Towards a Discursive Representation of Public Opinion.: The Problems Involved in Building and Analysing Corpuses of Open-Ended Poll Questions.

Progress regarding the theory and methodology of public opinion polls is now allowing us to envisage experimental survey devices which give more room for open-ended questions, or for sequences which combine open and closed questions. They thus make it possible to build veritable corpuses of "expressed public opinion". This article attempts to present the collections formed by the responses to these devices, by examining their pretension of constituting political corpuses. We do not set out the tools or the methods - in particular the analysis of textual data applied to this type of corpus - but instead we identify the socio-political and linguistic conditions which govern the creation of such corpuses and which also partly determine the strategies for analysis and interpretation. Such an enterprise means looking first of all at the notion of "the political discourses of ordinary citizens", and then examining the survey from a socio-technical angle by analysing, in particular, its pretensions of constituting an enunciation device. Can an opinion poll constitute a "stage" for public debate? This initial question involves, on the one hand, thinking about the survey's interactions and the skills that it mobilises, along with the types of gain in generality created by the survey "stage", which would enable us to liken a response to a survey's open-ended question to a type of political discourse; and, on the other hand, to think about the statistical representativeness, linked to a conception of political representativeness, of these collection and processing devices. After clarifying these conditions, I will suggest we define corpuses "enunciated public opinion" as sequences of open and closed questions, composed of a chain of interactions created by the succession of question-answer couplets ; I will also provide an example of a device

A q-analog of certain symmetric functions and one of its specializations

Let be the symmetric functions defined for the pair of integers $\left( n,r\right)$ $n\geq r\geq 1$ by $p_{n}^{\left( r\right) }=\sum m_{\lambda }$ where $m_{\lambda }$ are the monomial symmetric functions, the sum being over the partitions $\lambda$ of the integer $n$ of length $r$. In this article we introduce a $q$-analog of $p_{n}^{\left( r\right) }$, through generating functions and give some of its properties which are $q$-analogs of its classical correspondent in particular when $r=1$. It is proved that this $q$-analog of $p_{n}^{\left( r\right) }$ can be expressed in terms of the classical $p_{n}^{\left( j\right) }$, through the $q$-Stirling numbers of the second kind. We also begin, with the same procedure, the study of a $p,q$-analog of $p_{n}^{\left( r\right) }$. In the rest of the article we specialize in the series $\sum\nolimits_{n=0}^{\infty }q^{\binom{n}{2}}t^{n}/n!$ . We show that $p_{n}^{\left( r\right) }$ is then related to the $q^{r}$-analog of $p_{n-r}$. The existence of a double sequence of polynomials with integer coefficients, denoted $J_{n,r}\left( q\right)$, is deduced. We identify these polynomials with the inversion enumerators introduced for specific rooted forests. These polynomials verify a ''positive'' linear recurrence which allows to build row by row the table of $J_{n,r}$ from the initial conditions $J_{r,r}=1$. The form of the linear recurrence is given for the reciprocal polynomials of \ $J_{n,r}$, which are the sum enumerators of parking functions. The linear recurrence permits to obtain an explicit calculation formula for $J_{n,r}$ . This formula leads us to introduce new statistics on rooted trees and forests for $\ J_{n,r}$ or its reciprocal.Comment: 17 pages, 1 figure. All the results are unchanged. Minor changes to improve English and writing of the text. One reference added and modification of the numbering of references. Equation (2.1) corrected. Section 5: Open problem replaced by Remark and shorcut. Lemma 6.1 replaced by Proposition 6.1, content unchanged. An additional paragraph in the conclusion. Change of legend of Figure

On a particular specialization of monomial symmetric functions

Let $m_{\lambda }$ be the monomial symmetric functions with $\lambda$ integer partition of $n=\left| \lambda \right|$. For the specialization of the $q$-deformation of the exponential, we prove that to each $m_{\lambda }$ is accociated a polynomial $J_{\lambda }\left( q\right)$% , whose coefficients belong to $\mathbb{Z}$. $J_{\lambda }$ is a generalization of the case $\lambda =\left( n\right)$ for which $J_{\left( n\right) }=J_{n}$ is the enumerator polynomial of inversion in tree on $n$ vertices. Some relations between $J_{\lambda }$ and $J_{n,r}$ are obtained, these $J_{n,r}$ having been introduced in $\left[ 4\right]$ from a $q$% -analog of certain symmetric functions, and being themselves inversion enumerator polynomials which generalize $J_{n,1}=J_{n}$. From the calculation of $J_{\lambda }$ for $\left| \lambda \right| \leq 6$, we conjecture that the coefficients of each $J_{\lambda }$\ are strictly positive and log-concave. As a consequence of Huh's works on the $h$-vector of matroid complex (Theorem 3 of $\left[ 7\right]$), it is shown that the coefficients of \ all $J_{n,r}$ are strictly positive and log-concave, which gives a second argument for these conjectures. We prove that the last $n-1$ coefficients of $J_{\lambda }$ are proportional to the first $n-1$ coefficients of column $n-r-1$ of Pascal's triangle, $r$ being the length of $\lambda$. This is a third argument to state the conjectures since the log-concavity of these columns are well known. The calculation of $J_{\left( 3,2,1\right) }$ shows the existence of a obstacle, if one wants to prove the conjectures by application of the theorem of Huh, quoted above.Comment: 1

Le Grenelle de l’environnement : corpus et dispositif d’écriture

L’hypothèse privilégiée dans ce travail est de considérer le Grenelle de l’environnement comme un dispositif d’écriture et comme un dispositif d’énonciation collectif. Son orientation pragmatique est double : il construit du consensus et produit des mesures d’action publique. Deux types d’approches sont privilégiés : une première approche, morphologique, est orientée vers l’analyse de la représentation des problèmes, une seconde, formelle, est dédiée à l’analyse de la formulation de mesures.The Grenelle of the Environment as a writing device The hypothesis favored in this work is to consider the Grenelle of the Environment as a writing device and a device for collective enunciation. Its pragmatic approach is twofold: it builds consensus and produces measures of public action. Two types of approaches are preferred: a first approach, morphological analysis is oriented toward the representation of problems, a second, formal, is dedicated to the analysis of the formulation of measures

Le Grenelle de l’environnement : corpus et dispositif d’écriture

L’hypothèse privilégiée dans ce travail est de considérer le Grenelle de l’environnement comme un dispositif d’écriture et comme un dispositif d’énonciation collectif. Son orientation pragmatique est double : il construit du consensus et produit des mesures d’action publique. Deux types d’approches sont privilégiés : une première approche, morphologique, est orientée vers l’analyse de la représentation des problèmes, une seconde, formelle, est dédiée à l’analyse de la formulation de mesures.The Grenelle of the Environment as a writing device The hypothesis favored in this work is to consider the Grenelle of the Environment as a writing device and a device for collective enunciation. Its pragmatic approach is twofold: it builds consensus and produces measures of public action. Two types of approaches are preferred: a first approach, morphological analysis is oriented toward the representation of problems, a second, formal, is dedicated to the analysis of the formulation of measures