experimenter -or (ii) or endogenously -in which case subjects decide on the enactment of the law by anonymous majority vote. Each subject participates in either the exogenous or the endogenous condition. In the exogenous condition, each subject makes a contribution decision for each of the sanction levels: no law, mild law, severe law. In the endogenous condition the sequencing is mild law, severe law. After each treatment, in the endogenous condition, subjects first participate in the referendum on the enactment of law and then make their contribution decision for all possible outcomes of the referendum. It is worth noting that subjects are not informed about the outcomes (the outcome of the referendum, the contribution level in their group, their earnings) of either sanction level until the end of the experiment. This is equivalent to playing a one-shot game.

The bold result of their study is that mild law works to change people's behavior solely when enacted endogenously. Further, contributions are significantly higher if either law was accepted than if it was rejected. However, cooperation levels appear to be lower when the mild law is rejected compared to the no-sanction treatment, even though the strategic environment is identical in the two conditions. While the authors do not report whether this difference is significant, it is important to highlight that in groups that rejected the mild law, the vote appears to have an overall negative effect on cooperation. Since the majority of subjects vote in favor of the enactment of the law, Tyran and Feld as well as the literature that followed focus on the positive effects on cooperation from voting to choose a specific environment.

In a related study, Sutter et al. (2010) investigate the comparative attractiveness of sanctions as compared to rewards. The authors use a design that systematically varies the following three factors: (i) the institution governing the provision of the public good (sanctions, rewards, nosanction and no-reward), (ii) the leverage of the sanction or reward, (iii) the way in which the institution is determined (exogenously by the experimenter or endogenously by the group itself through a voting procedure). Sutter et al. (2010) find that the endogenous institutional choice has a large and positive effect on cooperation levels compared to a setting in which the sanctions or rewards have been determined exogenously. Additionally, the reward option was chosen almost exclusively when the two institutions were highly effective (defined as the ratio of monetary consequences of being sanctioned or rewarded to the costs of sanctioning or rewarding).

While this literature shows how subjects democratically choose institutions so as to affect behavior, it does not necessarily disentangle the effect of the democratic choice from the effect through the choice of incentives that subjects will face. Dal Bo et al. (2010) present a laboratory experiment designed to disentangle these effects and test for a direct effect of democracy. Their experiment consists of two sequences. In the first sequence, groups of 4 subjects were created and each subject played 10 periods of a prisoner's dilemma with the other group members. The second sequence is similar to the first one but subjects could vote to implement a tax on unilateral defection. While under the initial payoffs the unique Nash equilibrium is mutual defection, under the modified payoffs both mutual defection and mutual cooperation are Nash equilibria.

The novelty in their experiment is that after subjects voted on the implementation of the tax, the computer randomly chose whether to consider the votes in each group. If the computer considered the votes, then the majority won [START_REF] Atkinson | Top Incomes in the Long Run of History[END_REF] . Conversely, if the computer did not consider the votes, it randomly chose whether to implement the tax in that group. The subjects were then informed whether the computer considered their group's vote -i.e. whether the environment within which they will interact is endogenously chosen -and whether the tax is adopted or not.

The authors present a decomposition of the total effect of implementing the tax on unilateral defection into a selection effect (the fact that subjects that voted to implement the tax are likely to behave differently than subjects who voted against it), a treatment effect and a direct effect from democracy. They find that of the total effect, 8% is due to the selection effect, 66% is due to the treatment effect and 26% is due to the direct effect of democracy. That is, the democracy dividend represents slightly less than 50% of the treatment effect. The literature following the aforementioned studies extend the "dividend of democracy" hypothesis to choices between formal and informal sanctions (Markussen et al., 2014, Kamei et al., 2015).

What is more, Markussen et al. (2014) suggest that voting affects behavior because people treat the voting outcome as a signal about the prosocial type of the other members of the community. In other words, for conditional cooperators, the voting outcome acts as a signal about the prosocial type of the other group members. In our experiment, the vote outcome may signal the extent to which subjects in the group identify with "others". If subject i voted in favor of sharing but was informed that the majority in his group voted against sharing, i may infer that there is a majority of selfish individuals in the group. Voting against sharing may indeed signal that one has no (or very low) altruistic inclinations, feels no warm-glow from helping others and does not care about high levels of inequality in income and wealth. Absent these three motives identified in the literature as the main drivers of prosocial behavior (Bowles and Gintis, 2013), conditional cooperators may want to respond by substantially reducing their own contributions. [START_REF] Bolton | ERC: a theory of equity, reciprocity, and competition[END_REF] 3 Experimental design

Experimental game

Standard public goods game: The basic structure of our experimental game follows the well-established design of a repeated linear public goods game employing standard parameters. Ledyard (1995) and more recently Chaudhuri (2011) provide elaborate descriptions of how public good games are implemented. Our experiment consists of two sequences of ten rounds each.

To correct for a surprise restart-effect (Andreoni 1988), subjects were informed that a second sequence would be played. However, written instructions were provided for the first sequence only.

In the first sequence of the game, subjects were randomly arranged into groups of five. Each group played ten rounds of the public goods game with the same partners. At the beginning of each round, each subject received an income of 20 tokens. These incomes stayed constant throughout the first sequence of the game and were common knowledge. Subjects then decided how many tokens to contribute to a public account. The remaining tokens were automatically placed in each subject's private account. Parameters were chosen to be consistent with those used in previous experiments. For every token that the group allocated to the public account, each of the five subjects in the group received 0.5 Experimental Currency Units (ECUs). For every token that the subject kept in his private account, he received 1 ECU (the exchange rate was 20 ECU = e1). The marginal per capita return (MPCR) from the public good is thus 1/2, as in previous studies (Andreoni, 1990; Croson 1998). Consequently, the individual payoff function (π i ) is the following:

π i = 20 -g i + 0.5 5 j=1 g j
where g i corresponds to the individual contribution decision to the public account and g j is the group contribution. [START_REF] Bolton | ERC: a theory of equity, reciprocity, and competition[END_REF] As noted by a referee, subjects may also reduce their contributions if the group votes against sharing because zero contributions at the group level reduce the difference in earnings between the positive-endowment subjects and the zero-endowment ones. However, our results at the individual level do not support this conjecture. Indeed, we observe that solely subjects who voted in favor, while the majority in their group voted against, reduce significantly their post-voting contributions.

At the end of each round the subjects received feedback about the number of tokens they contributed to the public account, the total contributions to the public account by their group, their earnings for that round, and their earnings to date (wealth).

Treatments

After the tenth round, subjects were given the set of instructions for the second sequence of the game. In the second sequence of the game subjects could be placed into one of four treatments.

Baseline treatment: In the Baseline treatment, subjects were informed that the second sequence of the experiment is identical to the first sequence: the second sequence has ten rounds and the group composition does not change.

In addition to the Baseline treatment, we implemented five treatments. In the five test treatments, after the first sequence of the game, subjects were informed that half of the groups in the room will be randomly selected to receive no endowment for the next ten rounds. Henceforth, we will refer to these groups as the zero endowment groups, and to the groups that would continue to receive an endowment identical to the first sequence of the experiment as the positive endowment groups. [START_REF] Buckley | Income and wealth heterogeneity in the voluntary provision of public goods[END_REF] The loss seriously impacted the zero endowment group's final earnings since in all of our treatments subjects knew that one of the two sequences would be randomly selected for payment at the end of the experiment.

No-solidarity treatment (NOSOL): In the NOSOL treatment, each positive endowment group played the same game as in sequence 1, while each zero endowment group was completely inactive and earned zero for this part of the experiment. When the second sequence of the experiment was selected for the final payment, the members of the zero endowment group earned e0 for the experiment and were paid only the e6 show-up fee. The NOSOL treatment was implemented in order to isolate the effect of the mere existence of zero endowment groups on the contributions of the positive endowment group members.

Voting treatment (VOTE):

In the second test treatment, subjects in the positive endowment groups were asked to vote. They could vote for one of the following two options: (i) to share the benefits yielded by their group's public account with one zero endowment group or (ii) to refuse to do so. [START_REF] Camerer | Measuring social norms and preferences using experimental games: A guide for social scientists[END_REF] Each session of the three test treatments were conducted with 20 subjects divided into 4 groups of 5 subjects each. Therefore, we always had two zero endowment groups and two positive endowment groups in the room. Thus, in the VOTE treatment each positive endowment group could vote in favor or against sharing the benefits from the group's account with one randomly chosen zero endowment group. The voting outcome was decided by simple majority. The instructions explained that if the majority of the positive endowment group votes against sharing the group's public account then the game played by the positive endowment group would be exactly the same as in sequence 1, while the zero endowment group would be inactive and would earn e0 for the second sequence of the experiment (and possibly for the entire experiment). Subjects also knew in advance that if the majority in the positive endowment group votes in favor of sharing the group's public account, then the benefits from the group's public account would be divided by 10 for the entire 10 rounds of sequence 2. [START_REF] Cappelen | The freedom to choose undermines the willingness to redistribute[END_REF] We employed the same explanation of how benefits from the public account would be divided among group members as in the other treatments, except that instead of an equal division by 5, subjects were informed that if the majority votes in favor of sharing then the benefits from their group's public account would be divided by 10.

After every subject in the group voted, they were privately informed about the outcome of the vote, but not about the individual voting decision of the other group members. That is, subjects knew only whether the majority in the group voted for/against sharing the benefits from their public account with one zero endowment group. This way, we capture the essential features of voting on collective issues in real-life settings where only the voting outcome is publicly known, but individual voting decisions are not directly observable. Additionally, we decided to not inform subjects about the aggregate number of votes against and in favor of sharing the public account.

This was done in order to keep constant the information given in each group that voted against or in favor of sharing, thereby increasing the number of independent observations for each voting [START_REF] Camerer | Measuring social norms and preferences using experimental games: A guide for social scientists[END_REF] The voting procedure was common knowledge. Subjects in the zero and positive endowment groups were aware that the positive endowment groups had to vote. [START_REF] Cappelen | The freedom to choose undermines the willingness to redistribute[END_REF] If the majority votes in favor of sharing, the group optimum still requires that subjects contribute all tokens to the group account; the dominant strategy, however, is to contribute nothing. We decided to divide the amount contributed by 10 because we did not want to assume that the technology to produce the public good changes with the sharing decision. In our experiment, the "internal" and "external" MPCR are equal (Goeree et al., 2002). These changes might influence the voting decision in different ways. However, in this experiment, we want to examine post-voting behavior and not voting itself.

outcome.

The VOTE treatment was introduced to test for the effect of voting on the subsequent contribution decisions of the positive endowment group members. In case the majority votes against sharing, the game's strategic environment is identical to the NOSOL treatment. The VOTE treatment, in this case, isolates the effect of the expression of one's preferences regarding solidarity with out-group individuals on the subsequent contribution decisions within the positive endowment group. However, another possible outcome is that the majority in the group votes in favor of sharing. The vote in favor of sharing implies a reduction in the individual return from the public account for subjects in the positive endowment group from 0.5 to 0.25 -yet, the reduction preserves the nature of the interactions as a social dilemma. This is why we need to control for a change in the MPCR effect, independently of the voting procedure.

Imposed solidarity treatment (SOL): Our third test treatment, the SOL treatment, introduces solidarity exogenously. Each positive endowment group was asked to share the benefits yielded by the group's public account with one zero endowment group. Thus, in this treatment, the group contributions to the public account were automatically divided by 10 (i.e., the MPCR was changed from 0.5 to 0.25 automatically).

Conditional solidarity (VOTE_Conditional and SOL_Conditional):

In our VOTE treatment, there is a high cost of sharing the group's public account with a zero endowment group because the members of the latter group are totally inactive. In the real-world, the less-endowed ones can put in some effort in the public interest. To investigate the voting and post-voting behavior of positive endowment subjects when the zero endowment subjects can put in some effort that would yield tokens placed directly on the shared public account, we implement the VOTE_Conditional treatment. This treatment is similar to the VOTE treatment with the following exception: if the positive endowment group votes in favor of sharing the group's account with a zero endowment group, then there is common knowledge that the zero endowed subjects will have the possibility to do 5 real-effort tasks at each period and for each completed task 2 tokens will be placed on the shared group account. The task consists of counting all the zeros in a matrix consisting of 1s and zeros. This way, each member of a zero endowment group has zero endowment but can work to increase the amount on the shared group account with up to ten tokens. [START_REF] Chaudhuri | Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature[END_REF] While in the VOTE treatment voting in favor or against sharing the group account does not matter if subjects act on the belief that all would keep their tokens on their private accounts, that is no longer the case in the VOTE_Conditional treatment. Indeed, subjects from the positive endowment groups who seek to merely maximize their monetary earnings should vote in favor of sharing if they expect the subjects from the zero endowment group to put in some effort.

The fifth treatment, SOL_Conditional, is the control for our VOTE_Conditional treatment. In the former treatment sharing is automatically decided by the computer, similarly to the SOL treatment.

Table 1 provides detailed information about the experimental design as well as the number of subjects that participated in each treatment of the experiment. Total N of subjects: 470

Practical procedures

The experiment consists of 24 sessions conducted in a computerized laboratory at LEEM laboratory in Montpellier, France. The sessions were conducted between March 2016 and April 2017. [START_REF] Cox | How to identify trust and reciprocity[END_REF] Twenty subjects participated in each session conducted for the five test treatments, while for the Baseline treatment there were 15 subjects for each session. The 470 subjects, invited via the ORSEE software (Greiner, 2015), were randomly selected from a pool of more than 4,000 volunteers from the University of Montpellier. Nine out of ten subjects participated previously in a laboratory experiment. We ensured, however, that none had previously participated in a public goods game. Terminals were separated by lateral partitions to ensure complete anonymity.

Payments were made privately at the end of the session. Subjects earned an average of e20.

Sessions lasted about one hour, including initial instruction and payment of subjects.

Data

We introduce our data by first identifying the treatments by pseudoname. There are six treatments within our design that are separately run in the second sequence of the experiment. In addition, for the VOTE and VOTE_Conditional treatments, we separately consider the two voting outcomes -that is, when groups voted in favor and against sharing. First, we ran sessions where the Baseline treatment was run in the second sequence, which acts as our comparison treatment. Second, a treatment where subjects were not permitted to share the local public good with the zero endowment group, which we label No_Sol for no solidarity. Third, a treatment where subjects could share their local public good with the zero endowment group that could not make contributions to the public account, which we label Sol. Fourth, a treatment where subjects could share their local public good with the zero endowment group that could work to make contributions to the public account, which we label Sol_Conditional. Fifth, a treatment where subjects could vote to share their local public good with the zero endowment group that could not make contributions to the public account, which we label Vote. We break these data into groups that vote in favor, Vote_Favor, and those that vote against, Vote_Against. Finally, a treatment where subjects could vote to share their local public good with the zero endowment group that could work to make contributions to the public account (Vote_Conditional ), which we break apart into Vote_Condional_Favor for those voting in favor and Vote_Conditional_Against for those voting against. [START_REF] Croson | Theories of commitment, altruism, and reciprocity: Evidence from linear public goods games[END_REF] Table 2 breaks down the average number of public goods contributions across the treatments within our experiment, while Figure 1 visually displays the distribution of contributions. [START_REF] Dal Bo | Institutions and behavior: Experimental evidence on the effects of democracy[END_REF] Two observations are immediately obvious even upon visual inspection. First, in the Vote_Against treatment the average contributions to the public account are significantly lower than the average [START_REF] Croson | Theories of commitment, altruism, and reciprocity: Evidence from linear public goods games[END_REF] Note that no group ever voted to not share the public account with the zero endowment group in the treatment where the zero endowment group could work to contribute to the public account. [START_REF] Dal Bo | Institutions and behavior: Experimental evidence on the effects of democracy[END_REF] We do not display the boxplot of the Vote_Favor treatment since only one group ever voted in favor of sharing the public account with a zero endowment group that was incapable of working to contribute to the public account. Second, contributions in the Vote_Conditional_Favor treatment are significantly different from contributions in the Baseline treatment. So, even in simple summary statistics we find some evidence that voting treatments could be altering the decision-making process. However, these summary statistics could be masking treatment, session and period effects that are capturing some of the heterogeneous effects that are being observed in the summary statistics. In the following section we more carefully dissect the impact of voting on the choice to share the public account with our two types of zero endowment groups.

Results

We now dig further into our results to identify the impact of voting on public goods contributions decisions. As a starting point, we display the evolution of average group contributions in Figure 2. We first note that no matter the treatment, all contributions decay with the number of rounds in a sequence. However, the decay is much more pronounced in the non-voting treatments.

Concentrating on the Baseline treatment, we observe the common restart effect between the first and second sequence of the experiment (Andreoni, 1995). Importantly, the Sol, No_Sol and, to a lesser extent, the Sol_Conditional treatments also display the restart effect. However, both of our voting treatments (Vote_Against and Vote_Conditional_Favor ) do not display the restart To further examine the differences in contribution decisions across these treatments, we now turn to a formal econometric analysis.

While Figure 2 displays the average effects across all subjects within our treatments, individual, group or session-specific effects could be influencing the observed behavior. To account for these potentially confounding effects, we conduct a Tobit regression analysis that examines the effect of each of these treatments on public account contributions in the second sequence of our experiment by using the following specification for each subject i in group g facing treatment j:

Contribution igj = α + β j T reatment j + θ g Group g + γ i controls i + δP eriod + φSession + igj (1)
Equation 1 controls for group-and session-specific variation as well as period fixed effects. Additionally, we include controls for the previous period contribution, average contribution of other group members and average contribution in the first sequence of the experiment in our analysis so that β j identifies the between subjects effect of each treatment relative to the omitted treatment (Baseline). [START_REF] Dannenberg | Participation and commitment in voluntary coalitions to provide public goods[END_REF] As such, we can think of the coefficients for each of the treatments variables as the average treatment effect. [START_REF] Engel | Give everybody a voice! The power of voting in a public goods experiment with externalities[END_REF] Column 1 of Table 3 utilizes the full sample to assess the impact of the separate treatments.

A couple results are worth noting. First, relative to the Baseline treatment, the Vote and Vote_Conditional treatments generate higher contributions to the public account. Alternatively, the Sol treatment generates fewer public account contributions than the Baseline treatment.17

Importantly, the non-voting analog to the Vote treatment (No_Sol ) and the non-voting analog to the Vote_Conditional treatment (Sol_Conditional ) yield statistically significantly different results when comparing these coefficient estimates. We therefore find some evidence that the voting environment matters in determining whether there is a democratic dividend. To control for restart and end-of-sequence effects, we restrict our sample to only periods 3-8 in column 2 and rerun the same econometric specification. Our results remain largely unchanged and the analogous voting and non-voting treatments continue to yield statistically different coefficients.

To further explore the effect of the voting treatments, we break down the voting treatments into those individuals that voted in favor of sharing the public account, and those that did not.

Since there were two environments where voting occurred, we further split voting decisions by those treatments where the zero endowment individuals can conditionally contribute and the treatments where they cannot. Given that only one group ever shared the public account with the zero endowment group in the Vote treatment, the Vote_Against variable can be viewed as the majority vote within the Vote treatment. Similarly, in the Vote_Conditional treatment, we can view the Vote_Conditional_Favor as the majority vote since all groups voted in favor of sharing the public account with the zero endowment group. The results of breaking voting decisions apart are presented in columns 3 & 4.

Separating the vote conditions into those that did and did not vote in favor of sharing the public account with the zero endowment group reveals an interesting relationship between voting behavior and public contributions. In the Vote condition, we find that those voting against and in favor of sharing the public account both increase their contributions to the public account, although the contributions are greater in the majority group (those voting against sharing the public account). [START_REF] Fehr | The theory of fairness, competition, and cooperation[END_REF] A different phenomena is observed in the Vote_Conditional treatments, however. That is, those individuals voting in favor of sharing the public account (the majority group) reduce their contributions to the public account, whereas those voting against sharing the public account actually increased their contributions. [START_REF] Feld | Achieving compliance when legal sanctions are non-deterrent[END_REF] Thus, the majority group (those voting in favor of sharing the public account) voted to share the public account, then reduced their contributions by approximately one unit relative to the baseline treatment.

In sum, when we examine the average treatment effects, controlling for time-invariant features of each session, as well as period-specific fixed effects across sessions, we learn a few intriguing features about the role of voting in experiments. First, the Vote treatment yields higher average contributions to the public account than the equivalent non-voting treatment (No_Sol ). Second, when we enable the zero endowment group to work to contribute to the public account, the

Conclusion

Voting is a commonly utilized democratic mechanism that is used to determine a state of the world, typically when more than one state of the world could be realized. The use of voting is ubiquitous in democratic environments, leading many to believe that it improves the well-being of societies. This sentiment is reflected generally in academic research, and more specifically in experimental public choice research (Tyran and Feld 2006).

In this work we examine a common social dilemma in experimental economics, the public goods game, to determine how voting impacts pro-social behavior. As noted in Markussen et al. ( 2014), a democratic dividend exists. Couching the public goods game in a phenomenon that is playing out in much of the world (drastic income inequality), we examine the decision of societies to share local public goods with a population that has, effectively, no endowment to contribute toward public goods. We test this social dilemma in two situations. The first situation does not enable subjects endowed with zero funds to contribute to the public good, while the second enables zero endowment subjects to work to contribute to the public account. Subjects that are positively endowed are given the option to vote to share their contributions to a public account with the zero endowment group in each treatment of the experiment. Moreover, these treatments are compared to environments where subjects are placed into situations where their contributions are automatically (not) shared with the zero endowment group.

Our results reflect the complexity of voting, as we confirm that a dividend from voting does exist, in that subjects are inclined to increase their public contributions in a voting environment.

However, they are not inclined to share the public account with the zero endowment group that cannot work to contribute to the public account. Alternatively, when the zero endowment group can contribute to the public account, positively endowed subjects are now inclined to share the public account with the zero endowment group. However, the positively endowed subjects now reduce their contributions to the public account, preferring instead to free-ride on the zero endowment group's working contributions. Investigating the contribution decisions amongst those who voted in favor and against sharing the public account reveals that subjects voting in favor of sharing the public account reduce their contributions, but the rationale for the reductions likely differs. When subjects in favor of sharing are in the minority, they likely treat the voting outcome as a signal about the intentions (not) to cooperate of the majority in the group that voted against sharing. Alternatively, subjects voting against sharing the public account increase their contributions to the public account to enhance the payoffs of the in-group.

In the treatment where the zero endowed subjects can work, the subjects in favor of sharing are in the majority but since the incentives to vote in favor are now different, those voting in favor of sharing are not necessarily prosocial (or inequity averse). The post-voting behavior in this treatment reflects the majority's intention to take advantage of the subjects in the zero endowment group that can work to contribute to the public account.

This research has implications for the use of voting in social dilemmas, and contributes to a growing area of public choice research relating to the use of voting in democratic environments.

While most research highlights the dividend gained in democratic environments, it is worth noting that there are potential dark sides to democracy that could result in socially undesirable environments. Voting on immigration is one domain where democracy may lead to undesirable effects on cooperation in the voting community. One could think of many economic, political and social crises that pressed millions of people to cross the border and led governments to raise the question of whether and how local citizens should be consulted and how this will affect social cohesion. Mexican immigration in the United States of America is one bold example. More generally, Hatton (2016) shows how each year about 60 million people flee their home country and seek to cross into developed countries, thus urging the latter to develop different policy responses to face the growing concerns about how immigration may affect social order. Our experiment shows that voting to help (or not) less endowed individuals may increase cooperation in the voting groups at the cost of refusing solidarity, but it may also decrease cooperation in the voting group and lead to an exploitation of less endowed citizens. Robust standard errors clustered at the session level in parentheses; *** p<0.01, ** p<0.05, * p<0.1. We include session and period fixed effects, as well as the previous period contribution, average contribution of other group members and average contribution in the first sequence of the experiment in our analysis. Columns 1 and 3 include the full sample, while columns 2 and 4 use only periods 3-8.

Appendix

Table 2 provides the equivalent OLS estimates to the Tobit estimates reported in Table 3. In general, the point estimates tend to be larger and more statistically significant than the Tobit results. This is to be expeeted, since the OLS estimates tend to downward-bias slope coefficient estimates and upward-bias intercept estimates due to the inconsistency of utilizing an OLS estimate on censored data. We include session and period fixed effects, as well as the previous period contribution, average contribution of other group members and average contribution in the first sequence of the experiment in our analysis. Columns 1 and 3 include the full sample, while columns 2 and 4 use only periods 3-8.

Table 3 displays the environment and treatment effects that include data from both the first and second sequences. This analysis, therefore, examines the environment/treatment effect by comparing behavior in the first sequence to behavior in the second sequence. By including additional controls, we can identify the environment/treatment effect that is separate from idiosyncratic group or individual behavior. As expected, contributions in the Baseline treatment do not vary from contributions in the first sequence. However, contributions are significantly lower in the Sol, No_Sol and Vote treatments. Relative to behavior in the first sequence, those voting against sharing the public account tend not to change their contribution behavior, while those voting in favor of sharing tend to contribute significantly less. In the conditional voting environment the behavior flips. This behavior persists in the conditional voting environments.

  , Ertan et al. (2010), Sutter et al. (2010) and Markussen et al. (2014) found that punishments and rewards in public goods games have a greater impact on behavior when they are allowed democratically.[START_REF] Andreoni | Why free ride? Strategies and learning in public goods experiments[END_REF]

Figure 1 :

 1 Figure 1: Boxplot of contribution levels by treatment

Figure 2 :

 2 Figure 2: Evolution of average group contributions across treatments

  behavior of the treatment effects becomes slightly more complicated. Now, the majority group votes in favor of sharing the public account with the relatively poorer group, but their contributions now decline in the treatment where they are sharing the public account (Vote_Conditional treatments) relative to the treatment where subjects are not sharing the public account (Vote treatments). Tyran (2018) offers possible rationales for this behavior. In the vote treatment, those voting against sharing the public good become more pro-social toward the in-group once they determine that the public account will not be shared. Alternatively, those voting in favor of sharing learn, through the vote outcome, the prosocial type of the other group members, resulting in reductions in contributions to the public account. When we examine the Vote_Conditional and Sol_Conditional treatments, though, we see those in favor of (against) sharing the public good reducing (increasing) their public contributions (relative to the Baseline treatment), despite the group now voting in favor of sharing the public account. The rationale is now, however, different because the incentives to vote in favor are not the same as in the Vote treatment. Those voting in favor of sharing are not necessarily prosocial (or inequity averse). The post-voting behavior in the Vote_Conditional treatment reflects the majority's intention to take advantage of the less endowed ones.

Table 1 :

 1 Experimental design

	Subjects	Groups Matching	Sequence 1	Sequence 2	Active groups
				Periods 1-10 Periods 11-20	in sequence 2
	30	6	Partner	linear PGG	Baseline	6
	80	16	Partner	linear PGG	NOSOL	8
	120	24	Partner	linear PGG	VOTE	12
	80	16	Partner	linear PGG	SOL	8
	80	16	Partner	linear PGG	VOTE_Cond	8
	80	16	Partner	linear PGG	SOL_Cond	8

Table 2 :

 2 Contribution by treatment and sequence

	Treatment	Sequence	Mean	Std	Public Account Contributions Min 25% Median 75%	Max	Obs.
	Baseline	1	8.19	6.90 0.00	1.00	7.00	14.00 20.00	450
		2	8.32	6.92 0.00	1.00	8.00	15.00 20.00	450
	No_Sol	1	7.48	6.66 0.00	0.00	7.00	11.25 20.00	400
		2	7.19	6.83 0.00	0.00	5.00	11.00 20.00	400
	Sol	1	9.11	7.89 0.00	1.00	8.00	19.00 20.00	400
		2	6.24	6.78 0.00	0.00	5.00	10.00 20.00	400
	Sol_Conditional	1	9.81	6.99 0.00	4.00	10.00	16.00 20.00	350
		2	6.45	6.12 0.00	0.00	5.00	10.00 20.00	350
	Vote_Favor	1	13.06	9.07 0.00	2.00	20.00	20.00 20.00	50
		2	5.02	7.45 0.00	0.00	0.00	10.00 20.00	50
	Vote_Against	1	5.43	6.37 0.00	0.00	3.00	8.00	20.00	550
		2	3.98	5.32 0.00	0.00	2.00	6.00	20.00	550
	Vote_Cond_Favor	1	7.19	6.34 0.00	1.00	5.50	11.25 20.00	400
		2	5.39	5.73 0.00	0.00	4.00	9.00	20.00	400
	contributions in nearly every other treatment.

[START_REF] Dal Bo | Experimental evidence on the workings of democratic institutions[END_REF]

Specifically, contributions in the Vote_Against treatment are significantly different from contributions in the Baseline and No_Sol treatments.

Table 3

 3 Robust standard errors at the session level in parentheses; *** p<0.01, ** p<0.05, * p<0.1. We include session and period fixed effects, as well as the previous period contribution, average contribution of other group members and average contribution in the first sequence of the experiment in our analysis. Columns 1 and 3 include the full sample, while columns 2 and 4 use only periods 3-8.

	: Treatment Effects of Public Account Contributions
		1	2	3	4
	Sol	-1.554 * * *	-1.291 * * *	-1.559 * * * -1.298 * * *
		(0.251)	(0.112)	(0.248)	(0.111)
	No_Sol	-0.687	-0.948	-0.694	-0.958
		(0.722)	(0.656)	(0.726)	(0.662)
	Vote	1.774 * *	1.840 * * *
		(0.790)	(0.555)
	Sol_Conditional	-0.146	-0.072	-0.153	-0.083
		(0.673)	(0.483)	(0.679)	(0.486)
	Vote_Conditional	1.458 * * *	1.382 * * *
		(0.305)	(0.231)
	Vote_Against			2.057 *	2.238 * * *
				(1.25)	(0.800)
	Vote_Favor			0.901 * *	1.653 * * *
				(0.383)	(0.471)
	Vote_Conditional_Against			1.666 * * *	1.532 * * *
				(0.286)	(0.252)
	Vote_Conditional_Favor			-0.938 * * * -0.966 * * *
				(0.013)	(0.250)
	Intercept	-13.409 * * * -12.424 * * * -9.165 * * * -8.159 * * *
		(1.819)	(1.632)	(1.080)	(0.932)
	Num. obs.	3,730	2,625	3,730	2,625
	Pseudo-R 2	0.194	0.219	0.194	0.218

Table 2 :

 2 Environment Effects of Public Account Contributions -OLS 1 2 3 4 Sol -5.420 * * * -6.0861 * * * -5.420 * * * -6.086 * * *

		(0.057)	(0.078)	(0.037)	(0.029)
	No_Sol	-5.412 * * *	-6.085 * * *	-5.412 * * * -6.085 * * *
		(0.039)	(0.079)	(0.099)	(0.028)
	Vote	0.800 * * *	0.343 * * *
		(0.038)	(0.076)
	Sol_Conditional	-5.402 * * *	-6.086 * * *	-5.402 * * * -6.083 * * *
		(0.096)	(0.070)	(0.033)	(0.486)
	Vote_Conditional	2.760 * * *	0.524 * * *
		(0.040)	(0.073)
	Vote_Against			0.767	0.524
				(1.124)	(1.264)
	Vote_Favor			0.808 * * *	0.298
				(0.281)	(0.316)
	Vote_Conditional_Against			3.716 * * *	3.346 * * *
				(0.641)	(0.663)
	Vote_Conditional_Favor			1.326	0.910
				(0.961)	(0.995)
	Intercept	3.833 * * *	5.381 * * *	3.833 * * *	5.381 * * *
		(0.161)	(1.174)	(0.295)	(0.932)
	Num. obs.	3,730	2,625	3,730	2,625
	R 2	0.423	0.454	0.427	0.457

Table 3 :

 3 Comparing First to Second Sequence Decisions Robust standard errors clustered at the session level in parentheses; *** p<0.01, ** p<0.05, * p<0.1.

		1	2	3	4
	Baseline	-0.018	0.688	-0.017	0.688
		(1.361)	(1.435)	(1.361)	(1.434)
	Sol	-10.158 * * *	-10.293 * * * -10.153 * * * -10.287 * * *
		(3.312)	(3.369)	3.311)	(3.367)
	No_Sol	-11.553 * * *	-12.180 * * * -11.547 * * * -12.172 * * *
		(2.328)	(2.369)	(2.326)	(2.367)
	Vote	-4.248 * * *	-4.262 * *
		(1.922)	(2.080)
	Sol_Conditional	-12.160 * * * -6.086 * * * -12.154 * * * -12.335 * * *
		(2.641)	(0.070)	(2.639)	(2.807)
	Vote_Conditional	-2.638 * * *	0.524 * * *
		(0.752)	(0.073)
	Vote_Against			-4.542 *	-4.105
				(2.498)	(2.567)
	Vote_Favor			-4.097 * *	-4.338 * *
				(1.926)	(2.151)
	Vote_Conditional_Against			-1.689	-1.558
				(1.051)	(1.013)
	Vote_Conditional_Favor			-5.005 * *	-5.271 * *
				(2.214)	(2.352)
	Intercept	-0.140 * * *	2.982 * * *	-0.168	3.001 * * *
		(1.026)	(1.035)	(1.019)	(1.028)
	Num. obs.	8,480	5,950	8,480	5,950
	Pseudo R 2	0.084	0.085	0.084	0.085

On the power of commitment in public goods games, see[START_REF] Croson | Theories of commitment, altruism, and reciprocity: Evidence from linear public goods games[END_REF] and[START_REF] Dannenberg | Participation and commitment in voluntary coalitions to provide public goods[END_REF].

As noted by a referee, there are alternative explanations for why subjects would vote against sharing in our game. First, the game is subject to the typical problem of majority voting games: there are multiple equilibria. In particular, if j thinks nobody will vote in favor of sharing anyway, then sharing or not sharing does not make any difference. If we assume that j expects his vote to determine the voting outcome, then his voting decision reveals his willingness to share the group's account with one zero-endowment group.

In case of a tie, the computer broke the tie.

The language used in the instructions was neutral, we informed subjects that the computer will randomly select half of the groups in the room to have no endowment for the entire second sequence of the experiment.

In case of a vote in favor of sharing, all subjects that share the same group account would be informed about the total number of tokens on the group account. We decided to fix the maximum contribution of the zero endowed subjects to ten tokens in order to keep the inequality between the maximum possible of subjects from the positive endowment groups and subjects from the zero endowment groups.

It is worth noting that the implementation of a given treatment was always decided randomly at the very beginning of each experimental session.

Appendix Table 1 displays the Mann-Whitney tests for each of the comparisons of public goods contributions across all treatments.

We cluster standard errors at the group level.

The results presented in Table3are qualitatively similar if we instead use OLS regression analysis. See Table2in the Appendix

Tests for equality of average treatment effects are all rejected at the 1% level.

Note that there are only

subjects in total that voted in favor of sharing the public account, which could be driving the magnitude of these results. Moreover, these individuals appear to be behaving in manner that is consistent with conditional cooperation(Fischbacher et al.,

2001). The pairwise t-test of the difference in contributions is significant at the 5% level, indicating that contributions are higher among those voting against sharing. In addition, comparing first to second sequence decisions, we observe that relative to behavior in the first sequence those voting against sharing the public account tend not to change their contribution behavior, while those voting in favor of sharing tend to contribute significantly less. For the comparison of first to second sequence behavior, see Table3in the Appendix[START_REF] Feld | Achieving compliance when legal sanctions are non-deterrent[END_REF] The pairwise t-test of equality of contributions to the public account across these two treatments rejects the null hypothesis at the 0.01% level.


To be efficient the event management procedure has to provide decision-makers elements to anticipate an event and its impacts (prospective) and also to be reactive when an event appears (real-time project management). So, the system life-cycle modeling described in this section is too conceptual to be really operational. Next sections present a more precise decomposition of the functional, organic and operational models of the system and the use of a risk management approach to allow decision-maker managing design projects by anticipation and in real-time.

MODELLING THE SYSTEM AND ITS ENVIRONMENT TO MANAGE ITS EVOLUTION

To make appear all the relationships between the different levels of decision-making, we have to define each entity of the system and their interactions. The system regroups many projects, is composed with many teams, many actors, many resources. Moreover, in the system, projects begin and finish at different times, teams are created according to the needs of collaborations, actors take part of the project for specific activities, they could leave the enterprise, etc. In a nutshell, all these entities of the system and their own lifecycle have to be considered to understand the current and the possible evolutions of the system. So, we proposed to decompose the system by considering the enterprise, the design system and the actors which are essential to achieve project. The choice of the actor as smallest entity is justified by the fact that an actor is affected to projects, he works alone or in a team and he is in the design system, in the enterprise or in the other enterprises of the network. So, by focusing on the actor and factors influencing his evolution helps us to obtain a precise level of description of the factors impacting the design system and the enterprise. To take into account of the evolution of the system, we adopt a temporal view considering specific entities lifecycles.

Focus on the actor in the design system

In the context of extended enterprise, actors could be implied in the design project or not, could be in the design system or not, in the enterprise or not but they are compulsorily in the network of enterprises. The customers and the society have also to be taken into account regarding to their influences on the design product evolution [START_REF] Boztepe | Toward a framework of product development for global markets: a user-value-based approach[END_REF]. Factors influencing design performance concern in one hand the DFWRU&V(DFWLYLWLHV(DQG(RQ(WKH(RWKHU(KDQG(WKH(DFWRU&V(FRQWH[W(RI( evolution. These activities have to be analyzed regarding to the product, the process and the organizational viewpoints. 7KH( SURGXFW( YLHZ( SHUPLWV( WR( VKRZ( WKH( DFWRU&V( LQfluence on the product. The models manipulated by the actor could be product or service models (designers), process or activity models (co-coordinators) or different kind of models (enterprise modeling, etc.6( GHSHQGLQJ( RQ( WKH( DFWRU&V( attributions in a project. These models and their evolution have an interest only if we capitalized also the context in which they evolve. That obliges to consider the activities that bring the model evolution (process view) and the project associated to these activities (organizational view). Considering evolution of these models permits to define the UHDO( DQG( SRVVLEOH( DFWRU&V( DFWLRQV( RQ( WKH( PRGHOV( [START_REF] Gonnet | A model for capturing and representing the engineering design process[END_REF]. Models help to know what the actor has done, what he/she is doing and what he will be able to do on the product, in a given process and organization [START_REF] Patanakul | A competency model for effectiveness in managing multiple projects[END_REF] that GHVFULEH( WKH( DFWRU&V( FRQWH[W( RI( ZRUN;( 7R( VSHFLI\( WKH( DFWRU&V( context of evolution, we describe aspects from the actor himself to the system in which he has to work (figure 3). 6RPH( IDFWRUV( FRQFHUQV( DFWRU&V( SHUVRQDO( DVSHFWV( DQG( VWDWH( RI( mind to help decision-maker understanding the actor to adapt his management style (Yang, 2008) [START_REF] Girard | Analysis of collaboration for project design management[END_REF]. All these factors contribute to help decision-maker to optimize his management in the current projects and the future projects.

The design system in the company

Factors impacting performance of the design system are an aggregated vision of the lower description level (actor viewpoint). Managing information about each actor of the design allows building a global view of the design system. The partial product models of each actor designing this product are part of a more global product model in the design system. The aggregation of models of WKH( DFWRUV&( DFWLYLWLHV( permits to obtain a global vision of the design process model. And all the processes are parts of the design projects which are organized in the design system. These elements are local performance factors for the design system. Internal and external resources, knowledge are identified too. Internal and external interactions between these elements contribute to make evolve the model of the design system and favor performance of design process [START_REF] Chang | Organizational memory influences new product success[END_REF]. All these factors evolve with their own lifecycle and contribute to ensure performance of design [START_REF] Hicks | A framework for the requirements of capturing, storing and reusing information and knowledge in engineering design[END_REF].

The design system in the company

$FWRUV&(HYROXWLRQ(DQG(HYROXWLRQ(RI(WKH(GHVLJQ(V\VWHP(DUH(DOVR( influenced by the enterprise, the network of enterprises and their interdependencies. The design actors, the design system are described and we focus here on the interactions between them, the company and the network of enterprises. Factors influencing design project at a strategic level have to be LGHQWLILHG;( 7KDW( REOLJHV( WR( HQODUJH( WKH( QRWLRQ( RI( ?SURMHFW¥;( Projects not only concern design project. Projects of the company may be financial or investment projects, expansion projects, partnerships projects (find new industrial partners), etc. A decision in one of these projects could affect design projects and could modify their evolution. Many processes composed these projects and could also impact the design. The results of these processes (products) could change the design product evolution. Consequently, the local performance determinants concern these projects regarding to the product, process and organizational viewpoints and the global determinants describe the enterprise on the whole.

Presentation of the results

Table 5 shows the different project scenarios possible in this study. It is possible from this table to assess the relevance of the implementation of each corrective strategy for each risk scenario in terms of criticality. Criticality of zero means that the project complies with contractual commitments. Probability and impacts on duration and cost are identified.

Analysis of possible decisions

The objective of this research work is to give decision makers a methodological tool to compare the impact of risks and their treatment on the project, but also to have a light on the feasibility with regard on the availability of critical resources.

The proposed approach permits evaluate the relevance of corrective treatments of risk, this whatever the context of preventive treatment implemented. Knowing which corrective treatment will be decided in all possible cases, it is possible to decide what would be the best possible preventive treatment strategy. For each scenario, information about the feasibility is given. In a first approach it is possible to know whether the schedule is feasible with the availability granted E\( WKH( RUJDQL]DWLRQ;( ,I( LW( GRHVQ&W( FRUUHVSRQGC( WKH( SURMHFW( manager can specify the dates where critical resources are needed. If all its resources are already preempted for other projects over the periods of requirement, negotiation can be started with the business manager. If the business manager offers different resources with different ranges of availability, the PM can select those that can best ensure the progress of the tasks for which they would be in charge knowing the potential occurrence of risks.

The example is deliberately simple for the demonstration purposes, but the behavior of the proposed approach can be extrapolated to wider problems and situations more representative of actual project.

Risks do not relate directly to critical resources. But the impact of these risks can modify the period of critical resources requirement. Risks relating to resources are then transferred on the tasks, within the framework of this approach.

CONCLUSIONS

The choice of the best strategy for dealing with the risks of a project is often difficult. When the project aims to deliver a product with technological innovations, specific resources may be required. Resources with particular characteristics are often limited in organizations. It becomes necessary to ensure that they will be available at the right time and will be used when available. We propose an approach to model and assess the impact of risks on the duration and cost of the project. This approach uses the principles of the synchronized project planning and risk management. It is based on the concepts of risk scenario, risk treatment scenario and project scenario to characterize and evaluate the effects of risks on the project. This method evaluates the overall level of risk and selects the best risk treatment strategy while analyzing the feasibility. An estimate of the overall risk of the project gives an overview of possible scenarios. We illustrate the principles of our approach through a case study and a software tool has been developed.

It is often difficult to compare criteria antagonists such as compliance with contractual commitments and resource overload. The first perspective of this work is to facilitate the integration of the resource overload in the other two criteria (cost and duration). Given that different actors may be required for specific tasks, the second perspective of this research is to examine the influence of the skills required in the project in the model.

  . Far from personality, DFWRU&V( NQRZOHGJH( LV( DOVR( D( SHUIRUPDQFH( GHWHUPLQDQW;( ,I( ZH( identify what an actor knows, what he has to know and how he uses his knowledge, we are able to provide to him tools, methodologies, physical supports or training courses to achieve properly his tasks and to increase its self-esteem.

	Finally, to express his personality and his knowledge, actor
	PXVW(EH(LQ(?JRRG(FRQGLWLRQV¥;(&RQVHTXHQWO\C(ZH(KDYH(WR(trace
	KLV( LQWHUQDO( DQG( H[WHUQDO( UHODWLRQVKLSV( WR( LGHQWLI\( KLV( ?DXWR-
	RUJDQL]DWLRQ¥(DQG(WR(FUHDWH(D( favorable collaborative context
	of work

Table 3 :

 3 Treatment actions

		Predecessors	Successors		Duration	Fixed cost
					(UT)	(UM)
	A 111	Delineate the area	Prepare the core	1	4
	A 121	Core drilling of the area	Study carrots	1	4
	A 131	Core drilling of the area	Study carrots	0.2	24
	A 141	Delineate the area	Prepare the core	1	4
	A 142	Core drilling of the area	Study carrots	0.2	24
	A 211	Assembly of the structure	Equipping the structure	0.2	4
	A 221	Assembly of the structure	Equipping the structure	1	8
		Table 4: The critical resources
		Tasks requiring the CR		Beginning of the availability period	Duration of the availability (UT)
	Drum	Make the basement of the structure	t0		25
	Steamroller	Steam the access		t0		13

Table 5 :

 5 Set of project scenarios

	N° ScP	Probability	Couple (Risk,Strategy)	Duration (UT)	Cost (UM)	Criticality
	1	0,64	(.,ST11)	183	4	0,000
	2	0,56		180	0	0,000
	3	0,24	(R1,.)	195	0	0,000
	4	0,24	(R1,StT12)	185	4	0,000
	5	0,24	(R1,StT13)	181	24	0,000
	6	0,16	(R1,ST11)	183	4	0,000
	7	0,16	(R1,StT14)	186	28	0,022
	8	0,16	(.,ST11) (R2,.)	193	4	0,000
	9	0,16	(.,ST11) (R2,StT21)	183	8	0,000
	10	0,16	(.,ST11) (R2,StT22)	183	12	0,000
	11	0,14	(R2,.)	190	0	0,000
	12	0,14	(R2,StT21)	180	4	0,000
	13	0,14	(R2,StT22)	180	8	0,000
	14	0,06	(R1,.) (R2,.)	205	0	0,030
	15	0,06	(R1,.) (R2,StT21)	195	4	0,000
	16	0,06	(R1,.) (R2,StT22)	195	8	0,000
	17	0,06	(R1,StT12) (R2,.)	195	4	0,000
	18	0,06	(R1,StT12) (R2,StT21)	185	8	0,000
	19	0,06	(R1,StT12) (R2,StT22)	185	12	0,000
	20	0,06	(R1,StT13) (R2,.)	191	24	0,000
	21	0,06	(R1,StT13) (R2,StT21)	181	28	0,008
	22	0,06	(R1,StT13) (R2,StT22)	181	32	0,019
	23	0,04	(R1,ST11) (R2,.)	193	4	0,000
	24	0,04	(R1,ST11) (R2,StT21)	183	8	0,000
	25	0,04	(R1,ST11) (R2,StT22)	183	12	0,000
	26	0,04	(R1,StT14) (R2,.)	196	28	0,007
	27	0,04	(R1,StT14) (R2,StT21)	186	32	0,013
	28	0,04	(R1,StT14) (R2,StT22)	186	36	0,020


Lucas Bourneuf
email: lucas.bourneuf@inria.fr

An Answer Set Programming environment for high-level specification and visualization of FCA

This paper introduces Biseau, a programming environment dedicated to the exploration of relations through a graphical display. The use of Answer Set Programming enables the production of small code modules which are easy to maintain and debug since they are very close to the specifications. This paper shows how a mathematical framework such as Formal Concept Analysis can be efficiently described at the level of its properties, without needing a costly development process. We hope that it will help to quickly adapt a given code to the peculiarities of a data set, thereby speeding up the development of prototypes. Besides, it will also help the integration of the ideas of the FCA community in a readable and shareable format. From a practical point of view, Biseau provides an Answer Set Programming to (graphviz) dot compiler and uses the graphviz software to render in real-time the calculated graphs to user, for instance to produce concept lattices or aoc posets visualizations. Its relation with existing tools like LatViz and FCAbundles is also discussed.

Introduction

Large scale data production requires availability of high-level visualizations for their exploration. This is usually performed by building generic visualization models, that users may later use to explore their data. Thus, software environments oriented towards data mining use efficient implementations of data structures and their visualizations. For instance, in Formal Concept Analysis, LatViz is a lattice visualization software, allowing end-user to explore the lattice structure efficiently [START_REF] Alam | Steps towards interactive formal concept analysis with latviz[END_REF]. Lattice Miner builds and visualize Galois lattices and provides data mining tools to explore data [START_REF] Lahcen | Lattice miner: a tool for concept lattice construction and exploration[END_REF]. FCA Tools Bundle consists in a web interface exposing multiple FCA-related tools for contexts and (ternary) concept lattices exploration [START_REF] Kis | Fca tools bundle-a tool that enables dyadic and triadic conceptual navigation[END_REF]. In-Close algorithm reference implementation provides a concept trees visualization of contexts encoded in standard formats [START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF]. All these tools work with a formal model that provides an abstract view and a fixed search space on the data. Users cannot work on the model itself, they are expected to use the implemented methods, not to design new ones. In contrast, this paper introduces Biseau, a software focused on designing and exploring elements of the data structure, rather than the data itself. In this approach, data are only a support to the model validity, and the user's aim is the proper design of a general model. Biseau is a general purpose model builder that relies on graphs and logic languages.

Graphs are rendered in multiple ways, using field-specialized softwares like Cytoscape [START_REF] Shannon | Cytoscape: A software environment for integrated models of biomolecular interaction networks[END_REF] in biology, graph-specific softwares (like LatViz for lattices), or more generalist like Tulip [START_REF] Auber | [END_REF]. Another generic approach is dot, a graph description language specified by the graphviz software, which provides a gallery of visualization engines [START_REF] Gansner | An open graph visualization system and its applications to software engineering[END_REF]. Dot is the internal graphical language used by Biseau (see Section 3).

Together with a graph data structure, Biseau offers a logical view of the associated exploration methods. A pure declarative language is used for this purpose, Answer Set Programming (ASP). It allows users to transcript the formal properties they are looking for in a straightforward way (see Section 2). ASP has already been applied to FCA to accomplish expressive query languages for formal contexts [START_REF] Hitzler | Querying formal contexts with answer set programs[END_REF], later extended to n-adic FCA and improved with additional membership constraints, in order to handle large context exploration [START_REF] Rudolph | Membership constraints in formal concept analysis[END_REF]. In our approach, ASP is also used for visualization.

Biseau is supplied with a graphical user interface and a command line interface to write an ASP encoding. Biseau uses this encoding as a script to generate the dot files and the resulting visualizations. The main interest of Biseau is therefore to build graph visualizations directly from formal relations. Biseau is not only dedicated to lattices, and their (efficient or scalable) exploration. It provides instead a general purpose programming environment that is able to visualize any ordered structure. Biseau is therefore suited for rapid design and easy testing of works or extensions in the framework of FCA. It is freely available under the GNU/GPL license 1 .

The structure of this paper is as follows. Sections 2 and 3 quickly present the ASP and dot languages used by Biseau. Section 4 explains how Biseau takes advantage of these languages to allow the user to build models. Section 5 proposes as a case study the reconstruction of the Galois lattice. Section 6 shows how Biseau can easily handle some of the FCA extensions typically used in FCA applications as knowledge processing [START_REF] Poelmans | Formal concept analysis in knowledge processing: A survey on applications[END_REF]. Finally the paper concludes by some insights about Biseau interest when used in FCA and in artificial intelligence.

Answer Set Programming

The following presentation of ASP is taken from [START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF]. For an in-depth dive into the language, the reader is redirected to [START_REF] Gebser | Potassco User Guide[END_REF].

ASP is a form of purely declarative programming oriented towards the resolution of combinatorial problems [START_REF] Lifschitz | What is answer set programming?[END_REF]. It has been successfully used for knowledge representation, problem solving, automated reasoning, and search and optimization. Unlike Prolog, ASP handles cross-references of rules, enabling the writing of code much closer to the specification. In the sequel, we rely on the input language of the ASP system Potassco (Potsdam Answer Set Solving Collection [START_REF] Gebser | Potassco User Guide[END_REF]) developed in Potsdam University. An ASP program consists of Prolog-like rules h :b 1 , . . . , b m , not b m+1 , . . . , not b n , where each b i and h are literals and not stands for default negation. Mainly, each literal is a predicate whose arguments can be constant atoms or variables over a finite domain. Constants start with a lowercase letter, variables start with an uppercase letter or an underscore (don't care variables). The rule states that the head h is proved to be true (h is in an answer set) if the body of the rule is satisfied, i.e. b 1 , . . . , b m are true and one can not prove that b m+1 , . . . , b n are true. Note that the result is independent on the ordering of rules or of the ordering of literals in their body, as it is the case in Prolog. An ASP solver can compute one, several, or all the answer sets (stable models) that are solutions of the encoded problem. If the body is empty, h is a fact while an empty head specifies an integrity constraint. Together with model minimality, interpreting the program rules this way provides the stable model semantics (see [START_REF] Gelfond | Logic programs with classical negation[END_REF] for details). In the head part, A choice rule of the form {p(X) : q(X)} will generate p(X) as the powerset of q(X) for all values of X. In the body part, {p(_)} will count the number of atom p with one parameter, and N = {h} evaluates N to the cardinal of the set of h. In the body part, p(X) : q(X) holds if for all X, if q(X) holds, then p(X) holds. Finally, lines starting by % are comments. In practice, several syntactical extensions to the language that are not interesting for this paper are available. An example of ASP encoding is presented in Figure 1, using atoms to reproduce the context in Table 1 and a rule to build a bipartite graph linking objects and attributes. % Facts. age(john,7). age(eve,71). age(alice,15). male(john). male(bob). female(alice). mother(eve,bob). % Rules. rel(H,child):-age(H,A) ; A<12. rel(H,adult):-age(H,A) ; A>=18. rel(H,male):-male(H). rel(H,female):-female(H). rel(H,man) :-rel(H,male) ; rel(H,adult). rel(H,boy) :-rel(H,male) ; rel(H,child). rel(H,woman):-rel(H,female) ; rel(H,adult). rel(H,girl) :-rel(H,female) ; rel(H,child). rel(H,adult):-rel(H,male) ; not rel(H,boy). rel(H,female):-mother(H,_). % Build the visualization in Figures 2 and3.

link(O,A):-rel(O,A).

Fig. 1: ASP program encoding the context in Table 1, in the form of rel/2 relations between objects and attributes. The last line yield links/2 atoms that are compiled by Biseau as edges in the output dot file.

We used the Potassco system [START_REF] Gebser | Potassco: The Potsdam answer set solving collection[END_REF] that proposes an efficient implementation of ASP. ASP processing implies two steps, grounding and solving. The grounder generates a propositional program replacing variables by their possible values. The solver is in charge of producing the stable models (answer sets) of the propositional program. Of course, a dedicated algorithm for a specific problem will be generally more efficient than its equivalent compact ASP encoding. However, ASP systems are useful for the design of prototypes. It is an attractive alternative to standard imperative languages that enable fast developments.

adult child female male boy woman man alice

× bob × × × eve × × × john × × ×
Table 1: Formal context of human relations.

Graph Drawing With Dot

Dot is a graph description language, allowing one to generate a graph visualization from the definition of its content [START_REF] Gansner | An open graph visualization system and its applications to software engineering[END_REF]. Dot enables the control of precise visual properties, such as node and edge labelling, position, shape, or color. For instance, the dot line woman [color="blue"] will color in blue the node labelled woman. The full language is defined by the graphviz graph visualization software, which provides multiple engines to interpret and compile dot encoded files to other formats, including images. Figure 2 shows an example of a working dot description, which given to a graphviz engine yields the visualization in Figure 3. 1.

From ASP to Dot With Biseau

Biseau allows the user to write some ASP encoding and retrieve in real-time the corresponding graph visualization. To achieve this, it implements an ASP to dot compiler and a Graphical User Interface that helps writing the ASP encoding and that performs automatically all necessary compilations. As explained in Section 2, a given ASP encoding yields stable models consisting of true facts, which can be represented by atoms like link(woman,human). For each stable models found from the ASP user encoding, Biseau will convert atoms into dot lines. For instance, the ASP atom link(woman,human) will translate to woman -> human in the dot output. This controlled vocabulary will be only partially explored in Section 5, but note that it maps the full dot language, including colors, shapes, and general graph options. A complete documentation is available online 2 .

Because of the use of ASP to yield the dot description, the graph is therefore defined in intension: instead of describing manually all objects and properties, the user specify their definitions, and let the ASP solver infers all necessary relations. More generally, Biseau internal process can be seen as a compilation from ASP models to dot, then from dot to image (the last one being delegated to graphviz software, as seen in Section 3). As a matter of example, the ASP encoding in Figure 1 will be compiled to the dot description in Figure 2, itself compiled to the image in Figure 3. If the ASP expression color(A,blue):-rel(_,A). was added to the ASP encoding in Figure 1, the final figure would show in blue all attributes nodes. The reader familiar with software engineering may recognize the use of ASP as a metamodel, and dot as the model.

Biseau can be extented with scripts, units of ASP (or Python) code to add to (or run on) the user encoding. They may expose some options to tune their behavior. Moreover, user can implement and add its own scripts to Biseau, allowing him (and others he shares with) to encapsulate ASP or Python programs that behave accordingly to their preferences. Biseau is shipped with scripts related to FCA, for data extraction from standard format like SLF or CXT, concept mining or lattice visualization (as shown in Section 5).

This section shows how to build FCA basic mathematical relations in order to get a visualization of the Galois lattice in Biseau. The context in Table 1 will be used as case study, encoded in ASP using rel/2 atoms as shown in the first five lines of Figure 1.

Mining the Formal Concepts

In a formal context defined by objects O, attributes A, and the binary relation R ⊆ O × A, a formal concept is a pair (X, Y ), such as:

X = {y ∈ Y |(x, y) ∈ R ∀x ∈ X} (1)
Y = {x ∈ X |(x, y) ∈ R ∀y ∈ Y } (2)
Where X ⊆ O and Y ⊆ A. The search for formal concepts in ASP can be expressed like in the above definition:

ext(X):-rel(X,_) ; rel(X,Y): int(Y). int(Y):-rel(_,Y) ; rel(X,Y): ext(X).
rel(X,_) fixes variable X as the first term of a relation, i.e. an object. Notation rel(X,Y): int(Y) ensure that there is a relation between X and all attributes of the intent. As a consequence, ext(X), the extent, holds for all objects in relation with all attributes of the intent. The second rule is a symmetric definition for the concept's intent. For those familiar to Prolog, note that such a program would lead to an infinite loop. The treatment of loops is a nice feature of ASP that gives access to a fixed-point semantics. ASP search comes with the guarantee that all minimal fixed points will be enumerated. Therefore, each answer set is a different concept, or the supremum or infimum (where extent or intent are empty sets). To avoid the yield of supremum (infimum), one may include a constraint specifying that extent (intent) must include at least one element.

These models/concepts can be aggregated in order to produce an encoding containing ext/2 (and int/2) atoms, where ext(N,A) (int(N,A)) gives an element of N-th concept's extent (intent). This numbering is arbitrary and serves no other purpose than identifying the different concepts.

Galois lattice

A Galois lattice is defined by the partial order on the concepts, i.e. a graph with concepts as nodes, and an edge between a concept and its successors in the ordering:

% Shortcut to infimum, supremum and concepts identifiers. c(N):-ext(N,_). c(N):-int(N,_). % Ordering of two concepts: the first has all objects of the second. contains(C1,C2):-c(C1) ; c(C2) ; C1!=C2 ; ext(C1,X): ext(C2,X). % Concepts linked to another in the Galois Lattice . link(C1,C3):-contains(C1,C3) ; not link(C1,C2): contains(C2,C3). % Annotate nodes with extent and intent. annot(upper,X,A):-ext(X,A). annot(lower,X,B):-int(X,B).

These lines yield the visualization shown in Figure 4. Line 2 and 3 are here to enable the access to the infinum, supremum and concepts with one atom. Line 5 yields pairs of concepts that are included, based on their extent. Line 7 ensure that a link exists in the lattice between a concept C1 containing another concept C3 if there no link between C1 and a concept C2 smaller than C3. Finally, the annot/3 atoms are a Biseau convention (just as link/2 that define an edge in the dot output), allowing us to print the extent and intent of each concept, respectively above and below the node.

Reduced Labelling

The reduced labelling of a lattice is computed as the set of specific objects and attributes for each concept. This is easily defined as specext/1 and specint/1 atoms in ASP, using the following lines along the search for formal concepts in section 5.1: % An outsider is any object or attribute linked to an attribute or object not in the concept. With these lines and the collapsing into one model described in section 5.1, we obtain specext/2 and specint/2 atoms, describing the AOC poset elements, attached to each concept. We can then compute the reduced labelling of the lattice with the following lines, replacing the previously defined annot/3 definitions in section 5.2: % Minimalist annotation of nodes with their extent/intent : annot(upper,X,A):-specext(X,A). annot(lower,X,B):-specint(X,B).

Using these definitions, Biseau produces the visualization shown in Figure 5.

Pulling Constraints On The Model

This section exposes the implementation in ASP and Biseau of some FCA variants and extensions often used in knowledge processing [START_REF] Poelmans | Formal concept analysis in knowledge processing: A survey on applications[END_REF].

Fig. 4: Visualization of the Galois Lattice of context in Table 1 using Biseau, with extent and intent shown for each node/concept. Fig. 5: Visualization of the Galois Lattice of context in Table 1 using Biseau, with reduced labelling.

Object and Property Oriented Concept Lattices

Following definitions from [START_REF] Yao | Concept lattices in rough set theory[END_REF], it is also possible to encode the mining of object oriented concepts (X, Y ) defined by X = Y ♦ and Y = X , such as: The code for property-oriented concepts is similar, and both replace the encoding in section 5.1.

Y ♦ = y∈Y Ry X = {y ∈ A|Ry ⊆ X} With Ry = {x ∈ O|(x, y) ∈ R}.

Iceberg Lattices

The iceberg lattice, loosely defined as the Galois lattice stripped of all concepts with a too small support (i.e. number of objects in their extents) [START_REF] Stumme | Conceptual clustering with iceberg concept lattices[END_REF], can be built by discarding any model containing too few objects in his extent. For instance, the Figure 3 of [START_REF] Stumme | Conceptual clustering with iceberg concept lattices[END_REF], reproduced in this paper in Figure 6, shows the iceberg lattice of the running example MUSHROOMS database of nbobj objects with a minimal support of minsupp%. It can be reproduced by discarding models using a constraint: % The number of ext/1 atoms must not fall behind the minimal. :-{ext(_)} < nbobj * minsupp/100. This constraint can be generated by Biseau knowing the number of objects and the minimal support.

n-adic FCA

n-adic FCA [START_REF] Lehmann | A triadic approach to formal concept analysis[END_REF] can be encoded the same way as regular FCA, by extending the number of parameters for rel atoms. For instance, in triadic FCA, conditions are given as the third argument of rel/3 atoms, such as rel(O,A,C) is true when the relation between object O, attribute A and condition C holds. Triadic concepts can thus be generated using the following encoding: ext(X):-rel(X,_,_) ; rel(X,A,C): int(A), cnd(C). int(X):-rel(_,X,_) ; rel(O,X,C): ext(O), cnd(C). cnd(X):-rel(_,_,X) ; rel(O,A,X): ext(O), int(A).

Pattern Structures

As introduced in [START_REF] Ganter | Pattern structures and their projections[END_REF], a pattern structure is a generalization of FCA applied on attributes structured in semi-lattices. Pattern concepts are pairs of objects and lattices, producing the expected pattern lattice. This technics have been applied to gene expression data [START_REF] Kaytoue | Mining gene expression data with pattern structures in formal concept analysis[END_REF]. Here, we reproduce the pattern lattice construction for an example of non-binary data from the same publication:

rel (1,1,5) . rel [START_REF] Alam | Steps towards interactive formal concept analysis with latviz[END_REF][START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Ganter | Pattern structures and their projections[END_REF] . rel [START_REF] Alam | Steps towards interactive formal concept analysis with latviz[END_REF][START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Gansner | An open graph visualization system and its applications to software engineering[END_REF] . % 5 objects rel [START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Alam | Steps towards interactive formal concept analysis with latviz[END_REF][START_REF] Gansner | An open graph visualization system and its applications to software engineering[END_REF] . rel [START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Gebser | Potassco User Guide[END_REF] . rel [START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Auber | [END_REF] . % 3 situations rel [START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Alam | Steps towards interactive formal concept analysis with latviz[END_REF][START_REF] Auber | [END_REF] . rel [START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Gebser | Potassco User Guide[END_REF] . rel [START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF] . % one value from 4 to 9 rel (4,1,4) . rel (4,2,9) . rel [START_REF] Auber | [END_REF][START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Gebser | Potassco User Guide[END_REF] . rel [START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF][START_REF] Alam | Steps towards interactive formal concept analysis with latviz[END_REF][START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF] . rel [START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF][START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF][START_REF] Gebser | Potassco User Guide[END_REF] . rel [START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF][START_REF] Andrews | A tool for creating and visualising formal concept trees[END_REF][START_REF] Bourneuf | FCA in a Logical Programming Setting for Visualization-Oriented Graph Compression[END_REF] .

Note that data are encoded in rel/3 atoms over 5 objects, 3 conditions, and expression values in the interval [4; 9] associated with a given gene and condition, such as rel(O,S,V) holds when object O in situation S has an expression value of V. Similarly to section 5.1, we can enumerate the pattern concepts: The use of the meta-programming directives #min and #max allows us to retrieve the minimal and maximal value associated to the extent. Therefore, interval(C,Min,Max) stands for the minimal and maximal values on condition C, e.g. 5 and 6 for condition 1 when extent is {1, 2, 5}. Unlike the concept model seen in Section 5.1, this model relies on an explicit choice rule for the extent with subsequent constraints to ensure its maximality. Line 2 generates an answer set for each element of the power set of the object set. Following lines will discard answer sets that are not infinum, supremum or concept. Line 4 associate for each condition the minimal and maximal values over the extent. Line 7 selects an object and a condition such as they are associated to a value in the interval. Line 9 selects all objects that are valid for all conditions, and line 11 ensure that they belong to the extent.

The code in section 5.2 can be reused without modifications to produce and show the resulting pattern lattice.

Discussion & Conclusion

Using the ASP language in the Biseau environment, some well-known FCA structures (Galois, object-oriented, iceberg, integer pattern lattices) have been reconstructed. The main contribution of Biseau lies into the straightforward use of the structure specifications to produce a simple code and a proper visualization. To achieve that feat, Biseau is compiling a controlled subset of ASP atoms to dot lines, effectively building a dot formatted file that is compiled to an image by graphviz software. By letting the user manipulate the visualization with the full power of ASP, Biseau enables definition of graphs in intension. This gives an abstract access to dot expressions and lets the user focus on the fast prototyping of data exploration and the elaboration of mathematical properties. In other words, Biseau allows user to work on the model in which data are processed, instead of providing an implementation of a single model to be used on particular data, as usually performed in field-specialized softwares.

ASP limits lies into the absence of float numbers handling, and scaling problems inherited from the total grounding of data before solving. However, Potassco system users may benefit from several extensions of the language like linear programming [START_REF] Liu | Answer set programming via mixed integer programming[END_REF] or propagators [START_REF] Gebser | Theory Solving Made Easy with Clingo 5[END_REF], allowing one to take advantage of other programming paradigms. It is also possible to improve performances by an iterative replacement of bottlenecks by dedicated algorithms. For instance, the standard concept mining can be replaced by an implementation of the in-close algorithm [START_REF] Andrews | In-close, a fast algorithm for computing formal concepts[END_REF].

Biseau current state is a very simple proof of concept, and therefore miss a lot of features typically found in text editors and IDEs, that could help user to write, understand and debug produced ASP code.

Future work will focus on the Biseau generalization : other languages like GML allow to describe graphs, some are field-specific, and some enable outsourcing of the visualization to other (field-)specialized softwares. Future development of Biseau could provide support for ASP advanced features, and embedding of more scripts for FCA and its extensions.

Fig. 2 :

 2 Fig. 2: Dot encoding of the graph in Figure 3.

Fig. 3 :

 3 Fig.3: Visualization of the relations described by context in Table1.

  outsider(X):-ext(X) ; rel(X,Z) ; not int(Z). outsider(Y):-int(Y) ; rel(Z,Y) ; not ext(Z). % The specific part of each concept contains no outsider. specext(X):-ext(X) ; not outsider(X). specint(Y):-int(Y) ; not outsider(Y).

%

  Any object linked to an attribute in the intent is in the extent . ext(X):-rel(X,Y) ; int(Y). % Objects in the complementary set of the extent. not_ext(Nx):-rel(Nx,_) ; not ext(Nx). % The intent is made of attributes exclusively linked to objects of the extent . int(Y):-rel(_,Y) ; not rel(Nx,Y): not_ext(Nx).

Fig. 6 :

 6 Fig. 6: Iceberg lattice with a minimal support of 85% of the MUSHROOMS database.Figure extracted from [22].

  Fig. 6: Iceberg lattice with a minimal support of 85% of the MUSHROOMS database.Figure extracted from [22].

%

  Choose a subset of objects as the extent . { ext(O): rel(O,_,_) }. % The intervals of extent . interval(C,Min,Max):-rel(_,C,_) ; Min=#min{V,O: rel(O,C,V), ext(O)} ; Max=#max{V,O: rel(O,C,V), ext(O)}. % Object is valid on Condition. valid_on(O,C):-rel(O,C,V) ; interval(C,Min,Max) ; Min<=V ; V<=Max. % Object is valid for all Conditions. valid(O):-rel(O,_,_) ; valid_on(O,C): rel(_,C,_). % Avoid any model that do not include maximal number of objects. :-not ext(O) ; valid(O).

https://gitlab.inria.fr/lbourneu/biseau

https://gitlab.inria.fr/lbourneu/biseau/blob/master/doc/user-doc.mkd