Aurélie Girard
email: aurelie.girard34@gmail.com

Bernard Fallery
email: bernard.fallery@univ-montp2.fr

Integration of Social Media in Recruitment: A Delphi Study (draft)

Keywords: social media, recruitment, employer branding, Delphi, e-HRM

 Purpose

The development of social media provides new opportunities for recruitment and raises various questions. This chapter aims to clarify areas of agreement and disagreement regarding the integration of social media in recruitment strategies.

 Methodology/approach A Delphi study was conducted among a panel of 34 French experts composed of 26 practitioners and 8 academics.

 Findings Three quantitative results and five qualitative results are presented. Social media appear as an opportunity to raise the strategic role of HR professionals through employer branding strategy, internal skills development and a greater involvement of managers within the sourcing process.

 Practical implications This study points out several barriers and limits regarding the integration of social media in recruitment strategies and encourage HR professionals to take up the challenge. Multiple recommendations are addressed to HR professionals.

 Originality/value of paper This chapter is based on an innovative application of the Delphi method. Moreover, it offers a more comprehensive and critical look on the integration of social media in recruitment strategies.

Introduction

In 2011, 77% of French Internet users are members of at least one social networks site [START_REF] Ifop | Observatoire des réseaux sociaux[END_REF]. This number has risen sharply: they were only 27% in 2008 (IFOP, 2008). For several years, the term "social network" is therefore widespread in the Internet sphere. When users talk about "social networks", they refer to sites "2.0", such as Facebook, Twitter, LinkedIn, and YouTube. Many terms are used by the media and researchers: Web 2.0 (O' Reilly, 2005), social network sites [START_REF] Boyd | Social Network Sites: Definition, History, and Scholarship[END_REF], social media [START_REF] Kaplan | Users of the world, unite! The challenges and opportunities of Social Media[END_REF])… We will use the term "social media" to characterize these tools (it includes social network sites but also blogs).

The rapid development of social media opens up new opportunities for businesses, particularly in e-HRM area [START_REF] Barker | How Social Media Is Transforming Employee Communications at Sun Microsystems[END_REF][START_REF] Heikkilä | A Delphi Study on E-HRM : Future Directions E-HRM[END_REF][START_REF] Joos | Social Media : New Frontiers in Hiring and Recruiting[END_REF][START_REF] Kaplan | Users of the world, unite! The challenges and opportunities of Social Media[END_REF][START_REF] Martin | Web 2.0 and HRM: A Discussion Document[END_REF][START_REF] Welbourne | Editor-in-chief's note: new media: opportunity or curse for hr?[END_REF]. [START_REF] Bondarouk | Electronic Human Resource Management: challenges in the digital era[END_REF] define e-HRM as "an umbrella term covering all possible integration mechanisms and contents between HRM and Information Technologies aiming at creating value within and across organizations for targeted employees and management." (p. 507).

Recruitment is one of the main HR activity impacted by the rise of social media. According to a French survey [START_REF] Regionsjob | Enquête Emploi & réseaux sociaux[END_REF], 49% of French recruiters are now using social media to recruit. 43% of them admit to "google" applicants and 8% say they had already rejected someone based on the results obtained though the search engine. These e-recruitment strategies remain largely unstudied in the literature. After conducting four case studies at two recruitment agencies and two companies that have developed innovative strategies through social media, we decided to realize a Delphi study to gather expert judgments and clarify points of agreement and controversy regarding these new approaches.

First, based on a literature review we demonstrate that social media represent an important issue for recruitment.

Then, we present a Delphi study conducted among 34 experts of social media and recruitment.

Three quantitative results and five qualitative results are highlighted. Finally, we discuss the results and provide suggestions for further research.

Social media and recruitment: literature review

The use of social media within recruitment strategies seems to be an important issue for two main reasons:

-To reduce the "noise" caused by previous e-recruitment tools; -To face the "war for talent" and adapt the communication to new Internet users' behaviours.

To reduce the noise caused by previous e-recruitment tools

Since the late 90s, Internet has taken an important place within the recruitment process. It has enabled organizations to extend their CV databases through three main instruments: job boards, careers websites and recruitment software applications. According to a recent survey conducted by the French association for executive employment (APEC, 2010), almost all executives job offers are broadcast on the Internet (through job boards or careers websites), of which 81% exclusively online.

Despite the widespread use of technology in the recruitment context, research is scarce and mostly applicants-oriented [START_REF] Lievens | Recent trends and challenges in personnel selection[END_REF]. From the employer perspective, [START_REF] Parry | What is the Potential of E-Recruitment to Transform the Recruitment Process and the Role of the Resourcing Team[END_REF] demonstrate that the use of both career websites and recruitment systems has several benefits: cost reduction, efficiency gains, improved service to clients and improved strategic orientation. Indeed, Internet has brought various benefits to recruiters in terms of job offers broadcasting (fast, large-scale and cheaper), CVs access, and application management.

However, although the labour market has become more transparent, it has also become noisier. [START_REF] Fondeur | Internet , recrutement et recherche d'emploi : une introduction[END_REF] calls this phenomenon the dilemma "transparency-noise". Internet has led to a trivialization of the act of application, lowered the level of self-censorship of the applicants and encouraged increased "unqualified" applications [START_REF] Dineen | Aesthetic properties and message customization : Navigating the dark side of web recruitment[END_REF][START_REF] Fondeur | Internet , recrutement et recherche d'emploi : une introduction[END_REF].

Today social media offer an opportunity for companies and applicants to solve this problem of noise induced by previous e-recruitment tools.

The literature has already demonstrated that «offline» social network, and thus the mobilization of social capital, do play an important role particularly within the recruitment process [START_REF] Bourdieu | The forms of capital[END_REF][START_REF] Lin | Social resources and strength of ties: Structural factors in occupational status attainment[END_REF]. [START_REF] Granovetter | The Strength of Weak Ties[END_REF] used the job market to illustrate "the strength of weak ties" that enables to get in touch with a large number of people and to access new information and opportunities. From an applicant's point of view, mobilizing a social network makes it possible to obtain more information about the company and the job [START_REF] Holzer | Search Method Use by Unemployed Youth[END_REF][START_REF] Lin | Social resources and strength of ties: Structural factors in occupational status attainment[END_REF][START_REF] Rees | Information Networks in Labor Markets[END_REF]. This method may also enable applicants to acquire better wages [START_REF] Granovetter | Getting a Job: a study of Contacts and Careers[END_REF][START_REF] Holzer | Search Method Use by Unemployed Youth[END_REF]. From an employer's perspective, according to [START_REF] Rees | Information Networks in Labor Markets[END_REF], making use of one's own network or that of the staff should limit the number of applications whilst simultaneously ensuring their quality and also reduce absenteeism and turnover. This method is both less expensive and more effective because of the confidence put in the applications [START_REF] Holzer | Search Method Use by Unemployed Youth[END_REF].

Social media, and SNS in particular, multiply the possibilities of interpersonal contact and exchange [START_REF] Roberts | Social Networking Web Sites and Human Resource Personnel: Suggestions for Job Searches[END_REF]. Both applicants and employers can maintain, mobilize and develop their social network more efficiently thanks to SNS. They can filter out relevant information and access new collaboration opportunities [START_REF] Dekay | Are Business-Oriented Social Networking Web Sites Useful Resources for Locating Passive Jobseekers? Results of a Recent Study[END_REF]Girard & Fallery, 2011).

To face the war for talent and adapt the communication to Internet users' behaviours

According to the Resource-Based View (Barney, 1991;[START_REF] Prahalad | The Core Competence of the Corporation[END_REF][START_REF] Wernerfelt | A resource based view of the firm[END_REF]) a firm's human resources, or human capital, is an important potential source of sustained competitive advantage [START_REF] Wright | Human resources and the resource based view of the firm[END_REF]. Recruiting is the first step to obtain such an advantage. Nevertheless, today the nature of work presents many challenges [START_REF] Ployhart | Staffing in the 21st Century: New Challenges and Strategic Opportunities[END_REF]: knowledge-based work places greater demands on employee competencies; demographic, societal, and cultural changes are widespread and are creating an increasing global shortfall in the number of qualified applicants; the workforce is also increasingly diverse. Several authors use the term "war for talents" to describe this phenomenon [START_REF] Chambers | The War For talent[END_REF][START_REF] Guthridge | Making talent a strategic priority[END_REF]. Companies are thus in competition and must implement effective strategies on one hand to detect talents and appreciate their skills, and on the other hand to attract, acquire and retain them in the organization. Moreover, in line with the increasing use of social media, Internet users' behaviours have evolved (as for applicants). Internet users are no longer spectators, they have become true "consum'actors" [START_REF] Rosnay | La révolte du pronétariat : des mass média aux médias des masses[END_REF] or "prosumers" [START_REF] Toffler | The Third Wave[END_REF]. They create, share and exchange many contents. They no longer hesitate to express their opinions online on many platforms and call into question the traditional broadcasters of information. Empowered by social media technologies, customers are now connecting with and drawing power from each other [START_REF] Bernoff | Harnessing the Power of the Oh-So-Social Web Harnessing the Power of the Oh-So-Social Web[END_REF]. They gain knowledge through Internet and social media in particular before making a decision, to forge an opinion about a brand, a company and why not about their future employer.

In parallel, they can also use social media to manage their online presence and develop their "personal branding" [START_REF] Dutta | What's Your Personal Social Media Strategy ?[END_REF][START_REF] Malita | Culture tips of online job searching[END_REF]. They can get in touch with other professionals, share their experiences, and thus develop their professional network and improve their employability. These behaviours are supposed to be characteristic of the so-called "Generation Y" (born between the late 70s and mid 90s) considered as interactive, impatient and demanding with employers and society in general [START_REF] Hewlett | How Gen Y & Boomers Will Reshape Your Agenda[END_REF][START_REF] Tapscott | Grown Up Digital: how the Net Generation is Changing Your World[END_REF].

Either way, these new behaviours seem to force companies to rethink the way they communicate. Social media bring the opportunity to develop their employer brand and to monitor they reputation. [START_REF] Backhaus | Conceptualizing and researching employer branding[END_REF] define employer branding as "the process of building an identifiable and unique employer identity". The concept of employer reputation "is based on what one does as an employer plus what one says one is doing" [START_REF] Hepburn | Creating a winning employer reputation[END_REF]. In other words, the employer brand is the desired image by the company, while the employer reputation is the projected and interpreted image by particular candidates.

Social media appear to be an interesting mean to improve both branding and reputation by being active and engaging the conversation with potential applicants and other stakeholders (Girard & Fallery, 2011).

The research approach

Origin and Rationale of the approach

As a first step, we conducted case studies at two recruitment agencies and two companies that have developed recruitment and employer branding strategies on social media [START_REF] Girard | The development of Social Media in the field of e-HRM: Employer branding and e-Recruitment[END_REF]. Two main types of data were collected: secondary data (internal and external documents) as well as semi-structured interviews with actors being primarily involved (26 interviews conducted between September 2009 and February 2011, 24 hours of recording). After a content analysis, it appeared some differences of views among the various actors interviewed.

As a second step, we therefore wanted to clarify points of agreement and disagreement about social media and recruitment. Delphi method proved to be appropriate to achieve this goal. Indeed, this method was originally developed by Norman Dalkey and Olaf Helmer (from RAND Corporation) in the 1950s to obtain and organize a group of experts' opinions on issues of prospective military operations [START_REF] Dalkey | An Experimental Application of the DELPHI Method to the Use of Experts[END_REF]. It permits to collect experts' opinions through a series of questionnaires (2 to 3 in general) iteratively. Delphi method is very adaptable and used in many fields for decision making, to explore a topic, to build models or to perform scenarios and forecasts [START_REF] Linstone | The Delphi Method: Techniques and Applications[END_REF][START_REF] Okoli | The Delphi method as a research tool: an example, design considerations and applications[END_REF].

There are no set rules for Delphi study, however, [START_REF] Rowe | The Delphi technique as a forecasting tool : issues and analysis[END_REF] characterize the classic Delphi method by four main features:

1. Participants' anonymity: it allows participants to express themselves freely and to avoid any influence based on respondents' personality or status.

2. Iteration: it enables participants to refine their views round by round.

3. Controlled feedback: it indicates to participants the ratings of others, and provides them the opportunity to clarify or modify their views.

4. Statistical aggregation of responses: it allows a quantitative analysis and the interpretation of data [START_REF] Schmidt | Managing Delphi Surveys Using Nonparametric Statistical Techniques[END_REF].

The aim of a Delphi study is usually to reach a consensus, through successive iterations, but in some cases, consensus is not necessarily the main goal. Therefore, our study is close to the "Argument Delphi" as defined by [START_REF] Kuusi | Expertise in the future use of generic technologies. Epistemic and methodological considerations concerning Delphi studies[END_REF]. Indeed, our approach encourages discussion and aims to highlight relevant arguments rather than just consensus.

Implementation of the approach

Based on the literature review and case studies, we formulated 20 proposals: 12 "validation proposals" (affirmatives), and 8 "prospective proposals" (written in the future). Proposals have been formulated to lead the experts to argue their position and answers (formulation not "consensual"). For example, the term "indispensable" has been preferred for proposal 4 (cf. table 2) to the term "useful" to encourage experts to discuss. Quite categorical words have been used (e.g., insufficient, forces, clearly, significantly...).

A pre-test was previously performed. Proposals were reviewed by several colleagues (4) to ensure their understanding. This resulted in a few changes in the wording of some proposals.

In general, the pre-test encouraged us to use a simple vocabulary and add some details in brackets when necessary.

We opted for Likert scales ranging from 1 (strongly disagree) to 7 (strongly agree). We selected seven points under the criteria of [START_REF] Cox | The Optimal Number of Response Alternatives for a Scale: A Review[END_REF] and [START_REF] Preston | Optimal number of response categories in rating scales: reliability, validity, discriminating power, and respondent preferences[END_REF].

Moreover, it allows participants to provide more flexibility in their answers. Questionnaires were sent by email as a Word document (see below).

-Selection of experts and data collection: The selection of "experts" is an essential element that determines the quality of results [START_REF] Adler | Gazing into the oracle: The Delphi method and its application to social policy and public health[END_REF][START_REF] Bolger | Assessing the quality of expert judgment[END_REF]. We selected experts following the three components suggested by [START_REF] Larréché | A framework for the comparison of marketing models: A Delphi study[END_REF]: industry experience, familiarity with the object of study and knowledge of the characteristics of the object. Thanks to our case studies and our professional use of various SNS, we have been in contact with a number of social media and recruitment experts. Their identification was thus facilitated. In order to achieve a sufficient sample we contacted 44 experts. 34 of them agreed to participate and did respond to the first questionnaire, (final response rate: 77%). Our panel consists of 8 academic researchers who have published and/or participated in seminars on the topic, and 26 "practitioners": consultants working in recruitment agencies (8), consultants working in management and HR consulting agencies (7), HR corporate managers (5), and job boards or SNS managers (6).

-A three round Delphi: The Delphi study was conducted between March, 28 and June, 20,

(12 weeks).

At the first round, we asked the experts to rate each proposal from 1 to 7, to comment on their vote if they wished, and to write any other proposals at the end of document (proposal 21 was thus added). Answer time ranged from 1 day to 3 weeks and one reminder was sent.

At the second round, we indicated to each expert for each proposal, the median, the histogram of the answers and their positioning in red. Experts had to:

-Confirm or change their rating for each proposal (given the discovery of other experts' opinions) -Comment on their position, especially if they changed their vote.

-Give a rate to each proposal, from A (very important) to D (not important).

This second round took 4 weeks and two reminders were needed.

At the third and last round we identified and communicated three groups of proposals:

-Group 1: proposals with a low level of consensus but judged as important to very important.

-Group 2: proposals with a high level of consensus and judged as important to very important.

-Group 3: proposals with a low level of consensus but considered as few or not important.

Regarding group 1 proposals, we asked the experts to explain why the level of consensus was low while proposal were classified as "important to very important". The median, the histogram of the answers and the positioning of the expert were reported. This last round took 5 weeks and two reminders were also necessary. Contrary to previous rounds, all experts did not respond. We obtained a response rate of 70% (24 of 34 experts).

1/ Careers websites and job boards are essential but with social media development, they are now insufficient to recruit. 2/ With the development of interaction through social media, companies and recruitment agencies have lost control of information; they must agree to interact with potential applicants. 3/ Social media use by applicants has amplified the demand for a more personalized, balanced and transparent relationship with the company / the recruitment agency 4/ Social media have become essential to develop long term relationships with "pre-candidate" who listen to the job market. 5/ To manage its digital identity (managing its online presence, be able to communicate on itself, to interact) has become a sought, valued and essential skill. 6/ Although Generation Y is well known for his personal use of social media, professional use of social media is not a matter of age. 7/ We must clearly distinguish between professional social networks used for the recruitment and other Social Media used to develop the employer brand. 8/ It is necessary to adopt differentiated and targeted strategies (between tools, topics people) to implement actions on Social Media. 9/ Social media monitoring (observations and reactions) is the most important to develop an employer brand strategy. 10/ The practice of Social media forces to create new positions in companies (Head of the Employer Brand, HR Community Manager). 11/ With the use of social media, internal-external boundaries are increasingly blurred (role of Community Manager, intranet / Internet tools, private-professional repercussions ...). 12/ Social media are just complementary tools to improve recruitment and manage the employer brand. 13/ Social media will change considerably applicant relationship management (with relations established in the long term, based more on exchange, with more proximity ...). 14/ Social media will give HR professionals a greater role in strategic decisions. 15/ Social media use for recruitment will concern only specific profiles (some sectors, some professional status, some age groups ...). 16/ Even if a formal piloting/management of communities on Social media is initially required (Community Manager), in the future communities will have more open structures with a voluntary commitment of members inside and outside the company. 17/ Because of difficulties in mastering social media, companies will increasingly outsource their recruitments to experienced recruitment agencies. 18/ By extending the possibilities of co-option, social media will lead to greater decentralization of recruitment responsibilities to managers and employees. 19/ Applicants' use of Social media will lead to a zapping (switching) behaviour in professional careers (high turnover). 20/ With the development of applicants' activity on Social media (interactions, blogs...), companies will pay more attention to competencies than to job profiles (competencies more visible ...). 21/ Social media development favours the appearance of unethical behaviour by the recruiters.

Table 2. List of the 21 proposals submitted to experts' judgment

Results

Numerous assessments and comments were collected along the three rounds. Data collection, descriptive statistics and comment analysis were performed with Excel. Statistical test were determined with SPSS. All the study was carried out in French, proposals and comments have been translated in English for this article. Three quantitative results and five qualitative results emerged.

Three quantitative results

(1) All proposals combined, the global level of consensus is low The global level of consensus is relatively low. Indeed, we used Kendall's W to measure this level and its robustness (statistical significance). Kendall's W ranges from 0 (no consensus) to 1 (total consensus) [START_REF] Schmidt | Managing Delphi Surveys Using Nonparametric Statistical Techniques[END_REF]). Second round W is equal to 0.337 with a high degree of significance. This level corresponds to a relatively low level of consensus according to [START_REF] Schmidt | Managing Delphi Surveys Using Nonparametric Statistical Techniques[END_REF].

(2) Two main groups of proposals are distinguished: with a high level of consensus and with a low level of consensus Therefore, two main groups of proposal can be distinguished: proposals with a relatively high level of consensus and proposals with a low level of consensus.

To measure the degree of consensus for each proposal we use the level of MAD [START_REF] Isaac | Ethical codes, a tool for quality management in professional services[END_REF][START_REF] Vella | Use of consensus development to establish national research priorities in critical care[END_REF][START_REF] Zenou | How to integrate the value created by a CEO within a firm's global value creation ? Contribution to the investigation of a CEO's value assessment[END_REF], refined through another measure of dispersion (% IM1).

We present the quantitative results in summary tables indicating for each proposal:

-Me: The median.

-MAD (Round 1 and 2): The mean absolute deviation around the median, for the two rounds.

-%IM1: The percentage of answers in the range [median -1, median +1].

-% changes: The percentage of changes by proposal between round 1 and round 2.

-Importance: The assessment of importance: + (important to very important) ; -(few important to not important). The proposals regarding the future are the most represented (6 / 8). Comments analysis allows us to better understand the various experts' arguments.

Me

MAD

(3) Opinions converged from round one to round two

Several elements allow us to affirm that opinions converged between round 1 and round 2 thanks to the Delphi process. First, Kendall's W of round 2 is higher than the W of the first round (0,337>0.241). The global level of consensus is still low but has improved between the two rounds.

Moreover, the number of proposals with a high level of consensus has increased between the two rounds. Proposals number 1, 2 and 4 moved from a low level of consensus to a high level of consensus, especially proposals 2 and 4 which have led experts to revise their assessments (over 20% of changes).

Finally, the Wilcoxon signed-rank test enables us to test the significance of answers convergence between the two rounds. Indeed, this nonparametric test measures the convergence or divergence of the assessments. We perform this test on the distribution of mean absolute deviation from the median (MAD) of all proposals. In line with the Wilcoxon signed-rank test, answers convergence between the two rounds of

Delphi is significant at a high confidence level (i.e. distribution of MAD2 < MAD1).

Five qualitative results

(1) Social media do not replace other e-recruitment tools and they can either be used to develop employer branding or to recruit.

Comment analysis of proposals number 1, 7 and 12 allow us to support this result Regarding the first proposal: "Careers websites and job boards are essential but with social media development, they are now insufficient to recruit" (Me=5), a form of consensus is reached. Indeed, the large majority of experts agree with the essential character of careers websites and job boards but most of them consider social media as more dynamic and relational tools. However, the term "insufficient" is often regarded as too categorical. Some experts stress that job boards are also evolving to incorporate social networking features.

"Corporate sites may be the place that provides information and so on. But social media allows sharing and virality, in short, a more extensive and efficient distribution" n23 "For recruitment, professional social networking sites expand sourcing and introduce another form of relationship with the applicants" n29

"From the "active applicant" perspective, job boards are essential. From the "passive applicant"

perspective, job boards seem inefficient and social media have become essential to create development opportunities" n15 "They (job boards) are insufficient in their current form but get better by providing social networking features" n31

A majority of respondents tends to reject proposal 12: "Social media are just complementary tools to improve recruitment and manage the employer brand" (Me=3) and do not perceive social media as "just complementary tools" but as more and more important tools for recruiting and employer branding strategies and having a significant organizational impact.

"On the contrary, they become more and more essential tools not only" gadgets "in charge of interns" n23 "In fact I have a problem with" complementary "because they are more than that due to the skill they require to develop, the time they take to manage, the impact they can have internally and externally" n24 "No, they change the mode of seduction, recruitment, retention" n26

Indeed, social media may enable a better fit, notably by a better visibility of applicant's competencies, however, positions differ regarding proposal 20: "With the development of applicants' activity on Social media (interactions, blogs...), companies will pay more attention to competencies than to job profiles/descriptions (competencies more visible ...)" (Me=5). Many experts consider that social media allow going beyond the simple resume, but the majority put forward different limits: organizational barriers, lack of flexibility in the selection process, or potentially superficial nature of "personal branding".

"Consideration of the individual applicant as a whole (competencies, network, recommendations, online engagement, opinions, personality, behaviour...)" n19 "I confirm my vote because I am a typical example of this phenomenon because I was recruited to duplicate my techniques of personal branding to the company (employer branding)" n1 "It's a fundamental shift ... but it faces certain inertia of companies. I think this will happen but not in the short term" n10 "[...] but it is still necessary that the recruiter has the possibility of varying the "bounds" of the profile he is looking for" n25 "Possibly, but social media enable also to "build" a profile (" personal branding") [...]" n23

Proposal 7 tends to be rejected: "We must clearly distinguish between professional social networks used for the recruitment and other Social media used to develop the employer brand" (Me=3). Most experts believe that it is not possible to categorically distinguish these two categories of social media and that all social media can be used both for employer branding and recruitment. Various reasons are evoked for rejecting this distinction: the symbiotic relationship between social media; the "war of positioning" of social media; others possible distinctions in terms of use, strategies and levels of communication.

"Today it is very difficult, if not impossible, to cleave its different practices and keep waterproof its diverse networks" n1

"For me, the network is all the networks, so there is no distinction" n21 "I do not think we should separate as much the two types of tools because we are in a war of positioning of these tools. On the other hand, it will depend on the users and we are only at the early beginning" n3 (2) In the short term social media can meet the demands of exchange; in the long term the change of applicant relationship will depend on the labour market and the appropriation of these tools.

Comment analysis of proposals 2, 3, 4, 13, 20 and 21 allow us to support this result.

Regarding proposal 2: "With the development of interaction through social media, companies and recruitment agencies have lost control of information; they must agree to interact with potential applicants" (Me=6), the majority of respondents actually think that recruiting agencies and companies do not -really -have the control of information and must exchange more with applicants through social media. Many argue that applicants have access to much more information via social media and that relationships are more balanced between recruiters and applicants.

"It's one of the major impacts that companies have to deal with" n8 "Companies do not have lost control of the information on their brand ... they never really had it. However, today, the applicants' speeches can be read and be seen more quickly. So we need to establish the dialogue" n3 "Indeed, it has become very easy for an applicant to inquire about a company, a recruiter, his future manager, through networks or by contacting directly current or former employees. The relationship has been balanced" n32 "A company that does not play the" game of conversation, "will damage its brand image and will be deprived of applications for which the "social media" identity is important" n1

A majority of experts agree with proposal 4: "Social media have become essential to develop long term relationships with "pre-candidate" who listen to the job market. ( Me=6). Social media are thus considered as essential or at least "very useful" due to several advantages: construction of an applicant pool, management of online communities, enhancement of the company, and development of a "conversational" employer brand.

"This logic of community enables to be proactive in terms of talent identification and recruitment rather than being in a reactive mode" n9 "Sourcing and conversational employer brand" n19 "I think social media make it possible to get in touch before and after stay in touch, even in case of non recruitment. In other words, to extend the life cycle of the prospect-applicant" n34

Indeed, most experts agree with proposal 3: "Social media use by applicants has amplified the demand for a more personalized balanced and transparent relationship with the company / the recruitment agency" (Me=6). This demand is considered by many experts as legitimate and transversal. Several emphasize the need for organizations to be more transparent and to adopt a less conventional discourse. More than half of the experts are in total agreement with proposal 13: "Social media will change considerably applicant relationship management (with relations established in the long term, based more on exchange, with more proximity ...)" (Me=6). Indeed some believe that there will be more proximity and more dialogue but another part believes that this change will depend both on the evolution of the labor market and the real appropriation of these media by recruiters (real exchanges, relational approach, ethical behavior ...).

"Yes because the applicant is better informed, he has more relational power» n23.

"Social media enable us to create more links. [...] Now, regarding the long term, I confess being more sceptical by now" n3

"Potentially, but it involves some additional costs. Probably this vision will be limited to niche segments (specific expertise, high potential, etc.)" n33 "Yes, if companies and recruiters use what these tools are offering more and better. But this will not prevent some recruiters using only social media to build a pool (as they would do with a job board) and missing the relational aspects" n25 " [...] The employer will remain still in a position of strength in most cases especially with difficult economic conditions as currently" n13

At the end of the first round, several experts stressed that this evolving relationship also includes ethical issues. We have thus submitted proposal 21 to experts' opinions: "Social media development favours the appearance of unethical behaviour by the recruiters" (Me=4).

Most experts believe that social media can facilitate (and not favour) unethical behaviour, these behaviours being more related to the recruiter than to social media themselves. It is worth noting that one expert wishes to stress the responsibility of applicants and three others even consider that social media will make unethical behaviours more visible.

"Unethical behaviour comes from people, not from tools implemented" n3 "[...] however, the applicant shares the responsibility for what happens to him" n30 "[...] On the contrary, social networks help identify these recruiters and to make known it at the speed of light" n24

(3) New behaviours become widespread independently of applicants' age and carriers strategies.

Proposals 5, 15, 6, 19 allow us to achieve this result.

The majority of experts had a balanced position regarding proposal 5: "To manage its digital identity (managing its online presence, be able to communicate on itself, to interact) has become a sought, valued and essential skill." (Me=5). The management of its "online traces" is seen as a generic skill (to be developed by all applicants), while the management of its online presence (be able to communicate on itself) is seen as a more specific skill currently restricted to certain occupations. Yet, most experts agree that these skills will involve a growing number of jobs and become more and more important, if not a norm.

"It depends on the position you are looking. In any case it has become essential for positions in communications, marketing, HR and web" n5 "It is generally true and it will be increasingly. It's a way to make a difference between two profiles a priori equivalent. But for certain qualifications or certain areas, it matters less (e.g. for construction and public works)" n10 "In and of itself the answer is "a big Yes" for digital identity, but concerning the "be able to communicate on itself and to interact" (which does not fall within digital identity) I'm not sure. The majority of Internet users do not express themselves" n2 " [...] This might evolve from a distinctive competence to a key success factor" n13

By consequences proposal 15 "Social media use for recruitment will concern only specific profiles (some sectors, some professional status, some age groups ...)" (Me=3.5) has a low level of consensus. A majority of experts think that the use of social media for recruitment will concern more and more profiles but the disagreement lies in the assessment of this generalization importance. Indeed, some consider that social media already concern very different profiles, while others believe some profiles will never be concerned.

"The trend is democratizing, and today we find already people from diverse backgrounds" n9 "It reminds me discourses at the beginning of job boards = where nobody believed that we would recruit non-executive ... With 20 million members on FB, 4M on Viadeo, the market is there ..." n29 "Even if the trend pushes more and more diverse backgrounds to come on social networks (different experience, education, age groups ...), it is true that at first glance it will always concern profiles with a computer access at their workplace" n15

Moreover, generation Y is often evoked regarding the use of social media but the vast majority of experts agree with proposal 6: "Although Generation Y is well known for his personal use of social media, professional use of social media is not a matter of age." (Me=7).

Indeed, they recognize that the younger generation has abilities but does not have a very professional approach of these tools. Other factors of use are underlined such as curiosity, experience, and interpersonal skills. Some experts even directly challenge the very existence of "gen Y".

"Absolutely, Gen Y has de facto developed abilities to manage multiple profiles, communicate in real time and in a transversal way, and to use mobility services but does not necessarily have a professional" and entrepreneurial approach of these technologies" n2 " [...] The proper use of social media goes beyond mere technical knowledge, and also requires common sense, experience, interpersonal skills, qualities that do not belong to a generation" n10 "Studies on uses (we have done a lot ...) show significant standard deviations within this "Generation Y"" n28

Besides, information and opportunities provided by social media activity could lead to a higher turnover; this idea is also widespread in the media. Yet experts are quite negative about proposal 19: "Applicants' use of Social media will lead to a zapping (switching) behaviour in professional careers (high turnover)" (Me=3). Indeed, the majority tends to reject the term "lead". One half of experts do not consider social media as the triggers of change but as enablers that can accentuate this phenomenon. The other half does not link the practice of social media and zapping behavior. Some even think that social media could favor a better match between the applicant's project and the strategic project of the company. Many also stressed the importance of employee retention, with or without the help of social media.

"The switching already exists, social networks could perhaps act as amplifiers" n17 " [...] Ultimately, the challenge is reversed: how to use it to keep applicants. But the tool can only be at the service of a policy ... that still remains to be built" n30 "On the contrary, transparency that social media entails rather could even curbs this behaviour. Similarly, being less in a selling behaviour, but rather in the search for a fit between strategic business project and personal/professional project should enable a healthier and long-term collaboration" n9

(4) Social media will enable either a greater involvement of employees in the sourcing or an outsourcing towards new types of recruitment agencies

Proposal 17 and 18 allow us to formulate this result.

Only one expert totally agrees with proposal 17 "Because of difficulties in mastering social media, companies will increasingly outsource their recruitments to experienced recruitment agencies" (Me=4). One third totally disagree with the proposal and think the opposite situation will occur, i.e. a greater internalization of recruitment activity for various reasons: cost reduction, facilitated sourcing through social media, outsourcing difficulty related to the need of interactivity and transparency. The opinions of the remaining two thirds are more nuanced. Several experts believe that recruitment via social media can be outsourced, subject to the emergence of new types of agencies: providing a real added value, specializing in certain jobs, and developing approaches and skills about social media.

"I confirm my vote but subject to the emergence of new types of recruitment agenciesbecause I still believe that traditional agencies will themselves have as much trouble (or more) than companies to turn to social media for carrying out their mission" n1 "I hope so, but I do not believe it ... ;) mainly because of the previously mentioned job aspect ... or via recruitment agencies specialized in specific jobs" n9

Opinions are also nuanced regarding proposal 18: "By extending the possibilities of co-option, social media will lead to greater decentralization of recruitment responsibilities to managers and employees" (Me=4.5). Some (7) strongly agree and think this is a logical evolution.

However, the majority actually believe that there will be a greater involvement of managers, more actors involved in the sourcing process, but that the rest of the recruitment process will remain rather centralized.

"This is a just reward -we have disempowered managers of recruitment for 20 years. We were giving an unlikely profile to HR professionals who had to cope with it" n27 "I 100% agree concerning the sourcing. For the rest of the recruitment process, including selection, this does not change much (except for references)" n9 "Greater involvement rather than greater decentralization" n25

It is worth noting that many experts mention organizational and French cultural barriers about the system of co-option by itself.

"It is hoped -it makes sense -but organizations do not like cronyism ..." n7 "We have seen that the French market, except some well-known sector, was not ready for cooptation ... Important ... but so very complicated" n30

(5) Social media provide an opportunity to raise the strategic role of HR professionals; if indeed HR professionals take up the challenge.

Proposals 10, 8, 9, 16, 11 and 14 allow us to support this result.

In order to manage HR social media strategy, some companies have already created new positions. Proposal 10 addresses this issue: "The practice of social media forces to create new positions in companies (Head of the Employer Brand, HR Community Manager)" (Me=5). A majority of experts consider that social media use can lead to create new specific positions, but most emphasize that this can be achieved also by an evolution of employees' roles and in addition to another position. Thus, many consider that the creation of specific jobs depends on the company size and the magnitude of the task. Some even argue that, in the long run, everyone will have to assume a part of these new roles.

"New skills in existing jobs and sometimes indeed new positions" n26 "In the short/ mid-term only. Then this will be part of the role of everyone" n30 "(...) The efficiency of this role will depend above all -on the capacity of employees to play a part of this role. Education and engagement is therefore fundamental" n9

Others consider that this evolution is still ongoing, and highlight different barriers: resistance to change, organisational and cultural barriers.

"5 in 2011, six in 2012: currently, companies should no longer be afraid of these tools, and select the ones they need according to their target. [...]" n24

"HRD is often hostile to social media, like the Legal Department, as they have a culture of" regulations "and" codes "while social media require a lot of creativity and risk" n23

Besides, regarding proposal 8 "It is necessary to adopt differentiated and targeted strategies (between tools, topics people) to implement actions on social media" (Me=7) a large majority advices HR professionals to distinguish media and targets, to adapt and personalize content but many emphasize that this must be done within the framework of a broader HR strategy and be consistent with it. Proposal 16 addresses the possible distribution of roles and trigger debates on participation and animation of "communities" gathered via social media: "Even if a formal piloting/management of communities on social media is initially required (Community Manager), in the future communities will have more open structures with a voluntary commitment of members inside and outside the company" (Me=5). Majority of experts believe that ultimately much more employees should participate through social media communities but several admit that some kind of management and support will remain necessary.

"Community management biodegradable" n26

"A regulation and moderation on these media seems indispensable" n5 "It is desirable because the current position of community manager in some companies makes them run a huge operational risk, in which the community manager attaches to his own name all communities! More than his employer!!!" n9

Different barriers are once again mentioned:

"Currently, companies are afraid of what they cannot control, but gradually, the greater use of social media will allow them to soften their point of view and accept that people outside the HR department express themselves" n15 "I'm uncertain that our corporate cultures lead us in this direction so quickly. Uncertain that employees will want to get involved more, either ..

." n30

With these new practices, internal-external boundaries seem to be increasingly blurred. A majority of experts agree with proposal 11: "With the use of social media, internal-external boundaries are increasingly blurred (role of Community Manager, intranet / Internet tools, private-professional repercussions ...)" (Me=6). Most experts consider that the use of social media tends to make the internal-external boundaries increasingly blurred and flexible. They regard this as both an opportunity and a matter of concern. Some stress the importance of establishing rules, social media guidelines. Finally, all proposals lead us to proposal 14: "Social media will give HR professionals a greater role in strategic decisions." (Me=4). Majority of experts consider social media as an opportunity for HR professional to play a more strategic role.

"If HR (professionals) decide to take power, yes! This is a great opportunity for us to be put forward and to influence the leaders ..."n3

However, most of them remain quite sceptical and emit conditions:

-HR professionals must develop specific skills, become true business experts, and adopt certain ethics.

"If they do not merely use them as job boards" n9

"Yes, but there are important ethical challenges because HR professionals often use it to "spy" on applicants or even employees (so they recognize the importance of these tools), but at the same time they ban those same tools within the company" n23

-Their use of social media must be aligned and integrated into the overall strategy. -An effective collaboration with other departments (communication, marketing, IT) seems important.

"I confirm my vote provided that the HR departments and communications/marketing departments could agree and collaborate effectively on the subject with a sufficient legitimacy from the executive committee" n1

As an expert pointed out rightfully:

"(...) as for all other topics, HR will play a more strategic role if they give themselves the means. Social media is an opportunity for HR, not a miracle..." n14

"

  [...] All depends on potential uses aligned with corporate strategy." n33

Table 3 . Kendall's W of the first and second round.

 3

	Kendall's W -First Round Kendall's W -Second Round	0.241 0.337
	Asymptotic significance	,000 (<1%)

Table 4 . Group of proposals with a high level of consensus

 4

Some proposals seem to reach a high level of agreement (median from 6 to 7): 8, 11, 6, 3, 4, 13 and 2. Others seem to reflect more balanced positions (median from 4 to 5): 5, 9, 10, 18 and 1. Comments analysis allows us to clarify these positions.

Table 5 . Group of proposals with a low level of consensus

 5

Table 6 . Wilcoxon signed-rank test

 6

  [...] the most important is the real HR offer of the company, social media are a medium to communicate about this offer, without offer, no message" n8

	"First, we must observe each media to choose how to interact and what to put inside according to
	what we like to say, transmit, and who we want to touch. This is the marketing side of HR
	communication" n25
	"Yes, but within the framework of a global strategy, otherwise it will be fragmented" n26
	Moreover, regarding proposal 9, "Social media monitoring (observations and reactions) is the
	most important to develop an employer brand strategy." (Me=4) most experts consider social
	media monitoring as an important element in developing an employer brand strategy, but not
	as the most important.

"

  "Strong porosity which begins to be confirmed in most studies[...]" n13 « [...] it is both an opportunity and a real concern. A risk. Properly position the cursor is essential" n30 "Yes this is the main problem. There is no longer hours to deliver a message, and public / private distinction is unclear. It is within the practice of networks that ambiguity must be removed (e.g. do not diffuse messages after 8pm!!!!)" n7 "[...] It is important to set some rules about this, guidelines are welcomed" n25

Discussion and Conclusion

The use of social media within recruitment strategies appears to be a real challenge for recruitment agencies and companies. The Delphi study helped clarify current controversies about these new practices and strategies. Although the global level of consensus is quite low, it has improved over the steps of the Delphi. This method allowed experts to be reflexive and provide rich comments.

Social media do not replace other e-recruitment tools, but many experts consider them as more dynamic and relational tools. Most experts do not consider social media as "just complementary" or simple gadgets but as more and more important tools both for recruitment and employer brand strategy. Nevertheless the indispensable nature of social media remains for the moment subject to controversy.

Today social media can meet the applicant's demands of exchange, which is considered as legitimate and transversal. Many experts emphasize the need for companies to be more transparent and to have less conventional speeches. But in the long term the evolution of applicant relationship is not regarded as systematic. This will depend on the labour market and the real appropriation of these tools by recruiters (real exchanges, development of a talent pool, ethical behaviours...).

New behaviours become widespread among applicants. Managing its personal digital identity is regarded as more and more important for a growing number of applicants and jobs but points of disagreement persist concerning this generalization importance. Professional use of social media does not seems characteristic of one generation (Y) and do not appears as the cause of switching behaviours in professional careers.

On one hand, social media can enable a greater internalisation of recruitment through the development of social media HR strategy and the involvement of employees in the sourcing (which is in line with the management decentralization phenomena through the implementation of e-HRM stressed by [START_REF] Ruël | E-HRM: Innovation or Irritation : An Explorative Empirical Study in Five Large Companies on Web-based HRM[END_REF] ). On the other hand, these practices could be outsourced subject to the emergence of new types of recruitment agencies (offering a real value added, specialised in jobs and developing competencies about social media).

Finally, social media provide an opportunity to raise the strategic role of HR professionals through employer branding strategy, internal skills development, a greater involvement of managers within the sourcing process and via social media communities. But disagreements persist and HR professionals are encouraged to meet the challenge.

Two main contributions can be emphasized.

From a methodological perspective, this work is based on an innovative application of the Delphi method. This Argument Delphi has allowed going beyond the consensus building in order to encourage discussion and highlight relevant arguments. Much attention was paid to the selection of experts; they have demonstrated reflexivity along the stages and provided rich comments. A summary of the results has been sent to get their final assessment.

From a managerial perspective, these study offers a more comprehensive and critical look on the integration of social media in recruitment. We can do several recommendations to HR professionals. They must develop their expertise and acquire specific skills related to social media, without neglecting ethical issues related to these new practices. Their use of social media should not be disconnected from the corporate strategy but rather aligned with it.

Efficient cooperation with other departments appears to be essential as well as obtaining some legitimacy from the hierarchy.

This study is not without limitations but offers as well perspectives for further research.

Regarding the expert panel, the sample is still limited, other actors could be interviewed. This would require modifying some proposals based on a monitoring of the literature and professional practices. Therefore, longitudinal case studies have to be conducted in order to enrich this study and gain in maturity. International case studies could be interesting to evaluate possible differences in strategies and opinions in several countries. Finally, applicants point of view is missing, interviews could be realized in order to collect their own experiences and opinions on these new behaviours and strategies.


Sana Damak Mallouli
email: sana.mallouli@malix-univ-paris1.fr

Saïd Assar
email: said.assar@telecom-em.eu

Carine Souveyet
email: carine.souveyet@univ-paris1.fr

Process behavior meta-modeling for the derivation of enactment engines Poster paper

Keywords: Meta-models, Behavioral semantics, Process enactment, Model Driven Engineering I

To specify process modeling language semantics and build corresponding enactment engine is a challenging problem. We propose a model driven approach which combines structural and event-based behavioral meta-modeling techniques. These specifications are transformed into a software architecture for a process enactment engine that exploits publish-subscribe patterns and message based asynchronous execution.

INTRODUCTION

Modeling languages are essential artifacts in Information Systems engineering. New requirements, e.g. domain specific modeling and Model-Driven Engineering (MDE), have increased the demand for such languages in combination with adequate software tool for model manipulation, i.e. editing, transformation, verification, validation, etc. Meta-CASE and languages workbenches are leveraged to design and build such tools. Meta-models are at the core of these environments, they are used to define modeling languages abstract and concrete syntax [START_REF] Favre | Guest Editors' Introduction to the Special Section on Software Language Engineering[END_REF]. However, meta-models do not fully describe model semantics [START_REF] Sprinkle | Model-Based Engineering of Embedded Real-Time Systems[END_REF] and additional techniques are necessary. For a process modeling language with concepts such as data flow, state and transition, semantics are inherently behavioral as they express the manner by which a process behave it is enacted [START_REF] Combemale | Towards rigorous metamodeling[END_REF]. The integration of behavioral semantics specifications into meta-models would facilitate understanding, analysis and validation of modeling languages definitions and would leverage automatic tool construction [START_REF] Bryant | Challenges and Directions in Formalizing the Semantics of Modeling Languages[END_REF]. It is, however, a challenging issue as structure metamodeling languages, e.g. MOF (Meta Object Facility), although complex endeavors by themselves, need to be complemented with other notations and formalisms. Beside, process model semantics includes two ways interaction with human actors and external software applications.

Process enactment is a fundamental issue in both business and software process modeling. Notations based on Petri nets have been used extensively either directly to model and enact business processes [START_REF] Van Der Aalst | YAWL: yet another workflow language[END_REF], or to express behavioral semantics for other process modeling languages, e.g. BPMN [START_REF] Dijkman | Semantics and analysis of business process models in BPMN[END_REF] and SPEM [START_REF] Bendraou | Definition of an Executable SPEM 2.0[END_REF]. Our work differs from these approaches as its focus is goal oriented process modeling notations. We seek to express graphically and in a declarative manner the behavioral semantics for a specific goal oriented modeling notation, i.e. MAP [START_REF] Rolland | A Multi-Model View of Process Modelling[END_REF], and to derive an enactment engine.

The goal of this work is to leverage MDE principles to construct software tool and develop a meta-modeling approach that bridges the gap between process semantics as conceptually perceived by the language designer, and process execution logic as implemented on computational platforms. Hence, we seek answers to the following research questions:

1. How to specify, in an explicit manner, process execution semantics at the meta-modeling level of abstraction? 2. How to exploit such specifications to build, in a full -or partial -automated manner, process enactment engine?

II. PROPOSAL

Our approach captures the execution semantics of a process modeling language directly at the meta-model level using a graphical notation (Fig. 1). We have introduced in [START_REF] Mallouli | Pour une perspective comportementale dans les méta-modèles de processus[END_REF] and [START_REF] Mallouli | A Model-driven Approach to Process Enactment[END_REF] this notation which is grounded in the Remora event based modeling formalism [START_REF] Rolland | Conception des systèmes d'information: la méthode REMORA[END_REF]. Using this notation, the language designer defines a behavior meta-model besides the traditional structure meta-model. This event oriented schema expresses the language semantics in an operational manner, i.e. as state changes and algorithmic computations on the elements of the abstract syntax (i.e. structure meta-model). In fact, because of its operational nature, this behavior metamodel can be considered as the specification of a process enactment engine. As it expresses a dynamic and interactive execution logic, we target the publish/ subscribe development patterns as building block for specifying the architecture of the target engine. Publish/subscribe patterns are recognized as the paradigm of choice to develop reactive application with asynchronous interactions [START_REF] Eugster | The many faces of publish/subscribe[END_REF]. The final code for the enactment engine can then be obtained using an existing UML code generator.

Transformation rules Code generation

Process enactment engine

Engine architecture (UML specification based on publish/subscribe patterns)

Behavior meta-model

(Event oriented schema)
OO meta-model

(UML class diag.)
Fig. 2 presents one of the transformation rules (for external interactions) that we are actually implementing and formalizing using the ATL language [START_REF] Jouault | Transforming Models with ATL[END_REF].

This approach is being applied on the case of the intentional process model MAP [START_REF] Rolland | A Multi-Model View of Process Modelling[END_REF]. MAP process models capture the goals that a business or engineering process is expected to fulfill, together with a set of available strategies to realize these goals. Fig. 3 shows the behavior meta-model and the execution semantics for the MAP. At the center of this specification is the class "SectionInstance". A Map is executed in an iterative manner, one section (i.e. two intentions linked with a strategy) at a time. Each time a section is executed (i.e. section state change from selected to executed), a new set of candidate sections is computed and displayed to the user. A new enactment cycle begins when the user, i.e. MapActor, selects a candidate section for execution.

The application of this approach on the MAP confirmed the feasibility and relevance of this approach in describing language semantics and deriving a complete and detailed engine architecture with full interactive capabilities.

III. CONCLUSION

The main innovation of the meta-modeling approach presented here is the explicit representation of semantics execution in a graphical and partially declarative manner. From this specification, it is possible to derive an enactment engine using transformation rule that adequately exploit asynchronous execution patterns. Moreover, this Model Driven Engineering approach enhances significantly maintainability and portability issues when building enactment engine. Indeed, any evolution in the process modeling language will correspond to changes in the meta-models which can be propagated to the engine architecture by applying the transformation rules and the code generation steps. Compared to previous efforts in relation with MAP enactment [START_REF] Velez | MAPExecutor: A Dynamic Enactment Support to Specify and Execute Methods with Maps[END_REF] and to similar approaches in the literature [START_REF] Bendraou | Achieving process modeling and execution through the combination of aspect and model-driven engineering approaches[END_REF], this method brings new insights to the realm of modeling languages design.

Fig. 1 .

 1 Fig. 1. Proposal overview.

Fig. 2 .Fig. 3 .

 23 Fig. 2. An example of a transformation rule


Burak Can
email: b.can@maastrichtuniversity.nl.

Ali Ihsan Ozkes

Ton Storcken
email: t.storcken@maastrichtuniversity.nl

Measuring Polarization in Preferences

In this paper, we study the measurement of polarization in collective decision making problems with ordinal preferences over alternatives. We argue that polarization can be measured as an aggregation of antagonisms over pairs of alternatives in the society. We propose a measure of this sort and show that it is the only measure satisfying some normatively appealing conditions.

Introduction

Higher polarization in ideologies or preferences over policies is generally considered as a bad feature in politics mainly due to representational concerns. It is argued to cause policy gridlock [START_REF] Jones | Party polarization and legislative gridlock[END_REF]), decrease turnout if it is only in elite level [START_REF] Hetherington | Turned off or turned on? how polarization affects political engagement[END_REF]) and increase economic inequality [START_REF] Mccarty | Political polarization and income inequality[END_REF]).

Due to the disagreements in measurement, we see disparity in the results of polarization analyses. For instance, the increase in polarization in the U.S. politics is somewhat unequivocal for the elite level although the literature on public polarization is inconclusive. For a review in line with this conclusion, see [START_REF] Hetherington | Review article: Putting polarization in perspective[END_REF]. This paper introduces yet another approach to the measurement of polarization. However, the major component of our contribution is in that of the subject of measurement. Although there are quite a number of articles analyzing the measurement of polarization for distributions that can be represented on a line1 , this paper is among the very first attempts for analyzing polarization measures for ordinal preference profiles.2 Some of the related concepts that could be found analyzed in the social choice literature could be listed as consensus [START_REF] Herrera-Viedma | Consensual processes[END_REF], assent [START_REF] Baldiga | Assent-maximizing social choice[END_REF] and cohesiveness (Alcalde- [START_REF] Alcalde-Unzu | Measuring the cohesiveness of preferences: an axiomatic analysis[END_REF].

According to numerous authors, as formulated in [START_REF] Bosch | Characterizations on voting rules and consensus measures[END_REF], consensus can be formulated such that it can be measured with mappings that assign to any profile of preferences a value in unit interval, which has the following two properties necessarily: first, the value given to a profile is highest, namely 1, if and only if all individuals agree on how to rank alternatives and second, the same value given to any two profiles if the only difference in between them is the names In what follows we argue, first, that polarization is not necessarily the opposite of consensus and hence calls for a particular treatment. The least polarized case naturally coincides with a fully consensual state, which is easily defined as a unanimous preference profile. However, there is no unique way of framing the most polarized situation. This would entail a normative approach, which we embrace in this paper as follows. Since we investigate polarization in preferences that are represented as linear orders, we restrict the most polarized situations to societies which are divided equally into two completely opposite linear orders.

Second, we impose that the polarization level should not depend on the number of individuals in a society but stay the same if the supporting individuals of each preference is multiplied by equal terms. Furthermore, we require a form of equal treatment of marginal changes in the composition of preferences.

More precisely, if a single individual changes her preference to conform with the majority view on a single issue, then the change in polarization should not depend on the size of this majority. Finally, we impose neutrality towards alternatives.

In this paper, we show that interpreting polarization as an aggregation of antagonisms in a society is the only way of measuring polarization with the properties above. In this context antagonisms are taken as disagreements over pairwise comparisons of alternatives.

We proceed as follows. In the next section we introduce basic notations and formal definitions regarding the axiomatic model. Section 3 provides our main results and proofs thereof. We conclude in Section 4 by pointing to a possible direction for further research. We show the logical independence of axioms in the appendix. For two profiles p and q of two disjoint sets of individuals, say N 1 and N 2 respectively, let (p, q) denote the profile, say r, such that r

Model

Preliminaries

(i) = p(i) if i is in N 1 and r(i) = q(i) if i is in N 2 .
Similarly define p 2 = (p, p) to be a profile where preference p is replicated once and p 3 = (p, p, p) twice, and so on.

Let p and q be two profiles in L N . We say that p and q form an elementary change from ab to ba whenever there is an individual i in N who ranks a and b consecutively in p and furthermore q(i) = p(i) ∪ {(b, a)} \ {(a, b)} and for all j in N \ {i}, p(j) = q(j). This means that q(i) can be obtained from p(i) by only reversing the ordered pair (a, b).

Finally, a polarization measure Ψ assigns to any profile p in L N a real number Ψ(p), where N is any finite and nonempty set of individuals. Next we discuss a few normatively appealing conditions on the polarization measures.

Conditions on Polarization Measures

We first impose a regularity condition on polarization measures to normalize between 0 and 1. The former value is reserved for profiles wherein each individual has the same preferences, i.e., a unanimous profile. In this regard, we see the maximal consensus as a case of minimal polarization. However, we furthermore restrict the maximally polarized case. The profiles (with even number of individuals) where half of the individuals have a preference R and the rest have -R, for some R ∈ L are considered to be the maximally polarized profiles.

Regularity : Ψ(R N ) = 0 and Ψ(R N1 , (-R) N2 ) = 1 for all preferences R and all finite and nonempty sets N 1 and N 2 of individuals such that N 1 and N 2 are disjoint and equal in size, i.e., #N 1 = #N 2 .

Neutrality is a standard property in social choice. In this context, it requires that a renaming of the alternatives does not change the polarization level.

Neutrality : Ψ(p) = Ψ(πp) for all permutations π on A and all profiles p.

The following condition requires that when societies are replicated by some positive integer, the polarization is unchanged. Note that this also implies anonymity, i.e., renaming the individuals does not change the polarization level.

Formally:

Replication invariance : Ψ(p k ) = Ψ(p) for all positive integers k, and all profiles p. Finally, we introduce our final condition which we call support independence.

This condition requires that elementary changes in favor of an alternative that has a majoritarian support against another lead to identical changes in polarization across profiles. For instance, if a majority of individuals agree that a is better than b in each of the two profiles, then an increase in the support of a over b should lead to the same amount of change in the polarization for both of these profiles.

Support independence : Ψ(p)-Ψ(q) = Ψ( p)-Ψ( q) for any two elementary changes p, q and p, q both from ba to ab for some alternatives a and b with n ab (p) ≥ n/2 and n ab ( p) ≥ n/2.

Result

Assume for simplicity that the issue in hand is a binary choice, that there are only two alternatives. If the absolute difference between numbers of individuals preferring a to b and b to a, i.e., d ab , is 0, then the polarization should intuitively be maximal. If this number is equal to n, then we have that everyone prefers a over b or vice versa, a full agreement. Hence polarization should be minimal.

Therefore, the polarization can be related to n-d ab . If we normalize by dividing by n, then we have a bound on the polarization (between 0 and 1) therefore regularity is also satisfied. For profiles on more than two alternatives, we iterate this process over all pairs of distinct alternatives. Thereafter we normalize this value with respect to the number of such pairs and the number of individuals.

Hence we obtain the following polarization measure:

Ψ * (p) = {a,b}∈ Ā n -d ab (p) n • m 2 .
It is easy to verify that Ψ * satisfies the conditions introduced in Section 2.2.

In the sequel, we will show that it is indeed the only measure that satisfies these conditions. Before, we discuss some features regarding elementary changes that are instrumental in what follows.

Let p and q form an elementary change from ab to ba, so that n ab (p) -1 = n ab (q) and n ba (p)+1 = n ba (q). This change can be of one of the following three;

(i) a minority decrement if n ab ≤ n/2, (ii) a majority decrement if n ab ≥ n/2 and (iii) a swing if n ab (p) > n/2 and n ab (q) < n/2.3

The first two changes are straightforward. For the third, consider the case where 4 individuals prefer a to b and 3 prefer b to a. An elementary change, in this case, from ab to ba makes the former minority a majority.

Remark 1. Note that if p and q form an elementary change from ab to ba that is a minority decrement, then q and p form an elementary change from ba to ab that is a majority decrement. This duality allows us to construct the forthcoming lemmas by focusing on either of the two first elementary changes.

The following Lemma shows that all minority decrements yield an equal change in polarization regardless of what alternatives are involved. By Remark 1, the result also holds for majority decrements. Let Ψ satisfy the four conditions; regularity, neutrality, replication invariance and support independence.

Lemma 1. Let p and q be a minority elementary change from ab to ba and let p and q be a minority elementary change from xy to yx. We have

Ψ(p) -Ψ(q) = Ψ( p) -Ψ( q).
Proof. Let p {a,b} be the profile obtained from p by shifting a and b to the two top positions for each individual while leaving preference between a and b as well as those between alternative in A\{a, b} unchanged. That is for all individuals i in N let p {a,b} (i) = p(i)| {a,b} 2 ∪ ({a, b} × A\{a, b})∪ p(i)| (A\{a,b}) 2 . Similarly define q {a,b} . Then by support independence we have Ψ(p) -Ψ(q) = Ψ(p {a,b} ) -Ψ(q {a,b} ).

Considering the permutation π on A such that π(a) = x, π(x) = a, π(b) = y, π(y) = b and π(z) = z for all z ∈ A\{a, b, x, y} neutrality implies Ψ(p {a,b} ) -Ψ(q {a,b} ) = Ψ(πp {a,b} ) -Ψ(πq {a,b} ).

Note that πp {a,b} and πq {a,b} are preferences at which the alternatives x and y are in the two top position for every individual. Furthermore they form a minority elementary change from xy to yx. Therefore support independence implies

Ψ(πp {a,b} ) -Ψ(πq {a,b} ) = Ψ( p) -Ψ( q).
So, all in all

Ψ(p) -Ψ(q) = Ψ( p) -Ψ( q).
Next we prove that all minority elementary changes yield a decrease of po-

larization by α = 2 n•( m 2 )
. By Remark 1, then, all elementary changes in majority increase polarization by that same amount α.

Lemma 2. Let p and q be a minority elementary change from ab to ba. Then

Ψ(p) -Ψ(q) = 2 n • m 2 .
Proof. By Lemma 1 it is sufficient to prove that at some minority elementary change, polarization decreases by

α = 2 n•( m 2 )
. Replication invariance implies that we may assume that the set of individuals is even, that is n = 2•k. Consider any two set of individuals #N 1 = #N 2 = k with N 1 ∩ N 2 = ∅ and a combined set of individuals N = N 1 ∪ N 2 . Given any preference R, consider the following two profiles (R N1 , (-R) N2 ) and R N . Note that there is a path of k • m 2 elementary changes from the former to the latter. By regularity Ψ(R N1 , (-R) N2 ) = 1 Ψ(R N ) = 0. By Lemma 1, each step in this path cause the same change in polarization, say α. Note that the amount of swaps from (-R) to R is m 2 . The number of individuals requiring this many swaps is n/2. Therefore each elementary change should decrease the polarization by 2/n m 2 .

We have shown that each minority (or majority) elementary change causes the same amount of decrease (or increase) in the polarization. Next we show that swing elementary changes does not affect the polarization level.

Lemma 3. Let p and q be a swing elementary change from ab to ba. Then

Ψ(p) = Ψ(q).
Proof. Consider the profiles p 2 , (p, q) and q 2 . Both p 2 and (p, q) as well as q 2

and (p, q) form minority elementary changes. The former pair from ab to ba the latter pair from ba to ab. So, Ψ(p 2 ) -Ψ(p, q) = α = Ψ(q 2 ) -Ψ(p, q). Hence, Ψ(p 2 ) = Ψ(q 2 ). Therefore by replication invariance we have Ψ(p) = Ψ(q). Now we can state our main theorem.

Conclusion

In this paper, we have modeled polarization as an aggregation of antagonisms per issues within a profile. The polarization measure we introduce simply check for each issue, i.e., pairwise comparison of alternatives, and compares the strength of a majority versus minority. These pairwise comparisons on issues are then aggregated and normalized to a real number between 0 and 1. The measure is very intuitive and is characterized by a few plausible conditions.

There are many directions for future research. The relation between the extent of polarization and the social aggregation outcomes would be a natural route of inquiry. [START_REF] Gurer | Do impossibility results survive in historically standard domains?[END_REF] studies the Arrovian impossibilities when the preferences in the society cluster, in some sense, around a preference, where it is also conjectured that in a bipolar society the sum of the distances from the two opposite clusters, around which the society is polarized, will be decisive concerning whether we end up with possibilities. The analysis is dependent on a metric-based approach to alienation between preferences. Thus, the relevance of polarization measures based on pairwise comparisons of alternatives to social aggregation outcomes is an open and immediate question one might ask.

Note that the current analysis treats pairs of alternatives impartially, i.e., every issue is of equal importance for polarization. Of course, in many real life situations we may have differing weights on issues. Another question for future research would be analyzing richer domains of preferences, e.g., weak orders, or restricted ones, e.g., single-peaked domains which are politically relevant and interesting.

  of either the alternatives or individuals. Alcalde-Unzu and Vorsatz (2008) have introduced some axiomatic characterizations in this vein. García-Lapresta and Pérez-Román (2011) analyze properties of a class of consensus measures that are based on the distances among individual weak orders.agreement in their top choices. They then use an aggregate-assent maximizing approach to the selection of the choice rule, where the assent between preferences is the probability that these preferences would be conflictual on a random feasible set.Finally, Alcalde-Unzu and Vorsatz (2013) denote the level of similarity among preferences in a profile as cohesiveness and characterize a class of cohesiveness measures with a set of plausible axioms. This class of functions falls within the above definition of consensus.

Let

  A be a finite and nonempty set of m alternatives. For any finite and nonempty set of individuals N , and for any individual i in N , let p(i) denote the preference of i in terms of a linear order, i.e., a complete, antisymmetric and transitive binary relation on A. Furthermore, p indicates a profile, a combination of such individual preferences and L the set of all preferences on A. So, p is an element of L N . We denote by Ā the set of all subsets of A with cardinality 2. For a given profile p in L N and different alternatives a and b in A let n ab (p) denote the number of individuals who prefer a to b, i.e., n ab (p) = #{i ∈ N : (a, b) ∈ p(i)}. Let d ab (p) = |n ab (p)-n ba (p)| denote the absolute difference between the number of voters preferring a to b and those preferring b to a at profile p. For a preference R, let R N denote the unanimous profile where all individuals have preference R. Let -R = {(y, x) : (x, y) ∈ R} be the preference where all pairs in R are reversed. If π denotes a permutation on A, then the permuted preference of R is πR = {(π(a), π(b)) : (a, b) ∈ R} which naturally defines the permuted profile πp in a coordinate-wise manner, i.e., (πp)(i) = π(p(i)).

Theorem 1 .

 1 A polarization measure Ψ satisfies regularity, neutrality, replication invariance and support independence if and only if Ψ = Ψ * . Proof. Assume Ψ satisfies the conditions. Take any preference R and consider the profile R N . By regularity, Ψ(R N ) = Ψ * (R N ) = 0. Any profile p in L N can be acquired by a sequence of elementary changes beginning from R N by minority decrements, majority decrements or swings. By Lemmas 2 and 3, the increase (or decrease) induced by each of the elementary changes should be the same. Hence for any p in L N , we conclude Ψ(p) = Ψ * (p).

See, inter alia,[START_REF] Esteban | On the measurement of polarization[END_REF] and[START_REF] Montalvo | Ethnic polarization, potential conflict, and civil wars[END_REF].

For a measure of ordinal preference polarization which adopts the methodology of[START_REF] Esteban | On the measurement of polarization[END_REF] with the use of a metric à la[START_REF] Kemeny | Mathematics without numbers[END_REF], see[START_REF] Ozkes | Preferential polarization measures[END_REF].

Hence n ab (p) = n ba (q).

This research was partially financed by the Netherlands Organisation for Scientific Research (NWO) with project nr. 400-09-354. Most of this work has been accomplished when Ozkes was visiting Maastricht University in July 2013. This visit has been partially supported by

Appendix: Logical independence of axioms

Regularity: The following measure satisfies replication invariance, neutrality and support independence but not regularity:

n .

To show it satisfies the first three axioms is rather straightforward. To see violation of regularity it would suffice to consider a unanimous profile.

Support independence: Consider the function

Then the following measure satisfies neutrality, regularity and replication invariance but not support independence:

.

Neutrality is straightforward. Replication invariance is due to the fact that dab stays the same in case of replication. To see regularity, note that dab (p) = 1 for all a, b ∈ A whenever p = R N for some R, hence we have 0. In the case where

Let q, (respectively q) be constructed such that from p to q (respectively from p to q), the third agent changes its preference to a over b. Support independence 11 requires that the change of polarization should be the same for p, q and p, q, which is not the case under Ψ.

Neutrality: For any set of alternatives A, let x, y ∈ A be a predefined choice of pairs. The following measure satisfies replication invariance, regularity and support independence but not neutrality: This measure satisfies neutrality, support independence, regularity but not replication invariance.