Annelies Fryberger
email: annelies.fryberger@gmail.com

indifference, and disagreement in the evaluation of

Keywords: The fuzzy middle. Uncertainty, indifference, and disagreement in the evaluation of contemporary art music Evaluation, singularities, contemporary art music, peer review, quality uncertainty I

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

I really found this work very strong -I was really into her music, the samples really impressed me. I really liked the project.

There's not a lot of strong for or againsts really, it's just kind of there.

The work itself didn't grab me. The samples, you know, didn't stand out to me as something remarkable, though I recognize the craftsmanship and the effort, and the creativity and so forth.

(excerpts from panel debates, American organization, 2012) evaluation takes place in two peer review settings, one in France, the other in the United States.

Peer review, when it includes face-to-face discussions as these panels did, explicitly values the interpersonal influence of this setting, although, as we will see, many safeguards are in place to control and channel this influence.

When I was conducting this fieldwork, from 2011 to 2016, I noticed that the judgments I observed were largely decisive and quick -as has been observed in other, similar settings: an architectural competition [START_REF] Kreiner | Organizational Decision Mechanisms in an Architectural Competition[END_REF], editorial meetings of the fiction staff at a literary magazine [START_REF] Merriman | The Editorial Meeting at a Little Magazine: An Ethnography of Group Judgment[END_REF], fashion producers choosing models [START_REF] Godart | How Do Cultural Producers Make Creative Decisions? Lessons from the Catwalk[END_REF], or an admissions test for a design school [START_REF] Strandvad | Contingencies of Value: Devices and Conventions at a Design School Admission Test[END_REF]. Given the quick, intuitive character of the judgments I observed and which are described in the literature, I began to question the role that uncertainty plays in the day-to-day workings of these settings, where singularities [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF]) -despite being incommensurable -are regularly compared. This article teases out where uncertainty in these types of judgments arises and why it might appear. Based on empirical material from two cases, I will show that outcomes are significantly more unpredictable for candidates ranked toward the upper middle of a ranked list, and less so for those to be found at the top or bottom of such a list. This is the area I have chosen to call the "fuzzy middle", as this is where outcomes are unclear. This focus on the upper middle, on this musical reserve army, if you will, is important as much of the literature on this type of evaluation looks at how success at the top can be explained. In the cases studied, the unpredictability in the "fuzzy middle" arose from disagreements and indifference within the peer review panels, and was not due to uncertainty regarding quality judgments. This means that the uncertainty present in these evaluative settings -in the form of unpredictable or arbitrary results -was the result of interpersonal dynamics of the collective work of these peer review panels, and not due to the intrinsic characteristics of the objects being evaluated. This article is organized as follows: in the next sections, I will first (I.a.) give a definition of the term "contemporary art music" and the milieu to which this refers, followed by a discussion of the sociological literature on evaluation under conditions of uncertainty (I.b.). Then (I.c.), I will present in more detail the organizations I studied and the kind of data I was able to collect. Following this, I will look at some general features of the evaluative panels I studied (II.a.), and specifically how the upper middle of a ranked list was treated differently from the top and the bottom. This will lead me to look in detail at one specific case (II.b.), to understand better the underlying dynamics of evaluation in this milieu. A discussion (III) of these results will follow, and the article will close with a brief conclusion (IV) outlining the main contributions of this research and its applicability to other settings.

I.a. Definition: Contemporary art music

The fieldwork for this study was conducted in the world of contemporary art music. Though, as in any art world, determining what is part of an artistic genre is an object of considerable attention within the art world in question (Becker 1982, 36), the following general definition gives the context necessary to understand what is at issue in the present study:

[Contemporary art music comprises] pieces that [are] composed or preplanned reflectively, fixed in some sort of notation for a performer or creator to interpret or execute, and intended to be listened to by an attentive, informed, and critical audience. We might add that it is a style of music that traces its primary lineage back to the courts and churches of pre-Renaissance Europe, and although those courts and churches are today mostly long defunct or culturally marginal, contemporary art music maintains an important relationship with their modern-day descendants and the structures of production and listening that they represent (Rutherford-Johnson 2017, 3).

To situate this more precisely, some composers who have become more or less household names working in this genre include, historically, John Cage, Karlheinz Stockhausen, and Pierre Boulez -and for composers working currently, we might cite John Adams or Philip Glass. In terms of funding, government structures and non-profit organizations have primarily taken on the role once played by courts and churches, and the world of contemporary art music, both in France and the United States, is indeed highly subsidized. It is made up of a majority of actors who do not make a living from their artistic practice, as most composers and performers working in this domain have a "day job," so to speak, as is the case in most artistic professions (Menger 2014, 124), often as teachers [START_REF] Jeffri | Taking Note: A Study of Composers and New Music Activity in the U[END_REF]).

However, it must be stated that "contemporary art music" is not the term that the organizations I studied use to describe the music they fund. I have chosen to use this term nonetheless, for two reasons. Firstly, to keep the organizations I studied anonymous, as this is a field in which idiosyncratic terminology tends to proliferate, and secondly, because this term is relevant in the sociological literature on art, where scholars have studied extensively how distinctions between art and craft [START_REF] Becker | Art Worlds[END_REF] or highbrow and lowbrow cultural production [START_REF] Levine | Highbrow/Lowbrow: The Emergence of Cultural Hierarchy in America[END_REF] have emerged. This term is widely used in the field of musicology and other fields which study music2 , and the use of this term indicates where this production is situated in terms of its cultural and symbolic legitimacy.

I.b. The uncertainty of evaluating singularities

Much of the literature on value in cultural fields tries to understand why some individuals and works are more successful than others. Pierre-Michel Menger posits that small, underlying differences in talent become exaggerated in processes of cumulative advantage [START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF], while John C. Huber argues for the importance of simply not giving up -tenacity [START_REF] Huber | A Statistical Analysis of Special Cases of Creativity[END_REF]. What I will argue here is that these are plausible explanations for the success of the "winners", but that the dynamics of the middle players are much less clear and can often be arbitrary. Given that these mid-level players represent a much larger population than the one at the top, it is important to understand how their work is evaluated in these fields.

Any process of evaluation, valuation, appreciation, appraisal… begins with attention [START_REF] Hennion | Paying Attention: What is Tasting Wine About?[END_REF]. Attention can be focused in different ways. Importantly for this study, quantitative commensuration makes certain things visible and hides others [START_REF] Espeland | Noticing Numbers: How Quantification Changes What We See and What We Don't[END_REF], and this "rigorous relativity […] prevents the expression of singularities" (Espeland et Lom 2015, 25). Singularities are goods whose fundamental value is their uniqueness and no "objective hierarchy" can be used to evaluate them (Karpik 2010, 39). The present case, that of contemporary art music, is one where uniqueness is prized and the expression of the subjectivity of the composer in her music is of the essence. How, then, do we arbitrate between these unique expressions of individuals? Lucien Karpik states that the public presentation and marketing of singularities necessarily implies an "arbitrary selection of certain dimensions to the detriment of others" (Karpik 2010, 41). Thus, "all valuation hinges on relations of visibility" (Espeland et Lom 2015, 35). What is hidden or ignored cannot be compared, and evaluation processes seek precisely to organize attention through the use of formal criteria or quantification, for example, in order to obtain results that are coherent with a certain ideology or other standard. I am combining two contrasting bodies of work here. I use [START_REF] Bourdieu | The Rules of Art: Genesis and Structure of the Literary Field[END_REF] to understand the shape and features of the contemporary art music milieu, which fits into what he describes as the "pure" pole of the classical music field. This pole is one of restricted production, wherein immediate, popular success is shunned and the admiration of a restricted circle of peers is sought instead (Ibid.). Thus, the lay audience's opinion is disregarded, and it is the approval of peers working in this milieu that is necessary to achieve success as it is defined here. To this descriptive perspective, I add the work of Lucien [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF], who looks primarily at the point of view of the consumer unable to mobilize the expertise necessary to choose between singularities, and who therefore turns to judgment devices of various natures to make his decisions. Karpik's analysis does not distinguish between pure and commercial poles. Rather, he tries to understand in detailed ways how consumers overcome informational and cognitive deficits in order to choose between seemingly incomparable products. Works of contemporary art music would qualify as "singularities" in Karpik's theoretical analysis, in that they "must differentiate themselves by their degree of originality, which, in theory, renders them poorly comparable" (Menger 2014, 160). This means that the evaluators in these milieus are using techniques like those described by [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF] for the consumer faced with singular products. Evaluators also resort to judgment devices, which, for contemporary art music, might be educational background, interpersonal networks, or the judgment of festivals and orchestras. These individuals are working in a subfield of restricted production [START_REF] Bourdieu | The Rules of Art: Genesis and Structure of the Literary Field[END_REF], which implies a certain level of expertise, but I will argue that they are making decisions like the humble consumers described by [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF].

I will argue in what follows that evaluation is first and foremost a question of categorical fit, in that the arguments that I encountered are less about quality than they are about whether or not the production in question fits the categories proposed by the organizations as it is understood by the evaluators. In addition, the categories themselves, as will be seen clearly in the cases presented, also emerge through evaluation. Even a category as taken for granted as "nature" is "dependent on the methods -legal, economic, and ecological -that [are] mobilized to account for it" [START_REF] Fourcade | Cents and Sensibility: Economic Valuation and the Nature of "Nature[END_REF]. Depending on the evaluator's place in the field in question, her way of drawing disciplinary boundaries will change [START_REF] Lamont | How Professors Think: Inside the Curious World of Academic Judgment[END_REF]) -and the judgments made on the manuscripts or works to be evaluated are also implicit judgments of the work of one's colleagues sitting around the same table (Hirschauer 2010, 92). One aspect of these judgments is cultural matching [START_REF] Childress | Encultured Biases: The Role of Products in Pathways to Inequality[END_REF][START_REF] Rivera | Hiring as Cultural Matching: The Case of Elite Professional Service Firms[END_REF]): applicants that have similar backgrounds and artistic ambitions to the evaluators are viewed more favorably.

But whence the uncertainty? Whether in the market for contemporary art (Velthuis 2003, 193) or in the careers of artists more generally [START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF], value is seen to be radically uncertain for artistic production. Lucien Karpik sees incommensurability as a primary source of uncertainty when singularities are under the microscope [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF]. This means, simply put, that when uniqueness is the leading evaluative criteria, comparison is inherently difficult. In Menger's analysis, artists cannot know the value of their work until they enter this field of competition, and participating in comparative tournaments is seen as a demand for information on their own relative level of talent [START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF]. The value of creative labor can only be known from comparative evaluation (Ibid.,118), and can only be measured in relative terms (Ibid.,179). These tournaments act to lessen uncertainty as to whose work is most valuable, by magnifying minute differences in talent in a process of cumulative advantage [START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF], with talent being defined as "the quality gradient attributed to the individual artist through these relative comparisons" (Ibid.,180). This definition of talent assumes that there are intrinsic differences in ability, but that they are not fully observable and that we infer qualities from the attention others give to an individual (Ibid.,(230)(231). The present article will look closely at the inner workings of such comparative tournaments and the role that talent and uncertainty may or may not play in these judgments.

I.c. Materials and methods

Two case studies inform this text, one conducted in the USA, the other in France. The US case study investigated a semi-public, non-profit organization whose sole purpose is to support contemporary art music, whereas the French organization is a governmental body which funds and legislates cultural matters. Within these organizations, I looked exclusively at funding schemes for composers of contemporary art music and the way their applications for funding were evaluated. Some of the data were derived from direct observation, in 2012 and 2013, of two peer-review panels in the American organization. I conducted semi-structured interviews with the evaluators in the days following these panels. In addition to these interviews, I conducted a series of interviews with panelists from the organization between 2011 and 2016, as well as interviews with all members of staff of the organization. The French organization did not allow me to directly observe jury discussions, and thus I gathered my data via interviews with the participants of the evaluation committees and staff members of the organization in question over the years 2012 to 2016. These interviews were enriched by a series of interviews with other members of the contemporary art music world in both countries, including composers, performers, commissioners, critics, and others. A complete list of interviews is included in Appendix 1.

The American organization convened juries of 3 composers who met over the course of 2-3 hours. The composers were recruited from the field of previous recipients of the grant being distributed, with an eye for diversity: at least one woman was recruited of the three, and the composers were supposed to represent different aesthetics within the world of contemporary art music, and geographical diversity was also important. The grants awarded by the juries I observed ranged from a few hundred dollars to a maximum of 5,000 USD, whereas the French grants ranged from 5,500 to 38,500 EUR. The French organization also had much larger panels -14 members, with six being composers, two musicians, two concert or festival organizers, three representatives from the governmental organization, and a chair (all members had voting rights). This panel met for five full days over the course of one week. Similar to the American organization, the primary condition for being recruited was to have been a recipient of the grant in question, and stylistic diversity was also important. Starting in 2014, the French panels were required to be 50% women. Prior to that, in the years 2002-2013, women represented between 10% to 30% of the panel. I transcribed and inductively coded my interviews using Atlas.ti in order to reveal the different evaluative schemas used by the evaluators. Justifications for quality assessments were coded in detail, such that operative judgment criteria could be clarified. I also transcribed the panel discussions I was able to observe directly and inductively coded them for operative criteria, as well as for argumentation strategies and patterns of interaction and turn-taking, following conversation analysis methods [START_REF] Have | Doing Conversation Analysis: A Practical Guide[END_REF] 3 . These cases are meant to be compared as two most similar cases: two organizations working to find a solution to the same problem, namely, how to evaluate contemporary art music. These cases are complementary and additive, in the sense that when they are taken together, we gain a greater understanding of how evaluation of artistic production in the pure pole takes place, and glean insight into cultural differences in this supposedly international milieu. Because of the difference in access I had to these two organizations, however, I present them here with a focus on the American organization, with the French organization serving primarily as a foil to understand how things could be done differently. The organizations are different in their funding structures, in that the American organization is a semi-public organization, whereas the French program is purely government funded. For the American organization, this implies conflicting priorities of different donors, and the evaluation process is set up to resolve these conflicts (see Author, Forthcoming).

When this fieldwork was done, both the French and American organizations convened their juries for face-to-face meetings (online in the US, in person in France) in order to evaluate the applications they had received. For the funding schemas studied here, the American organization required their jury members (3 per jury) to evaluate all the applications (around 70, of which approximately 30 were funded) prior to the meeting and to provide a numerical score (from 1 to 6, 6 being the best) on three criteria (see Table 1). As such, these panels were similar to those studied by [START_REF] Lamont | How Professors Think: Inside the Curious World of Academic Judgment[END_REF], in that they involved the creation of a rough ranking which was then refined in discussion. The French organization asked each of its panelists (14 total) to evaluate a subset (10 to 12, typically) of the applications received (between 130 and 220, of which 50-60 were funded) and to act as a rapporteur for these applications during the meeting. Every application was presented with an opportunity for discussion, whereas in the much shorter American meeting, only a selection of applications was discussed. In the French organization, there was a secret and binary vote -each jury member had to check on their ballot if each of three criteria (see Table 1) was met or not, and the ranked list thus obtained was not discussed by the panel. The American organization based its final, ranked list on the discussion results -the final list was approved by the panelists at the end of the meeting. The organizations asked their jury members to evaluate applications based on the criteria presented in Table 1. We will look at how these criteria were used in the judgment process, but, for now, it is important to understand the meaning given to these criteria by the organizations themselves. In the American organization, only one criterion dealt directly with the artistic merit of the proposed project and the composer -that would be the first, that of "artistry." The other criteria were more technical and intended to be more objective: "impact" designated the impact that the proposed project would have on the composer's career, while "appropriateness" referred to the feasibility of the project and an assessment of the actual costs of the project compared to the sum requested in the application. The latter criterion was meant specifically to evaluate the project's budget, as the organization required that costs be correctly documented and explained in the application. In the French organization, all three criteria dealt in some way with the artistic merit of the proposed project and the composer. The first criterion addressed the composer herself and her previous work -the proposed project was not to be taken into account. The second looked at the quality of the proposed project, and the third the performance conditions. Inherent to the third criterion was an assessment of the musician or ensemble who would premiere the piece, while "career of the work" referred to whether or not subsequent performances were scheduled.

US

II.

Evaluating contemporary art music

II.a. The fuzzy middle

The evaluation panels I observed in the American organization had similar features in terms of the way results were distributed: they both featured a silent consensus regarding the applications ranked highest and lowest, with the most discussion being about the applications that ended up in the upper middle. It is easier to understand this fuzzy middle -the "gray zone" (Composer 13, France) -if we look closely at the jury discussions observed in the American organization in 2012 and 2013. In Figure 1, we see the amount of time (in seconds) spent on applications in these peer review panels. For the two years presented in Figure 1, most of the discussion centered around the applications in the middle and lower part of the "fundable" zone, between spots 13 and 33 approximately (the line was drawn around number 30 both years). Despite the fact that divergence in scores was higher in the lower ranked candidates (see Fig. 2), it was clear that justification was more important for positive decisions in funding, whereas the applications that were not funded rarely required justification and were largely not discussed -one notable exception, the candidate at spot 58, will be discussed in detail in the following section (II.b.).

Figure 2 gives a visual representation of the consensus at the top of the ranked list (where the score spread is between 1 and 2 points -out of 6), with greater divergence in scores as one moves downward. The discussion focused on the areas of greater divergence in the upper middle section, as divergence creates the need for rationales (Hirschauer 2010, 88). When cases are actively discussed, this makes it possible for interpersonal influence to take place, as this is where persuasive efforts are focused. Two factors played an important role in these discussions: the first is the panelists' memory of the applications (or lack thereof) and how this created feelings of indifference, the second is how disputes over differing judgments of artistic quality were resolved. I will address the former now, and the latter will be the subject of section II.b. The panelists' memory of the applications they discussed in this upper middle zone was blurry, with their recall being significantly better for the applications they strongly disliked or which truly impressed them -this is not surprising. When one is tasked with evaluating seventy applications, it is likely that one forgets the vast majority. The evaluators were able to recall their impressions when specifically asked to do so, by looking at their notes (if they had taken any) or by looking at the application again. Here is an exchange from the panel conversation of 2013 which illustrates this: R14 : Let's see where we are. Look at the first 13 -seems like we agree. Although we had mentioned [application ranked 10 th ]. C7: Yeah, just based on the current work sample, I didn't think it was that amazing. It's a major performance -the [XX] conference. […]And also, the current work sample was not that great. But one of the prior work samples was probably the best piece I heard from all of the work samples. R1: Would you still want to move her lower? C7: I guess I just have to remember what all the other music is -everybody in the top 13 had really strong music. R1: I think that's where we have the most agreement.

C7: [Applicant ranked 10 th ] is not asking for that much money, so I think it's fine if we leave her. It is clear here that the lack of recall leads them to latch onto obvious details -a small monetary request, for the composer ranked N. 10 (this was by no means an evaluative criteria determined by the organization, nor was it used for other applications) -which is used to justify a decision which is difficult to justify otherwise, since the other applications were not immediately accessible in the evaluator's memory. The honesty of Composer 5's comment at the end of this exchange reflects the potential arbitrariness of the results in this middle section. Nothing stands out in particular, and even if these applications were to be moved out of the fundable zone, the evaluators would be hard pressed to recall them in enough detail to rescue them, without explicitly being asked to do so.

The corollary to this lack of recall is indifference. We do not care about that which we cannot remember. It is not possible to pay attention to it in the way meant by Antoine Hennion (2015): a "decentring both of the self toward the object and of the object towards the self" (Hennion 2015, 39), which implies a willingness to commit certain emotional resources to an external object. The applications in the middle simply did not evoke strong feelings one way or the other for the evaluators:

You know, after the first ten, I didn't really have a preference one way or the other, but I was happy that 20 other composers got funded (Composer 7, USA, 2013).

Generally, there are a few people at the very top, and a few at the very bottom. There are a lot of people in the middle, [with a score of] 24 [out of 42]. With a score over 30, you're sure to be funded, but there's a lot of people in this intermediary zone. I think it's the result of a mix of indecision and a desire to not sink people, stay positive, but without great enthusiasm. So, the place where the line is drawn is critical (Composer 13, France, 2012).

What we witness here is a profound lack of engagement, a lack of commitment in the evaluative process for these applicants in the upper middle zone. No one objects to them being funded, nor is anyone ready to defend their merits if they were not to be funded. This is very different from saying that quality here is uncertain -in fact, the evaluators largely agree on the candidates that they believe produce high quality music. They are willing to play around with the results in the middle because the stakes are low -their vision of the world of contemporary art music remains intact regardless of how these candidates are ranked. There is thus an implicit consensus that arises, similar to the "cream rising to the top" discussed by Lamont (2009, p. 13), which may be questionable or problematic from an outside perspective, but which is taken for granted during these evaluations.

The more apt description may be, however, that the conventional [START_REF] Becker | Art Worlds[END_REF] rises to the top -in this sophisticated game of boundary drawing, that which clearly fits the field in question is less subject to divergent evaluations, and this consensus is what allows it to come out on top, without, however, it being remarkable in ways that would make the evaluators recall its specifics. Applications that were unconventional, in that they did not fit a generally accepted definition of the field in question, were more present in the minds of the evaluators and were the ones that were discussed the most, with the extreme example being the candidate ranked 58 th in 2012, which was by far the longest discussion on any one application in the 2 years observed5 . The level of detail in this discussion was striking, and it was clear that the evaluators could easily access their memory of this application in order to find arguments to justify their opinions. I will use the next section to look at this discussion at length, as it helps us understand a number of the dynamics at work in this evaluative process, which were, for the most part, unspoken.

II.b. Disputes over artistic quality

Actual disputes over artistic quality were the exception in the panels I observed. However, one application in 2012 was subject to a rich, contentious debate specifically on artistic quality (see Fig. 1 -this is the application ranked 58 th ). I will quote at length from this debate, in order to clarify how quality is assessed and decisions are made in this context. There are four active participants here: Representative 1 from the American organization, who recruited the evaluators and led the meeting, Composer 6, who is primarily an improviser, Composer 9, the only woman on the panel and a composer who focuses on electronic music, and Composer 15, a university professor whose artistic output focuses on orchestral music. This debate took place on an online platform, and everyone was connected via webcam except for Composer 9, as her Internet connection was too slow to handle the video. This was the first time these composers had met, and for Composers 6 and 9, it was their first time participating in an evaluation panel. For the application they discuss here, there was a tremendous discrepancy in their pre-panel scores for artistry (see Fig. 2) -Composer 15 gave the candidate the lowest score possible (1), Composer 6 gave her the highest score possible (6), and Composer 9 gave her a mid-range score (4). Her application was ranked 58 th , which put her far outside the fundable zone (which ended roughly at spot 30). She was asking for a grant for a concert, where she would do a structured improvisation on her instrument of choice. Her instrument is a very playful, non-standard one, which I have chosen to replace with flower pots. The discussion begins with Representative 1 bringing up this application: […] I feel I should just speak up right away, and just say that the moment I started listening to this and looking at the proposal, I had a very, very strong reaction to this. And this... was an emotional reaction, in many ways, so perhaps my number got skewed to the low side as a result of that, but, you know, thinking about it in retrospect, I just feel that there's so many other proposals out there which really demonstrate stronger artistry than this one, and I stand by that. C9: I have to say, at the first concert I curated here […], I heard a lot of her pieces. […] I heard [candidate ranked 58th]'s music and a piece for her and voice. And, actually, after hearing her music for that, and then listening and also looking at this proposal, even though I gave her a fairly high score, I noted that I feel that, like this is all she's done for a while, this [flower pot] thing, and I feel that the sound palette of the instrument itself, not because it's the object that it is, but just because of what it does, it's very limiting and restricted, which, for me, it doesn't have that much artistic merit, because of that. Because I feel like everything I've heard, it's very similar and I'm trying to think about this, ok, it's not a [flower pot], but then it is when you listen to it! [laughter] R1: Well, beyond even the artistic stuff, I think what jumped out to me about this proposal is it sounds like she's working with organizations that she's worked with for a very long time. She just hasn't been back to […] recently, but these are relationships that she has that are very strong, so, automatically it didn't seem quite as compelling as some of the other ones that we've had, but that's aside from the artistic... […] I'm curious, [Composer 6], I'd like to hear your thoughts on this one. C6: You know, I think you all have some great thoughts about the career significance. You know, I didn't know her work when this first came up, like probably, you, [Composer 15], I raised my eyebrows, and I listened to the samples, and was actually really won over. [laughs] And surprised myself by how won over I was, and then I realized that she's in the circle of improvisers that I work with, and we have a lot of one-step away connections, and that helps me see that she's a serious improviser. I wrote down in my notes that though one could sense a gimmick in this stuff, and, I mean, there is a gimmick involved, of course, but that she's clearly working at a high level as an improviser. The sample that she put in, which I gave some significant time to, to make sure that I wasn't succumbing to the gimmick, it impressed me, as I said, it won me over, which I think is sort of what she has to do with what she wants to do. But I totally agree with you guys, and I didn't make sense of it when I was looking through it, you're right, this is a continuation of what it seems like she's been doing for a while, and that is definitely worth noting. As a strike against her for this. […]You know, it's so interesting, if she were a soprano saxophonist, I just don't know if we'd be having this conversation. C6: ...but it's the [flower pots] that make the discussion what it is, but when I listened to it beyond that, there's craftsmanship there as an improviser, and that's worth something. C9: Yeah, there's definitely craftsmanship in her work and merit and the collaborations that she's done, the few ones that I've heard, do have each their own thing, so it's not like it's the same thing over and over again. […] R1: I'm curious about the career aspect of this. Is this something that we feel would help move this forward? […] C6: You know, this is really a valid point, I mean, imagine if everything about her samples was the same, but she was doing a project where she was playing with a community orchestra, or doing some project where she was doing pieces for kids in the schools... where it was going to be promoting this to a different audience. That would change this for me in some ways. […] The fact that she's doing it for the same audience that she's been doing it for ten years, is something that I didn't take into consideration. And I do think it's a real problem. […] R1: Right. Ok. So, there are lots of different things about this one, but I think we're all kind of agreeing that it may not be as significant in the long run as some of the other ones, so... (excerpt from panel debates, US organization, 2012).

To begin, we can observe that these evaluators are clearly trying to use the criteria provided by the organization, in particular "artistry" and "impact" (meaning impact on the composer's career). They are engaged in a well-intentioned effort to make sense of this application in the terms provided by the organization, but this conversation also shows how difficult this actually is. Given the restricted milieu that is contemporary art music, it is highly unusual for composers to actually diversify their audience in any concrete sense, with the exception of forays into more educational initiatives. This criterion was certainly not applied in this way uniformly across applicants, and what we see here is their efforts to justify their rejection of this application, which is required because of the presence of one evaluator willing to defend this application -otherwise this discussion would not have been necessary.

The evolution of this discussion is as follows: Composer 15 begins with his emotional reaction of distaste, which he immediately disqualifies because of its emotional nature. Composer 9 then introduces an element which will prove decisive for what follows: i.e., the limited sound palette of the instrument in question. Representative 1 then presents another argument in the applicant's disfavor: the stagnation of her career. Composer 6, who, like this applicant, is primarily an improviser, waits during this opening salvo, which reinforces his subsequent expression of support for the applicant. He begins by stating that he started out in agreement with Composer 15, but then shows how his opinion shifted to come to an opposite conclusion. His persuasive efforts are unsuccessful, however, and it is when Composer 6 adopts Representative 1's negative assessment of this applicant's career development, shared especially by Composer 15, that the wagons are circled and the discussion ends with a negative consensus.

"Birds of a feather flock together" -it is hardly surprising to see that this application receives the strongest support from a composer who is also an improviser. Michèle [START_REF] Lamont | How Professors Think: Inside the Curious World of Academic Judgment[END_REF] shows that in multidisciplinary peer review situations, there is a strong presence of "homophilia", meaning, a preference for work that resembles one's own and one's own discipline. Indeed, Composer 15's negative emotional reaction can be explained in part by this, or by what Lauren Rivera (2012) calls "looking glass merit" -wherein evaluators construct "merit in a manner that validate[s] their own strengths and experiences and perceiv[e] similar candidates as better applicants" (Ibid., 1012). This strategy is often active and intentional (Ibid.). Since the evaluators have few reliable indicators of quality here, aside from their emotional response to the music, they use their own experiences as "models of merit" (Ibid.). Composer 15 explains his position in the world of contemporary art music in the following terms:

It was actually kind of made clear to me that [laughs] my voice in this process was to be kind of like, for lack of a better word, kind of the traditionalist of the panel. […] I'm not necessarily fond of that word, but, I mean, my output as a composer has been largely with orchestral, wind ensemble, chamber music. […] So, I [laughs] am pretty much straight up on, you know, using the written note and large, traditional forces (Composer 15, USA). This composer clearly struggled to see the artistic merit in the applicant's approach -in fact, he is never willing to concede that this applicant might have artistic merit or could be considered a skilled improviser, which the other two willingly do. This reticence certainly comes in part from his vision of this applicant's work being at far remove from his own, which is clearly in opposition to Composer 6, who is himself an improviser. The latter's evaluative work involved realizing that the applicant was actually part of his networks, which put him in a position of wanting to defend her work, as the colleagues he respects clearly respect her work, and his position is also affected by her application being excluded. Composer 6 sees himself as being on the margins of the world of contemporary art music, especially as compared to Composer 15, and so he believes that it is his role to defend applicants who could also be seen as more marginal:

Well, my role on the panel was to speak about the applicants who were maybe a little more left of center. I mean, somebody like [Composer 15] obviously can speak pretty well towards people who are writing string quartets and orchestral music, and so forth. There was an opportunity, I think, for me to suggest that some of the improvisers were doing very good work. I mean, for instance, the one classic case was that woman who plays [flower pots]. That was such an interesting moment for me, because, though I recognize the novelty of her playing [flower pots] and so forth, because of my background, I was able to look past the novelty, [and see] that she was working at a very high level. I don't think [Composer 15] was able to do that (Composer 6, USA).

With this discussion, Composer 6 was clearly trying to shift the borders around the world of contemporary art music. By doing this persuasive work, he tries to bring this "left of center" applicant more toward the center, principally basing his argument on technical ability and networks.

Both Composers 6 and 15 express some level of distrust of their evaluation of the artistic merit of this applicant -Composer 6 was "surprised" by his positive evaluation, whereas Composer 15 disqualified his because it was "emotional". Interpersonal networks are used to reinforce their evaluations -positively for Composer 6, who is part of the same networks as the applicant, and negatively for Composer 15, who sees these networks as being distant from his own. As such, the interpersonal network becomes a judgment device, in [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF] sense -it is used to inform the decision of the evaluators when they are unable to find sufficient arguments to defend or degrade this application. It is clear that the aesthetic judgment pronounced by these evaluators could not stand on its own, and could not be used as a means to persuade others. This affects how a "peer" can be defined in this context: Composer 15 does not believe that this applicant will be able to integrate the networks that he frequents, and he is not interested in being part of her networks. Thus, he does not risk one day being judged by the applicant in a similar setting. To keep themselves separate, and to give this applicant the status of "other" rather than "peer", Composer 15 opposed her application, despite pressure from the evaluator (Composer 6) who was better equipped to judge her application, given that he was a peer in a true sense to this applicant. This was a clear case of "disciplinary gate-keeping" [START_REF] Huutoniemi | Communicating and compromising on disciplinary expertise in the peer review of research proposals[END_REF], which can be present even in a context which would seem to be monodisciplinary.

Composer 15 has traits of a high-status individual in the milieu of contemporary art music in the United States -he is a professor of composition at a major university and writed music that is performed by symphonic orchestras. Given that status is an accumulation of "acts of deference" (Sauder, Lynn, & Podolny, 2012, p. 268), it is important to note that Composer 15 was able to accumulate precisely these acts during the panel meeting: he never spoke the name of the other evaluators during the meeting, but the others addressed him, using his name, fifteen times. He never explicitly ceded the floor to another panel member, and did not hesitate to interrupt his peers -contrary to the other two panel members. His opinion also prevailed 55% of the time in cases where there was disagreement amongst the three composers. Sauder et. al. conclude that status matters more when uncertainty is higher [START_REF] Sauder | Status: Insights from Organizational Sociology[END_REF]. But in this setting, where aesthetic judgments are discounted because of a perception of being unreliable and subjective (not because they are felt to be uncertain), a flank is opened which allows status to play a greater role in the evaluation due to the interpersonal dynamics of the panel. It is important to note that this deference was based on status and not expertiseindeed, it was Composer 6 who had greater expertise for the application discussed here.

What is uncertain here is the role that the subjectivity of aesthetic judgment should play, and how a disagreement should be resolved when knowledge is not shared equally amongst the evaluators. The evaluators' judgments were informed by personal tastes and interests, which is inevitable but nonetheless seen as undesirable for these participants, as in academic evaluation as well [START_REF] Lamont | How Professors Think: Inside the Curious World of Academic Judgment[END_REF]. When there was disagreement on the artistic quality of an applicant, divergent opinions were seen as expressions of personal taste, while unanimously shared opinions (reflected in the top of the list) were not seen as subjective or problematic in any way. Thus, to make decisions when disagreement was present, evaluators turned to factors that were less debatable, less "subjective," such as the criterion of audience diversification used above. Except, of course, the use of these supposedly objective factors is indeed highly subjective. Let us look at two further extracts from the debates on applicants in the "fuzzy middle" to clarify this shift from the subjective to the objective: I was put off by the fact that I didn't like the musical style. But it's clear that it's a major work, so you shouldn't take my score of 2 [out of 6] too seriously (excerpt from panel discussion on applicant ranked 25th, American organization, 2013). I wanted to start off here because […] I put a low score for artistry. […] I could see that she had real craftsmanship in her music, but I didn't find the final result captivating at all. But I recognize that that's just my opinion, so I can put that in check if others don't agree, which seems to be the case, so I can set my opinion aside (excerpt from panel discussion on applicant ranked 36th American organization, 2012).

We can see here the panelists' efforts to move away from the subjectivity of their judgment (e.g. "I can set my opinion aside"). The discussions that followed these statements were primarily focused on finding other ways to disqualify these candidates, using criteria that were easier to measure and less "emotional:" for example, the composer's career trajectory, networks, the reputation of the musical ensembles associated with the composer, etc. For the applicants at the top of the list, this kind of secondary criteria was not questioned, so the struggle was to justify non-consensual, "subjective" judgments with other, more "objective" criteria. It is apparent from the examples cited that criteria were invented on a case by case basis to do this. We could contrast the flower pot case from 2012 with a case from 2013, where precisely the same argument of audience diversification was used -in that case, an applicant (ranked 14 th ) was specifically presenting his music to a new audience, but this factor was not sufficient to overcome a negative aesthetic judgment from one of the panel members, and he was moved to the bottom of the fundable section: "if we have any money left, maybe we can fund him" (excerpt from panel debate on applicant ranked 14 th , US organization, 2013). Every application requires a specific mix of criteria, and a criterion that is decisive for one could be utterly meaningless for another (see also [START_REF] Kreiner | Organizational Decision Mechanisms in an Architectural Competition[END_REF].

The present case shows us that the problem of uncertainty in artistic quality judgments (e.g. [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF][START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF][START_REF] Velthuis | Symbolic Meanings of Prices: Constructing the Value of Contemporary Art in Amsterdam and New York Galleries[END_REF] can derive not from doubts regarding the artistic quality of the products being evaluated, but rather from disagreement amongst evaluators and confusion as to how these disagreements should be resolved in the intersubjective setting of peer review. The evaluators come to this setting with different abilities and willingness to play the game of persuading others [START_REF] Lamont | How Professors Think: Inside the Curious World of Academic Judgment[END_REF]. In essence, in these disagreements, artistic quality judgments are seen as unreliable because they are subjectivenot because they are uncertain -and it is for this reason that they are removed from the debate, even though it is precisely these judgments that are at the root of the consensual (and undiscussed) choices. This also shows how value is indeed "practical" (Dewey 1915, cited in Stark 2011, 335) -value is determined to serve a specific purpose, that of evaluation, and this evaluation also has a higher purpose -that of legitimizing the work of this organization in the field in which it exists. It attains an objective reality in the process of this valuation work, and the way subjectivity and objectivity are defined in situ is essential for the meaning given to the process by the participants, but meaningless for any strict understanding of the actual properties of the works being evaluated.

III. Discussion

A first, important point: the organizations studied here are not trying to manage uncertainty by using a peer review system -if anything, this system introduces uncertainty, in the form of arbitrary results, into their decision-making processes. In the American case, by only recruiting evaluators from the highbrow end of music production, and never composers working in more popular genres, the organization can position itself in the "pure" pole without stating this goal explicitly. The organization can claim to simply fund the "best" of the applications it receives, satisfying both its public funders, who desire diversity and inclusion, and its private funders, who seek to reproduce the existing status hierarchy, where highbrow production aligns with other status markers. In both organizations, this evaluative system is mainly a factor for the legitimacy of the organization within the field. By publicly associating these experts with these organizations (both organizations publish the name of their evaluators in online platforms), they show their belonging in the field, and the prestige of the evaluators has a positive knock-on effect for the organizations. When these organizations and the results of their evaluations are seen to be legitimate, an illusion of quality certainty is created, regardless of the arbitrary nature of some of the decision-making processes used to obtain the results, as we have seen.

If these judgments were made in isolation, that is to say, if the panelists were not required to discuss their judgments with other panelists, the arbitrary movement in the fuzzy middle would disappear. The problem of incommensurability is resolved by each of these individuals working alone, but then this problem must be further resolved in the intersubjective setting of the peer review panel. By making evaluation an explicitly social process, these organizations participate in maintaining what Bourdieu calls the "illusio":

It is in the relationship between the habituses and the fields to which they are adjusted to a greater or lesser degree (according to the degree to which they are produced by them) that the foundation of all scales of utility is generated: that is to say, the fundamental adhesion to the game, the illusio, recognition of the game and of the utility of the game, belief in this value of the game and in its stakes (Bourdieu 1996, 172-173).

These face-to-face discussions are an opportunity to show one's belief in the evaluation system and to develop an appropriate habitus; they make it possible to create and maintain this recognition of the game and its utility. Even though some of the young composers used my interviews with them to formulate a critique of these evaluation systems -this is indeed to be expected of those who are not yet "adequately acculturated" in a given community (Smith 1983, 17) -they inevitably rescinded this critique by the end of the interview to say that, in the end, the system was not so bad, and it was even fair, or at least as fair as it could be.

According to Phillipa Chong, "the first 'indicator' of artistic quality is embodied: an emotional response" (2013, p. 273) -these are indeed objects that are designed to elicit such a response. As in the selection of fiction manuscripts, an "emotional connection can be a legitimate selection criterion" (Childress and Nault,123) -which is primarily the case for the upper part of the ranking I studied here, where the positive evaluations were consensual and therefore unquestioned. In the "fuzzy" middle, however, this emotional response must be translated post hoc into official criteria in order to give a reasoned evaluation, as similarly observed by Sara Malou Strandvad in her study of design school admission tests (2014), Kristian Kreiner in his work on an architectural competition (2012), and Franssen and Kuipers (2013, 65) on book editors7 . In her work on peer review in academia, Michèle Lamont draws a parallel between the ritual distinction between the sacred and the profane and efforts to distinguish objective and subjective judgments (Lamont 2009, 110-11). Her hypothesis, after Max Weber and Émile Durkheim, is that the production of belief necessitates a ritual distinction between the sacred and profane, which translates in peer review as a designation of subjective judgments as "impure" (Ibid). The existence of "objective" criteria, which allow panelists to distinguish between a "pure" and an "impure" judgment, facilitates the production of belief in the evaluative system itself, which is essential for it to be operational within its artistic subfield.

In France, however, voting by secret ballot allowed panelists to use personal taste as a prime means for evaluating applications, or to decide for themselves what role their emotional response to the music should play. The representatives of the French organization interviewed placed great importance on allowing panelists to vote according to their "âme et conscience"typically translated as "in good conscience," but which literally means according to their "soul and conscience." This type of evaluation is therefore fundamentally a private affair which should not be questioned -especially by an outside observer -and accountability is not necessary. Whereas in the case of the American non-profit organization, accountability to donors and board members, as well as a transparent, traceable evaluation, are tantamount for the longevity and legitimacy of the organization itself.

In some fields, maintaining an autonomy of opinion is a value in and of itself, as is the case for the reviewers of fiction studied by Phillipa Chong, who wanted to avoid the "potential 'stain' of peer opinions" (Chong, 2013, p. 272). This is indeed impossible in a panel setting, and different voting systems and discussion frameworks will encourage or discourage this type of interpersonal influence [START_REF] Huutoniemi | Communicating and compromising on disciplinary expertise in the peer review of research proposals[END_REF]). The American system explicitly valued this interpersonal influence, and therefore saw the movement in the rankings as a result of it as justified by the process itself, whereas the French system tried to limit this influence as much as possible through a secret ballot. When evaluators are not independent, when their evaluations are known to others, they "must coordinate their decisions with others" (Zuckerman 2017, 53). It is indeed this coordination imperative which creates much of the arbitrary movement of the applicants in the fuzzy middle. This is different from seeing the uncertainty of aesthetic judgments as stemming from the singular properties of the works themselves (e.g. [START_REF] Karpik | Valuing the Unique: The Economics of Singularities[END_REF][START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF]. In a sense, because art, to be art, indeed requires an art world [START_REF] Becker | Art Worlds[END_REF], the uncertainty created by the social nature of peer review is structural and stems from the inherently social nature of these judgments.

This discussion shows how significant the panel composition is for the fate of the applicants, especially for those who find themselves in this fuzzy middle area -just as in hiring in elite professional firms, where "candidates who might otherwise have been rejected could be given a chance or even an edge in evaluation when paired with similar evaluators who believed in the validity of their experiences" [START_REF] Rivera | Hiring as Cultural Matching: The Case of Elite Professional Service Firms[END_REF](Rivera , 1013)). The underlying basis for homophily and cultural matching processes is that "people experience positive feelings when interacting with others who validate their attitudes and identities" (Ibid., 1014), and they assume "that people who make them feel good are good" (Ibid., 1015). Cultural matching and encultured bias [START_REF] Childress | Encultured Biases: The Role of Products in Pathways to Inequality[END_REF][START_REF] Rivera | Hiring as Cultural Matching: The Case of Elite Professional Service Firms[END_REF]) are particularly relevant here for the applications that were left undiscussed at the bottom, some of which were from other musical genres (hiphop, for example), and which were seen as clearly outside of the genre of contemporary art music. As Childress and Nault demonstrate in the milieu of trade fiction publishing, intermediaries who actively seek a cultural match with the manuscripts they evaluate are simply doing "good" work [START_REF] Childress | Encultured Biases: The Role of Products in Pathways to Inequality[END_REF]. Artistic genres arise out of cooperative networks of individuals [START_REF] Becker | Art Worlds[END_REF]) and these obviously have socio-demographic features. It is therefore no accident that the contemporary art music genre -a highly legitimate genre with tremendous symbolic wealth -is overwhelmingly white and male8 , and that an applicant who displays markers of a blacker genre, for example, hip-hop, would be rejected out of hand. "Comparative rankings do not merely reveal unequally distributed qualities and then select individuals on that basis. These competitions cause divergences in contenders' career paths, despite the fact that their abilities may have been similar" (Menger 2014, 186). What results is a ranking which separates the pack into winners and losers, with relative levels of talent being attributed to these individuals through this process [START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF]. Talent as a quality gradient (Ibid., 180) is constructed in this socio-evaluative process. Menger's analysis assumes that it is because the quality of the objects being evaluated is uncertain that we end up falling back on factors like reputation, status, gender, race, and other socio-cultural traits in the evaluation, whereas the perspective of encultured bias presumes that we start with these features [START_REF] Childress | Encultured Biases: The Role of Products in Pathways to Inequality[END_REF][START_REF] Rivera | Hiring as Cultural Matching: The Case of Elite Professional Service Firms[END_REF], as intermediaries actively and intentionally choose people with similar backgrounds and ambitions as themselves. The case I analyzed in detail here showed how easily an aesthetic argument from the evaluator with the most expertise on an application could be overcome in favor of the perspective of the composer with the most status, as defined by this subfield. This leads me to argue that the focus on uncertainty is a way to pretend that the work itself is actually being evaluated, when in fact we are simply reproducing inequalities that are structural and damningly certain elsewhere in society. This is possible not because the evaluators express uncertainty about their quality assessments, but because there is not a consensus on how emotional reactions should be handled in this setting.

IV. Conclusion

This research was conducted on peer review in contemporary art music, on systems that use rankings to make funding decisions. The conclusions discussed here likely apply to other similar situations, settings where artists are applying for grants or where panels are tasked with arbitrating acquisitions or other, similar settings in the "pure" pole [START_REF] Bourdieu | The Rules of Art: Genesis and Structure of the Literary Field[END_REF] of the artistic field. I would hesitate to apply these findings to more popular artistic fields, as the desire to appeal to a mass audience changes evaluation settings considerably. With this in mind, the main thrust of this text has been to clarify how evaluation changes based on where an applicant sits on a ranked list. The top and bottom of such a list are not handled the same way as the upper middle -this is where unpredictable outcomes cluster, as the result of disagreement and/or indifference on the part of evaluators, but not as a result of evaluators expressing doubts about their judgments of artistic quality.

An important finding here is that the primary function of official criteria is to provide a shared vocabulary when justifications are necessary. These justifications only become necessary in an intersubjective setting when divergent opinions are present, whereas shared opinions go largely unquestioned. This divergence and the desire for justification is a feature of the "fuzzy middle" that I have described here -the area of a ranked list near the cut-off line, where the fate of applicants somehow needs to be justified. This area is characterized by disagreement amongst evaluators, but also a lack of recall leading to indifference to the fate of the applicants. Divergence of opinion tends to be emotional or subjective, but not uncertaini.e., deeply personal reactions to the music being evaluated. However, evaluators do feel uncertain about the role that the subjectivity of their evaluations should play, which becomes problematic when their views do not match that of their peers. When emotional reactions align, they are seen as unproblematic. The official criteria give the evaluators a way to formulate their personal reactions in objectifiable terms, thus giving their evaluations the necessary critical distance [START_REF] Chong | Legitimate judgment in art, the scientific world reversed? Maintaining critical distance in evaluation[END_REF]) for them to be deemed legitimate. The actual, operative criteria used to justify these assessments are largely developed after the evaluations are done in isolation, and modified in the discussion to fit the cases at hand. Because the criteria are activated in this intersubjective setting, their use is heavily dependent on the interpersonal dynamics of the group. This is done fluidly and competently, without misgivings being expressed about the validity of the final judgments. This clarifies -at least in part -how decisions are made in milieus known to be affected by quality uncertainty: in essence, quality uncertainty derives from doubts about how emotional responses should be accounted for when disagreement is present in these socio-evaluative settings.

•

  Composer's technical competence and skill • Artistic merit and originality of the proposed musical project • Merit of the production and perspectives for the career of the work

Figure 1 :

 1 Figure 1: Amount of time (in seconds -on y-axis) spent on each application during the meetings of the peer review panels of the American organization, in 2012 and 2013. The x-axis shows the pre-panel rank of the applications (1 being highest, 73 being lowest).

  13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 Amount of time (in seconds) spent on each application 2012 2013

Figure 2 :

 2 Figure 2: Score spreads pre-panel in 2012 and 2013, American organization. The x-axis shows the pre-panel rank of the applications (1 being highest, 73 being lowest).

  R1 6 : […] let's tackle this last one, and then we'll take a little break. It's [candidate ranked 58 th ]. It's just, the discrepancy is so wide, we have to at least address it. C6: Oh yeah! Yeah -the [flower pots]! Wooo! C15: What can I say, I had a very... I had a very strong reaction to this one [laughs].

  C15: It's hard to say. I mean, in a way, you cannot separate the instrument from what she's doing, because it's such a large amount of what she's doing... […]

Table 1 :

 1 Official criteria, American and French organizations

  We were considering moving these applicants lower: [#17], [#18],[#24], and [#26]. So, we're going to take them to the bottom, and see how that looks. Some will automatically move up -[#23],[#25]. How does it look? C5: So far so good -but it's so hard to remember, even the composers we talked about, I'm just trying to get my head around this. But based on what I can remember it looks fine (excerpt from panel debates, US organization, 2013).

	Score spread
	6
	4
	2
	0
	1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73
	score spread 2012	score spread 2013

S:

See the definition of this term in section I.a.

See, for example, Born (1997),[START_REF] El-Ghadban | Facing the music: Rituals of belonging and recognition in contemporary Western art music[END_REF],[START_REF] Menger | The Economics of Creativity: Art and Achievement under Uncertainty[END_REF][START_REF] Gidal | Contemporary Latin American Composers of Art Music in the United States: Cosmopolitans Navigating Multiculturalism and Universalism[END_REF], among many others.

I have kept these individuals anonymous because the committee meetings I observed and discussed with my interviewees are not open to the public and the content is intended to be confidential. I have also changed certain details about the applications discussed (specifically instrumentation of the pieces -a string quartet could become a wind quintet, for example).

R1 is Representative 1 of the American organization, C stands for composer. See Appendix 1 for more details about these individuals.

The 2 nd most discussed applicant was the person ranked 10th in 2012, and her application was actually used as a point of comparison for the applicant ranked 58th, which explains why that application was also so present in the discussion.

This transcript has been shortened and edited for readability.

This could also be brought in connection with the "garbage can" model of decision making, which sees intuition as a way of getting around the problem of incommensurability[START_REF] Kreiner | Organizational Decision Mechanisms in an Architectural Competition[END_REF].

See, for example, McClary (1991),Redhead (2015), and Parsons Smith (1993).

Funding: Research funded by a PhD contract from the CRAL (Centre de recherches sur les arts et le langage) of the EHESS (Ecole de accompanied her PhD thesis when it was submitted.

them, is available from the author on request. These documents


Keywords: Chaos, Discrete time systems, Floating point arithmetic, Random number generation

Generation of random or pseudorandom numbers, nowadays, is a key feature of industrial mathematics. Pseudorandom or chaotic numbers are used in many areas of contemporary technology such as modern communication systems and engineering applications. More and more European or US patents using discrete mappings for this purpose are obtained by researchers of discrete dynamical systems [1], [2]. Efficient Chaotic Pseudo Random Number Generators (CPRNG) have been recently introduced. They use the ultra weak multidimensional coupling of p 1-dimensional dynamical systems which preserve the chaotic properties of the continuous models in numerical experiments. Together with chaotic sampling and mixing processes, ultra weak coupling leads to families of (CPRNG) which are noteworthy [3], [4].

In this paper we improve again these families using a double threshold chaotic sampling instead of a single one.

We analyze numerically the properties of these new families and underline their very high qualities and usefulness as CPRNG when very long series are computed.

I. INTRODUCTION

Efficient Chaotic Pseudo Random Number Generators (CPRNG) have been recently introduced. The idea of applying discrete chaotic dynamical systems, intrinsically, exploits the property of extreme sensitivity of trajectories to small changes of initial conditions. They use the ultra weak multidimensional coupling of p 1-dimensional dynamical systems which preserve the chaotic properties of the continuous models in numerical experiments. The process of chaotic sampling and mixing of chaotic sequences, which is pivotal for these families, works perfectly in numerical simulation when floating point (or double precision) numbers are handled by a computer.

It is noteworthy that these families of very weakly coupled maps are more powerful than the usual formulas used to generate chaotic sequences mainly because only additions and R. Lozi is with the Laboratory J. A. Dieudonné, UMR CNRS 6621, University of Nice Sophia-Antipolis, 06108 Nice Cedex 02, France and the Institut Universitaire de Formation des Maîtres Célestin Freinet-académie de Nice, University of Nice-Sophia-Antipolis, 89 avenue George V, 06046 Nice Cedex 1, France (corresponding author to provide phone: 04-93-53-75-08; e-mailrlozi@unice.fr). multiplications are used in the computation process; no division being required. Moreover the computations are done using floating point or double precision numbers, allowing the use of the powerful Floating Point Unit (FPU) of the modern microprocessors (built by both Intel and Advanced Micro Devices (AMD)). In addition, a large part of the computations can be parallelized taking advantage of the multicore microprocessors which appear on the market of laptop computers.

In this paper we improve the properties of these families using a double threshold chaotic sampling instead of a single one. The genuine map f used as one-dimensional dynamical systems to generate them is henceforth perfectly hidden.

II. ULTRA WEAK MULTIDIMENSIONAL COUPLING

A. System of p-Coupled Symmetric Tent Map

When a dynamical system is realized on a computer using floating point or double precision numbers, the computation is of a discretization, where finite machine arithmetic replaces continuum state space. For chaotic dynamical systems, the discretization often has collapsing effects to a fixed point or to short cycles [START_REF] Lanford | Some informal remarks on the orbit structure of discrete approximations to chaotic maps[END_REF], [START_REF] Gora | Absolutely continuous invariant measures that cannot be observed experimentally[END_REF]. In order to preserve the chaotic properties of the continuous models in numerical experiments we have recently introduced an ultra weak multidimensional coupling of p one-dimensional dynamical systems which is noteworthy [START_REF] Lozi | Giga-Periodic Orbits for Weakly Coupled Tent and Logistic Discretized Maps[END_REF].

In this specific case we have chosen as an example the symmetric tent map defined by

x a x f a - = 1 ) ( (1)
with the value a = 2, later denoted simply as f, even though others chaotic map of the interval (as the logistic map) can be used for the same purpose. The dynamical system associated to this one dimensional map is defined by the equation on the

interval J = [-1, 1] ⊂ ℝ [8]. n n x a x - = + 1 1 (2)
The system of p-coupled dynamical systems is then:

( ) (
)

) ( n n 1 n X f A X F X ⋅ = = + (3)
          = p x x X ⋮ 1 ,           = ) ( ) ( ) ( 1 p x f x f X f ⋮ (4)
and

                = p p p 2 2 2 2 1 1 1 1 ε 1) - (p - 1 ε ε ε ε ε 1) - (p - 1 ε ε ε ε ε 1) - (p - 1 ⋯ ⋯ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮ ⋱ ⋮ ⋯ ⋯ A (5)
F is a map of J p into itself.

Several combinations can be given for the relative values of the i ε , in this paper we choose

1 i ε ε i = i = 2, …, p (6)
The matrix A is always a stochastic matrix iff the coupling constants i ε verify

i 1 0 ε 1 p ≤ ≤ - (7)
When i ε 0 = the maps are decoupled, when i 1 ε 1 p = -they are fully cross coupled. Generally, researchers do not consider very small values of i ε because it seems that the maps are quasi decoupled with those values and no special effect of the coupling is expected. In fact it is not the case and ultra small coupling constant (as small as 10 -7 for floating point numbers or 10 -14 for double precision numbers), allows the construction of very long periodic orbits, leading to sterling chaotic generators.

Moreover each component of these numbers belonging to p ℝ is equally distributed over the finite interval J ⊂ ℝ . Numerical computations show that this distribution is obtained with a very good approximation. They have also the property that the length of the periods of the numerically observed orbits is very large [START_REF] Lozi | Giga-Periodic Orbits for Weakly Coupled Tent and Logistic Discretized Maps[END_REF].

B. Chaotic Pseudo-Random Generators

However chaotic numbers are not pseudo-random numbers because the plot of the couples of iterated points (x n , x n+1 ) in the phase plane reveals the map f used as one-dimensional dynamical systems to generate them.

Nevertheless we have recently introduced a family of Enhanced Chaotic Pseudo Random Number Generators (CPRNG) in order to compute very fast long series of pseudorandom numbers with desktop computer [START_REF] Lozi | New Enhanced Chaotic Number Generators[END_REF]. This family is based on the previous ultra weak coupling which is enhanced in order to conceal the chaotic genuine function.

In the aim of hiding f in the phase space ( )

l n l n x x 1
, + two mechanisms are used. The pivotal idea of the first one mechanism is to sample chaotically the sequence A second mechanism can improve the unpredictability of the chaotic sequence generated as above, using synergistically all the components of the vector X, instead of two. This simple mechanism is based on the chaotic mixing of the p-1 sequences

( ) … … , , , , , ,
( ) … … , , , , , , 1 1 1 1 2 1 1 1 0 + n n x x x x x , ( ) … … , , , , , , 2 1 2 2 2 2 1 2 0 + n n x x x x x ,…, ( ) … … , , , , , , 1 1 1 1 2 1 1 1 0 - + - - - - p n p n p p p x x x x x using the last one ( ) … … , , , , , ,

C. Numerical Results

As an example we explicit both mechanisms taking 4-coupled equations for [START_REF] Hénaff | Observers design for a new weakly coupled map function[END_REF]. The value of 4 n x commands the chaotic sampling and the mixing processes as follows.

Let us set three threshold values T 1 , T 2 and

T 3 -1 < T 1 < T 2 < T 3 < 1 (8)
we sample and mix together chaotically the sequences

( ) … … , , , , , , 1 1 1 1 2 1 1 1 0 + n n x x x x x , ( ) … … , , , , , , 2 1 2 2 2 2 1 2 0 + n n x x x x x and ( ) … … , , , , , , 3 1
3 3 2 3 1 3 0 + n n x x x x x defining ( ) ⋯ ⋯ , , , , , , 1 2 1 0 + q q x x x x x by ] [ [ [ [ [      ∈ ∈ ∈ = 1 , , , 3 4 3 3 2 4 2 2 1 4 1 T x iff x T T x iff x T T x iff x x n n n n n n q (9)
Numerical results about chaotic numbers produced by ( 3) - [START_REF] Lozi | New Enhanced Chaotic Number Generators[END_REF] show that they are equally distributed over the interval J.

In order to compute numerically an approximation of the invariant measure also called the probability distribution function P N (x) linked to the 1-dimensional map f we consider a regular partition of M small intervals (boxes) r i of J.

J= 1 0 M i r - ∪ (10) r i = [s i , s i+1 [ , i = 0, M -2 (11) r M-1 = [s M-1 , 1] (12) M i s i 2 1 + - = i = 0, M (13)
the length of each box is

M s s i i 2 1 = - + (14)
All iterates f (n) (x) belonging to these boxes are collected (after a transient regime of Q iterations decided a priori, i.e. the first Q iterates are neglected). Once the computation of N+ Q iterates is completed, the relative number of iterates with respect to N/M in each box r i represents the value P N (s i ). The approximated P N (x) defined in this article is then a step function, with M steps. As M may vary, we define ( )

i i N M r N M s P # 2 1 ) ( , = (15)
where #r i is the number of iterates belonging to the interval r i and the constant 1/2 allows the normalisation of ) (

, x P N M on the interval J. i i N M N M r x s P x P ∈ ∀ = ) ( ) ( , , (16)
To be published in proceedings of: ICCSA 2009 The 3rd International Conference on Complex Systems and Applications, University of Le Havre, France, June 29-July 02, 2009.

3

In the case of coupled maps, we are more interested by the distribution of each component x 1 , …, x p of X rather than the distribution of the variable X itself in J p . We then consider the approximated probability distribution function P N (x j ) associated to one among several components of F(X) defined by (3) which are one-dimensional maps.

The discrepancies E 1 (in norm L 1 ) and E 2 (in norm L 2 ) between ) ( , x P iter disc N N and the Lebesgue measure which is the invariant measure associated to the symmetric tent map, are defined by

1 5 . 0 ) ( ) , ( , 1 L N N iter disc x P N N E iter disc - = (17) 2 2 ,
( , ) ( ) 0.5

disc iter disc iter N N L E N N P x = - (18)
In the same way an approximation of the correlation distribution function C N (x, y) is to obtained numerically building a regular partition of M 2 small squares (boxes) of J 2 imbedded in the phase subspace (x l , x m )

r i,j = [s i , s i+1 [ × [t j , t j+1 [ , i, j = 0, M -2 (19) r M-1,j = [s M-1 , 1] × [t j , t j+1 [ , j = 0, M -2 (20) r i , M-1 = [s i , s i+1 [× [t M-1 , 1] , i = 0, M -2 (21) r M-1 , M-1 = [s M-1 , 1] × [t M-1 , 1] (22) M i s i 2 1+ - = , M j t j 2 1+ - = , i, j = 0, M (23)
the measure of the area of each box is

( ) ( ) 2 1 1 2       = - ⋅ - + + M t t s s i i i i (24) Once N + Q iterated points ( ) m n l n x x ,
belonging to these boxes are collected the relative number of iterates with respect to N/M 2 in each box r i,j represents the value C N (s i , t j ). The approximated probability distribution function C N (x, y) defined here is then a 2-dimensional step function, with M 2 steps. As M can take several values in the next sections, we define ( )

j i j i N M r N M t s C , 2 , # 4
1 ) , ( = (25)
where #r i,j is the number of iterates belonging to the square r i,j and the constant 1/4 allows the normalisation of ) , ( ,

y x C N M on the square J 2 . j i j i N M N M r y x t s C y x C , , , ) , ( ) , ( ) , ( ∈ ∀ = (26)
The discrepancies , + instead of the phase space (x l , x m ). In order to control that the enhanced chaotic numbers ( )

⋯ ⋯ , , , , , , 1 2 1 0
+ q q x x x x x
are uncorrelated, we plot them in the phase subspace ( )

1 , + n n x x
and we check if they are uniformly distributed in the square J 2 and if f is concealed . Fig. 1 shows the values of ) , (

1 iter disc AC NSampl N E
for a system of 4-coupled equations when the three components x 1 , x 2 , x 3 are mixed and sampled by x 4 for the threshold values T 1 = 0.98, T 2 = 0.987, T 3 = 0.994 or T 1 = 0.998, T 2 = 0.9987, T 3 = 0.9994.

-

AC disc iter E N NSampl N disc =10 2 ×10 2 ,
NSampl iter = 10 3 to 10 10 , ε i = i.ε 1 , ε 1 =10 -14 . E N NSampl for a system of 4 coupled-equations when the three components x 1 , x 2 , x 3 are mixed and sampled by x 4 for the threshold values T 1 = 0.998, T 2 = 0.9987, T 3 = 0.9994.

N iter

III. DOUBLE TRHESHOLD CHAOTIC SAMPLING

A. Improved CPRNG On can again improve the CPRG previously introduced with respect to the infinity norm instead of the L 1 or L 2 norms because the L ∞ norm is more sensitive than the others to reveal the concealed f. For this aim, consider first that in the phase space ( )

l n l n x x 1
, + the graph of the chaotically sampled chaotic numbers is a mix of the graphs of all the f (r) (Fig. 2).

It is obvious as showed on Fig. 3 ( , ) ( , ) ( , ) 0

AC AC AC E M N E M N E M N ∞ = = = .
The autocorrelation function is different from zero only if M > 2 (Fig. 4).

Figure 2. Graphs of the symmetric tent map f, f (2) and f (3) ( , ) ( , ) ( , ) 0

AC AC AC E M N E M N E M N ∞ = = = for f (i) iff M < 2 i .
Hence for a given M, if we cancel the contribution of all the f (i) for 2 i < M, it is not possible to identify the genuine function f.

AC

x y is constant for the symmetric tent map f (2) are shaded for M = 8.

B. Algorithm and Numerical Results

We describe again the algorithm of the double threshold chaotic sampling in the case of 4-coupled equations.

Consider the sequence ( )

⋯ ⋯ , , , , , , 1 2 1 0 + q q x x x x x
we want to mix and sample. For each q-1 there exists n (q-1) in the original sequence. We introduce a second threshold ' N ∈ ℕ and then we define:

] [ [ [ [ [ 1 4 1 2 ( 1) 2 4 2 3 ( 1) 3 4 3 ( 1) , ' , ' , 1 '
n n q q n n q n n q

x iff x T T and n n N x y is constant for the symmetric tent map f (3) are shaded for M = 16.

x x iff x T T and n n N x iff x T and n n N

- - -  ∈ - >  = ∈ - >   ∈ - >  (28)
As shown previously [START_REF] Lozi | New Enhanced Chaotic Number Generators[END_REF] the errors in L 1 or L 2 norms decrease with the number of chaotic points (as in the law of large numbers) and conversely increase with the number M of boxes used to define , ( , )

M N AC x y . It is the same for the error in L ∞ norm. Fig. 8 shows that when M is greater than 2 5 , the sequence defined by (28) behaves better than the one defined by [START_REF] Lozi | New Enhanced Chaotic Number Generators[END_REF]. NSampl iter = 10 9 , thresholds T = 0.9 and N' = 20, ε i = i.ε 1 , ε 1 = 10 -14 .

Fig. 9 shows that when the number of chaotic points increases the error L ∞ decreases drastically. If N' > 100, it is necessary to use a huge grid of 2 100 x2 100 boxes splitting the square J 2 in order to find a trace of the genuine function f. This is numerically impossible with double precision numbers. Then the chaotic numbers appear as random numbers.

Others numerical results show the high-potency of theses new CPRNG. Due to limitation of this article, they will be published elsewhere.

IV. CONCLUSION

Using a double threshold in order to sample a chaotic sequence, we have improved with respect to the infinity norm the CPRNG previously introduced. When the value of the second threshold N' is greater than 100, it is impossible to find the genuine function used to generate the chaotic numbers. The new CPRNG family is robust versus the choice of the weak parameter of the system for 10 -14 < ε < 10 -5 , allowing the use of this family in several applications as for example chaotic cryptography.

x

  every time the value m n x of the m-th component m x , is strictly greater than a threshold T ∈ J, with l ≠ m, for 1 ≤ l, m ≤ p .

+

  with respect to a given partition T 1 , T 2 , …, T p-1 of J , to distribute the iterated points.

  Figure 1. Error of 1 ( , )

  that for r = 1 if M = 1 or 2, constant and normalized on the square hence 1 2

  Figure 2. Graphs of the symmetric tent map f, f(2) and f(3) on the interval [-1,1].

Figure 3 .

 3 Figure 3. In shaded regions the autocorrelation distribution , ( , ) M N AC x y is constant for the symmetric tent map f on the interval [-1, 1] for M = 1 or 2.In the same way as displayed on Fig.5, 6 and 7, 1 2

Figure 4 .

 4 Figure 4. Regions where the autocorrelation distribution , ( , ) M N AC x y is constant for the symmetric tent map f are shaded, for M = 4. (The square on the bottom left of the graph shows the size of the r i,j box). , ( , ) M N AC x y vanishes on the white regions.

Figure 5 .

 5 Figure 5. In shaded regions the autocorrelation distribution , ( , ) M NACx y is constant for the symmetric tent map f(2) on the interval [-1, 1] for M = 1, 2 and 4.

Figure 6 .

 6 Figure 6. Regions where the autocorrelation distribution , ( , ) M N

Figure 7 .

 7 Figure 7. Regions where the autocorrelation distribution , ( , ) M NACx y is constant for the symmetric tent map f(3) are shaded for M = 16.

Figure 8

 8 Figure 8. Error of ( , ) AC disc iter E N NSampl ∞

Figure 9 N

 9 Figure 9. Error of ( , ) disc iter E N NSampl ∞