Francesco Fedele
email: fedele@gatech.edu

Denys Dutykh
email: denys.dutykh@ucd.ie

VORTEXONS IN AXISYMMETRIC POISEUILLE PIPE FLOWS

Keywords: Navier-Stokes equations, pipe flows, solitary waves, peakons

We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (2012) [12]. The KdV dynamics of a perturbation is also investigated by means of an high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (2008) [10]. The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.

Introduction

The laminar Hagen-Poiseuille flow is believed to be linearly stable to periodic or localized infinitesimal disturbances for all Reynolds numbers Re (see, for example, [START_REF] Drazin | Hydrodynamic Stability[END_REF]), in contrast to rotating pipe flows that exhibit supercritical bifurcation [START_REF] Mackrodt | Stability of Hagen-Poiseuille flow with superimposed rigid rotation[END_REF]. Transition to turbulence in non-rotating pipe flows is thus triggered by finite-amplitude perturbations [22]. The coherent structures observed at the transitional stage are in the form of vortical patches known as puffs and slugs [START_REF] Wygnanski | On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug[END_REF]44] that are triggered by non-axisymmetric perturbations, although strong axisymmetric input can lead to similar turbulent structures [START_REF] Leite | An experimental investigation of the stability of Poiseuille flow[END_REF][START_REF] Duguet | Transition in pipe flow: the saddle structure on the boundary of turbulence[END_REF]. Puffs are spots of vorticity localized near the pipe axis surrounded by laminar flow. Slugs develop along the streamwise direction, while expanding through the entire cross-section of the pipe, and they are concentrated near the wall. Recent theoretical studies tried to relate slug flows to quasi inviscid solutions of the Navier-Stokes (NS) equations for non-rotating pipe flows. In particular, for non-axisymmetric flows [START_REF] Smith | Amplitude-Dependent Neutral Modes in the Hagen-Poiseuille Flow Through a Circular Pipe[END_REF] [34] revealed the existence of nonlinear neutral structures localized near the pipe axis (centre modes). They are inviscid travelling waves of small but finite amplitude, and unstable equilibrium states (see [39]). More recently, [START_REF] Walton | The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes[END_REF] [40] investigated the nonlinear stability of impulsively started pipe flows to axisymmetric perturbations at high Reynolds numbers and he found the axisymmetric analogue of inviscid centre modes. Walton's neutral mode and the inviscid axisymmetric 'slug' structure proposed by [START_REF] Smith | On Displacement-Thickness, Wall-Layer and Mid-Flow Scales in Turbulent Boundary Layers, and Slugs of Vorticity in Channel and Pipe Flows[END_REF] [START_REF] Smith | On Displacement-Thickness, Wall-Layer and Mid-Flow Scales in Turbulent Boundary Layers, and Slugs of Vorticity in Channel and Pipe Flows[END_REF] are similar to the slugs of vorticity that have been observed in both experiments [START_REF] Wygnanski | On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug[END_REF] and numerical simulations [START_REF] Willis | Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized 'edge' states[END_REF]. These inviscid structures may play a role in pipe flow transition as precursors to puffs and slugs, since most likely they are unstable to non-axisymmetric disturbances, as the centre modes (see [39]).

Recently [START_REF] Fedele | Travelling waves in axisymmetric pipe flows[END_REF] [12] investigated the dynamics of non-rotating axisymmetric pipe flows in terms of solitons and travelling waves of nonlinear wave equations. He showed that, at high Reynolds numbers, the dynamics of small and long-wave perturbations to the laminar flow obeys a coupled system of nonlinear Korteweg-de Vries-type (KdV) equations. These set of equations generalize the one-component KdV model derived by Leibovich [27] to study propagation of waves along the core of concentrated vortex flows (see also Benney 1966) and vortex breakdown [28]. Fedele's coupled KdV equations support inviscid soliton and periodic wave solutions in the form of toroidal vortex tubes, hereafter referred to as vortexons, which are similar to the inviscid nonlinear neutral centre modes found by Walton (2011) [40].

In light of these studies, a generic Navier-Stokes flow can thus be interpreted as a nonlinear sea state [START_REF] Fedele | Rogue wave in oceanic turbulence[END_REF][START_REF] Fedele | On nonlinear wave groups and crest statistics[END_REF] of interacting coherent wave structures of soliton bearing equations. Such sea states may, for example, explain the occurrence of steady 'puffs' observed in both numerical simulations and experiments of turbulent pipe flows [42,[START_REF] Willis | Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized 'edge' states[END_REF]. Indeed, puffs appear to be dynamically similar to solitons. As turbulence becomes selfsustained at Re ≈ 2000, puffs appear at Re ≈ 2250 and as Re increases they slowly delocalize by splitting into two or more puffs, eventually expanding in to slug flow ([2]). Similarly, a soliton loses energy as it interacts with the background or other solitons, and it delocalizes in space by splitting into many other smaller solitons leading to a solitonic sea state. Furthermore, the 'edge states' computed in numerical experiments of pipe flows at Re ≈ 10 5 [9] can be interpreted as 'semi-stable' localized travelling waves that neither relaminarize nor become turbulent. Similar studies for Blasius flows have shown that, at high Reynolds numbers, the dynamics is described by a Benjamin-Davis-Acrivos (BDA) integro-differential equation [START_REF] Ryzhov | Solitons in Transitional Boundary Layers[END_REF]. This supports soliton structures that explain the formation of spikes observed in boundary-layer transition [24].

In this paper, we confirm the validity of the theoretical vortexons derived by [START_REF] Fedele | Travelling waves in axisymmetric pipe flows[END_REF] [12]. To do so, we numerically compute traveling waves of the abovementioned KdV equations using the Petviashvili method [32, 46]) and discuss the associated vortical flow structures. Finally, the numerical investigation of the KdV evolution of a perturbation reveals new dynamical flow features that are physically interpreted and discussed.

Coupled KdV-type equations

Consider the axisymmetric flow of an incompressible fluid in a pipe of circular cross section of radius R driven by an imposed uniform pressure gradient. The time, radial and streamwise lengths as well as velocities are rescaled with T , R and U 0 respectively. Here, T = R U 0 is a convective time scale and U 0 is the maximum laminar flow velocity. Define a cylindrical coordinate system (z, r, θ) with the z-axis along the streamwise direction, and

(u = -1 r ∂ z Ψ, w = 1 r ∂ r Ψ)
as the radial and streamwise velocity components of a divergence-free axisymmetric velocity field given in terms of a Stokes streamfunction Ψ(r, z, t). Consider a perturbation to the laminar base flow W 0 (r) = 1r 2 and decompose Ψ as

Ψ = Ψ 0 + ψ,
where Ψ 0 = 1 2 r 2 1 -1 2 r 2 represents the stream function of the laminar flow W 0 , and ψ that of the disturbance. The curl of the NS equations yields the following nonlinear equation for ψ [23]

∂ t Lψ + W 0 ∂ z Lψ - 1 Re L 2 ψ = N (ψ), (2.1)
where the nonlinear differential operator

N (ψ) = - 1 r ∂ r ψ∂ z Lψ + 1 r ∂ z ψ∂ r Lψ - 2 r 2 ∂ z ψLψ, the linear operator L = L + ∂ zz , L = ∂ rr - 1 r ∂ r = r∂ r 1 r ∂ r ,
and Re is the Reynolds number based on U 0 and R. The boundary conditions for (2.1) reflect the boundedness of the flow at the centerline of the pipe and the no-slip condition at the wall, that is

∂ r ψ = ∂ z ψ = 0 at r = 1.
Drawing from [START_REF] Fedele | Travelling waves in axisymmetric pipe flows[END_REF] [12], the solution of (2.1) can be given in terms of a complete set of orthonormal basis {φ j (r)} as

ψ(r, z, t) = ∞ j=1 φ j (r)B j (z, t), (2.2)
where B j is the amplitude of the radial eigenfunctions φ j that satisfy the Boundary Value Problem (BVP) (see [START_REF] Fedele | Revisiting the stability of pulsatile pipe flow[END_REF]) L 2 φ j = -λ 2 j Lφ j , with 1 r φ j and 1 r ∂ r φ j bounded at r → +0, and φ j = ∂ r φ j = 0 at r = 1. Since φ j satisfies the pipe flow boundary conditions a priori, so does ψ of (2.2). Note that even for a finite number N of modes, the vorticity of the velocity field associated to the truncated expansion for ψ is divergence-free. The positive eigenvalues λ j are the roots of J 2 (λ j ) = 0, where J 2 (r) is the Bessel function of first kind of second order (see [START_REF] Abramowitz | Handbook of Mathematical Functions[END_REF]). For example, for the first two least stable eigenmodes λ 1 ≈ 5.136 and λ 2 ≈ 8.417, respectively. A Galerkin projection of (2.1) onto the Hilbert space spanned by {φ j } ∞ j=1 yields an infinite set of coupled generalized Camassa-Holm (CH) equations [START_REF] Camassa | An integrable shallow water equation with peaked solitons[END_REF]

∂ t B j + c jm ∂ z B m + β jm ∂ zzz B m + α jm ∂ zzt B m + N jnm (B n , B m ) + λ 2 j B j Re = 0, (2.3)
where

N jnm (B n , B m ) = F jnm B n ∂ z B m + G jnm ∂ z B n ∂ zz B m + H jnm B n ∂ zzz B m , (2.4)
and summation over repeated indices n and m is implicitly assumed. The tensors c jm , β jm and α jm of the advection and dispersive terms are function of the base flow W 0 . These and F jnm , G jnm , H jnm are given in Fedele (2012) [12]. In simple words, the equations (2.3) govern the nonlinear interaction of the radial structures {φ j (r)} that are advected and dispersed in the streamwise direction by the laminar flow. Note that CH type equations arise also as a regularized model of the 3-D NS equations, the so called Navier-Stokesalpha model [START_REF] Foias | The Navier-Stokes-alpha model of fluid turbulence[END_REF].

Starting from (2.3) Fedele (2012) [12] showed that the nonlinear dynamics of a small long-wave perturbation can be reduced to that on the 'slow manifold' of the laminar state spanned by the first few N least stable modes φ j . The higher damped modes (j > N) can be legitimately set as slaved and so neglected as long as (i ) the amplitudes B j remain for all time in a small neighborhood of zero (the laminar state), and (ii ) the non-resonant condition λ 2 i 1 + λ 2 i 2 + . . . + λ 2 in ≠ λ 2 j holds true, with {i 1 , i 2 , . . . , i n } any permutation of size n ≤ N drawn from the set j = 1, . . . , N (see [7]). For the BVP of (2.2) (ii) has been verified to hold numerically up to N ∼ 10 4 . As a result, in the long-wave limit higher order nonlinearities in (2.4) can be neglected and (2.3) reduces to the coupled damped KdV equations

∂ t B j + c jm ∂ z B m + β jm ∂ zzz B m + F jnm B n ∂ z B m + λ 2 j B j Re = 0, (2.5)
where j = 1, . . . , N. In particular, Fedele (2012) [12] proved that if

B j = εb j (ξ, τ ), with ε ∼ O(Re -2 5 ) and ξ = ε 1 2 (z -V t), τ = ε 3 2 t,
then the dynamics is primilary inviscid for time scales much less than t ∼ O(ε -5

2 ) = O(Re 6.25 ), and V is given approximately by the average of the eigenvalues of c jm . Moreover, the inviscid KdV system (2.5) supports analytical travelling waves (TWs). In physical space, they correspond to localized or periodic toroidal vortices, which travel slightly slower than the maximum laminar flow speed U 0 , i.e. V ≃ 0.77. For N = 2, Fedele (2012) [12] showed that the vortical structures are localized near the wall (wall vortexon, B 1 and B 2 have the same sign) or wrap around the pipe axis (centre vortexon, B 1 and B 2 have opposite signs). They have a non-zero streamwise mean, but they radially average to zero to conserve mass flux through the pipe. The wall vortexon is the axisymmetric analogue of the 2-D rolls+streaks stage of the selfsustaining process (SSP) of Waleffe [37,[START_REF] Waleffe | Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process[END_REF]38] in Couette flows (see also [START_REF] Gibson | Visualizing the geometry of state space in plane Couette flow[END_REF]) or that of [START_REF] Wedin | Exact coherent structures in pipe flow: travelling wave solutions[END_REF] [START_REF] Wedin | Exact coherent structures in pipe flow: travelling wave solutions[END_REF] in pipe flows (see also Hof et al. 2004). Instead, centre vortexons may be related to the inviscid neutral axisymmetric slug structures discovered by [START_REF] Walton | The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes[END_REF] in unsteady pipe flows, which are similar to the centre modes proposed by [START_REF] Smith | On Displacement-Thickness, Wall-Layer and Mid-Flow Scales in Turbulent Boundary Layers, and Slugs of Vorticity in Channel and Pipe Flows[END_REF] [START_REF] Smith | On Displacement-Thickness, Wall-Layer and Mid-Flow Scales in Turbulent Boundary Layers, and Slugs of Vorticity in Channel and Pipe Flows[END_REF].

In the following we will confirm Fedele's theoretical results by computing numerically TWs of the inviscid form of the KdV equations (2.5).

Cnoidal waves and vortexons

Consider the ansatz B j = q j +F j (z-ct), where q j are free parameters and c is the velocity of the TW (here both c an q j are normalized with respect to the maximum laminar velocity U 0 ). We make use of the Petviashvili method [32, 46] to solve numerically the nonlinear steady problem for F j (in the moving frame zct). This numerical approach has been successfully applied to derive TWs of the spatial Dysthe equation [START_REF] Fedele | Hamiltonian form and solitary waves of the spatial Dysthe equations[END_REF] and the compact Zakharov equation for water waves [14].

The Petviashvili method converged to both wall and centre localized TWs (solitons or solitary waves) in the range of parameters c ∼ [0.62, 0.68] and q j = q ∼ [0, 0.9]. The generic topology of the flow structure of the TW disturbance is the same as that of the theoretical counterpart derived by [START_REF] Fedele | Travelling waves in axisymmetric pipe flows[END_REF] [12]: toroidal tubes of vorticity localized near the pipe boundaries (wall vortexon, see Figure 1 ) or that wrap around the pipe axis (centre vortexon, Figure 2). In particular, the two-component wall vortexon is compared against the three-component counterpart in Figure 1, which reports the streamlines of the perturbations. As one can see, the topology of the two vortical structures is similar.

It appears that as N increases the effects of the higher modes tend to somewhat diminish, but a rigorous proof of this statement is far beyond the scope of this work. We just point out that the proper theoretical framework for such a proof is provided by slow-manifold type theorems (see, for example, [7]).

Vortexon dynamics

Hereafter, we investigate the dynamical evolution of a localized disturbance under the two-component KdV dynamics with dissipation (see, equation (2.5)). To do so, we exploit a highly accurate Fourier-type pseudo-spectral method that is described in Fedele & Dutykh (2012) [14]. Figure 3 depicts snapshots of the two-component KdV solution at different times and the streamlines of the associated vortical structures are shown in Fig. 4, (Re ∼ 5000). The waveform of each component initially steepens up to a limiting shape and then breaks into a soliton and radiative waves as a result of the competition between the laminar-flow-induced wave dispersion and the nonlinear energy cascade associated to the KdV nonlinearities. In physical space we observe a compression of the initial vortical structure that splits in to a centre vortexon and patches of vorticity in the form of weak wall vortexons. On the simulated time scales, the flow evolution is basically inviscid, but it eventually decays on the long time scale t ∼ O(Re 6.25 ), due to viscous effects (see [12]). The centre vortexon arises due to a radial flux F (ω) θr ∼ uω θ of azimuthal vorticity ω θ = -1 r Lψ from the wall to the pipe axis. This is the 'inverse cascade' mechanism of cross-stream vorticity identified by [START_REF] Eyink | Dissipative anomalies in singular Euler flows[END_REF] [10] in channel flows. The patches of radiated near-wall vorticity may further split causing a proliferation of centre and wall vortexons until viscous effects attenuate and annihilate the splitting process. The formation of a 'vortexon slug' is clearly seen in Figure 5, which reports the space-time plot of the difference β = B 1 -B 2 of the two wave components. Here, larger values of β trace centre vortexons (B 1 and B 2 have opposite sign), whereas smaller values of β are associated to wall vortexons (B 1 and B 2 have the same sign). The streamlines of the associated flow perturbation at different times are shown in Figure 6. Note that the evolution is similar to that of puff splitting observed in the spreading of pipe turbulence at transition [2]. Here, turbulence arises as a competition between puff decay (death) and puff splitting (birth) processes. A turbulence state can persist only when new puffs are produced faster than their decay. Instead, the proliferation of centre vortexons is mostly inviscid and due to the competition between dispersion and steepening of radial structures (the eigenmodes φ j (r)) that are advected and dispersed in the streawise direction by the laminar flow. Clearly, it is a bit of a stretch to identify vortexon slugs as the realistic ones observed in experiments, which also have a substantial non-axisymmetric component. However, similarly to the inviscid neutral modes found by [START_REF] Walton | The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes[END_REF] [40], centre vortexons most likely are unstable to non-axisymmetric disturbances, and may persist viscous attenuation as precursors to puffs and slugs.

Conclusions

In the limit of small and long-wave disturbances the axisymmetric Navier-Stokes equations for non-rotating pipe flows reduce to coupled KdV equations. In the inviscid limit they support analytical cnoidal solitary waves as proven by Fedele [15]. These theoretical results are in agreement with numerical solutions of TWs constructed using the Petviashvili method. The associated flow structures are toroidal vortices that travel slightly slower than the maximum laminar flow speed, and they can be localized near the wall (wall vortexon) or wrap around the pipe axis (centre vortexon).

We have also investigated numerically the evolution of a perturbation in accord to the KdV dynamics. We found that it evolves into a 'slug' of centre vortexons that split from patches of near-wall vorticity due to a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with [START_REF] Eyink | Dissipative anomalies in singular Euler flows[END_REF] [10]. The centre vortexon is similar to the inviscid neutral mode found by [START_REF] Walton | The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes[END_REF] [40], and it could be a precursor to puffs and may relate to the formation of a slug structure in pipe flows.

Finally, we wish to emphasize the relevance of this work to the understanding of transition to turbulence. For chaotic dynamical systems the periodic orbit theory (POT) in [START_REF] Cvitanović | Periodic orbit expansions for classical smooth flows[END_REF] [6] and [START_REF] Cvitanović | Dynamical averaging in terms of periodic orbits[END_REF] [5] interpret the turbulent motion as an effective random walk in state space where chaotic (turbulent) trajectories visit the neighborhoods of equilibria, travelling waves, or periodic orbits of the NS equations, jumping from one saddle to the other through their stable and unstable manifolds [START_REF] Wedin | Exact coherent structures in pipe flow: travelling wave solutions[END_REF]25,[START_REF] Kerswelll | Recurrence of travelling waves in transitional pipe flow[END_REF][START_REF] Gibson | Visualizing the geometry of state space in plane Couette flow[END_REF]. Non-rotating axisymmetric pipe flows do not exibhit chaotic behaviour (see, e.g., [31,42]), and so the associated KdV equations (even with dissipation). However, forced and damped KdV equations are chaotic and the attractor is of finite dimension

Figure 1 .

 1 Figure 1. Wall vortexon: (top-left) streamlines of the three-component KdV solution and (bottom-left) velocity profiles of the perturbed (solid) and laminar (dash) flows; (right) two-component KdV counterpart (c = 0.68, q = 0.1). (see, for example, [4, 21]). Thus, the study of the reduced KdV equations associated to forced axisymmetric Navier-Stokes equations using POT may provide new insights into the nature of slug flows and their formation.

Figure 2 .

 2 Figure 2. Centre vortexon: (top) streamlines of the three-component KdV solution and (bottom) velocity profiles of the perturbed (solid) and laminar (dash) flows (c = 0.62, q = 0).

Figure 3 .

 3 Figure 3. KdV dynamics of a perturbation: wave components B 1 (solid) and B 2 (dash) at different instants of times (Re = 5000, speed of the reference frame c 0 = 0.62).

Figure 4 .Figure 5 .

 45 Figure 4. KdV dynamics of a perturbation: streamlines of the vortical structures associated to the wave components B 1 and B 2 in Fig. 3.

Figure 6 .

 6 Figure 6. Long-time evolution of a perturbation: streamlines of the vortical structures associated to the wave dynamics of Fig. 5. The snapshot times from top to bottom are t = 10.2, 20.1, 30.3 and 65.5 respectively.

Acknowledgements F. Fedele acknowledges the travel support received by the Geophysical Fluid Dynamics (GFD) Program to attend part of the summer school on "Spatially Localized Structures: Theory and Applications" at the Woods Hole Oceanographic Institution in August 2012. D. Dutykh acknowledges the support from ERC under the research project ERC-2011-AdG 290562-MULTIWAVE.


Maxence Soumare

Vitting Jørgen

Francis Andersen

Alain Bouchard

Dominique Elkaim

Justin Guegan

Michel Leroux

Lars Miniconi

Stentoft

Jørgen Vitting Andersen
email: jorgen.vitting.andersen@gmail.com

Francis Bouchard

Alain Elkaim

Dominique Guégan

Justin Leroux

Michel Miniconi

Lars Stentoft

A theoretical framework for trading experiments

Keywords: decision making, game theory, complex systems theory, technical analysis, rational expectations

A general framework is suggested to describe human decision making in a certain class of experiments performed in a trading laboratory. We are in particular interested in discerning between two different moods, or states of the investors, corresponding to investors using fundamental investment strategies, technical analysis investment strategies respectively. Our framework accounts for two opposite situations already encountered in experimental setups: i) the rational expectations case, and ii) the case of pure speculation. We consider new experimental conditions which allow both elements to be present in the decision making process of the traders, thereby creating a dilemma in terms of investment strategy. Our theoretical framework allows us to predict the outcome of this type of trading experiments, depending on such variables as the number of people trading, the liquidity of the market, the amount of information used in technical analysis strategies, as well as the dividends attributed to an asset. We find that it is possible to give a qualitative prediction of trading behavior depending on a ratio that quantifies the fluctuations in the model.

INTRODUCTION

In order to gain new insight on how investors perceive investment possibilities as well as risks in financial markets, it appears important to confirm not only the background of theoretical studies on human decision making, but also to get knowledge from controlled experiments, where one can probe in detail the different assumptions of investment behavior. It is only recently that experimental Finance has begun to appear as a well-established field, the interest in particular sparked by the recognition in terms of the attribution of the Nobel Prize in Economics to Vernon Smith in 2002. However, so far the major part of experimental work in Finance has assumed (Vernon Smith included) human rationality and the ability of markets to find the proper price close to an equilibrium setting. Contrary to this approach Behavioural Finance takes a more practitioner-minded description of how actual decision making takes place in financial markets. It would therefore seem like a very natural approach to bridge the insight gained from Behavioral Finance and apply it to experiments done on financial markets. Interestingly, not much effort has been done in this direction. The main reason is maybe because the major part of research done in Behavioural Finance is concerned with how individual decision making takes place (Prospect Theory included [START_REF] Tversky | Judgment under uncertainty: heuristics and biases[END_REF], [START_REF] Kahneman | Prospect theory: an analysis of decision under risk[END_REF], and [START_REF] Tversky | Loss aversion in riskless choice: A reference-dependent model[END_REF] )) and in a static setting, whereas price setting in financial markets is clearly an aggregate and dynamic phenomenon. Documents de Travail du Centre d'Economie de la Sorbonne -2012.83 The efforts in this paper should be seen from such a viewpoint. Our theoretical foundation is based on a complex systems approach that places emphasis on social learning and group behaviour in order to understand the price formation in financial markets. The idea is that financial market participants are connected through their impact on the price as well as through the percolation of information through the group of market participants. For instance, "shocks" created by a large liquidation of a given market participant can have future impacts on the decision making of other market participants who in turn follow a similar decision to liquidate their positions. In the context where both dynamic behaviour as well as social learning and group behaviour are relevant, tools from complexity theory are particularly appealing, including for example agent-based modeling and game theory as presented here.

We are especially interested in discerning between two different moods (or states) of the population of investors, corresponding to i) investors using fundamental investment strategies as in the case of rational expectations and ii) the emergence of a speculative bias as seen in certain cases when investors use technical analysis strategies. The rational expectations case i) has been studied extensively in a large number of experiments under various situations and with different constraints [START_REF] Smith | An experimental study of competitive market behavior[END_REF], [START_REF] Smith | Experimental auction markets and the Walrasian hypothesis[END_REF], [START_REF] Plott | An experimental examination of two exchange institutions[END_REF]Smith (1978), Coppinger et al. (1980), [START_REF] Hommes | Expectations and bubbles in asset pricing experiments[END_REF]). In the simplest setup, which is included in our theoretical description further below, people trade shares of a given company based on their expectations of future dividends of the company. Throughout the experiment such expectations change due to the arrival of new information. The experiment ends with the closure of the company and the payout of the dividends to the participants in the experiments. It should be noted that in this case there is no incentive for the participants to speculate on the price itself since the full price of the company reflects the expected dividends payout at the end of the experiment. A case study was done for the opposite situation where expectations about dividends do not play any role, and reported in [START_REF] Roszczynska-Kurasinska | Short and long term investor synchronization caused by decoupling[END_REF]. In this experiment only the price was available for the investment decisions of the group of participants. However as was shown in [START_REF] Roszczynska-Kurasinska | Short and long term investor synchronization caused by decoupling[END_REF] , it requires coordination among the participants to profit from a speculation bias in this kind of experiments.

It should be noted that our approach differs from most of the Behavioral Finance/bounded-rationality literature in that the phenomena we study can only be understood by looking at the system level. In other words, although the phenomena that emerge depend on microscopic features of the agents, it is important to not only look at individual characteristics but to study the system as a whole. The state of the system (speculative or fundamentalist) is the macroscopic result of many microscopic decisions. We shall refer to this collective "choice" of the state of the system as "aggregate decision making".

Our setup is conducive to answering a number of well-defined questions-that of how prices form, for instancethat the Rational Expectations Hypothesis (REH), or even the bounded REH cannot address. Once one mixes in the two ingredients that are the asset price and the dividends, the situation becomes ambiguous: REH suggests agents should make their trading decisions based on dividends, but the matter becomes far from trivial once the price of an asset and an end date are factored in. Are decisions based on the price of the asset in anticipation of future price behavior (speculative state), or are dividends the only drivers of agents' trading decisions (fundamentalist state)?

In the following we introduce theoretical foundations encompassing the occurrence of both the speculative and the fundamentalist state. We do so by considering the "Dollar Game" (or "$-Game"), which is an investment game that combines the two key ingredients that are dividends and the asset price (Vitting [START_REF] Andersen | The $-game[END_REF]) . Although simple in principle, the $-Game yields rich system dynamics, the complexity of which can be acted upon by the choice of system parameters (memory length, liquidity, etc.). As will be seen, this thereby creates a dilemma in terms of the investment strategies of the participants. The pure cases i) and ii) will appear as special cases of the general theory.

This feature of the $-Game lends itself well to study using a general well-known theory of phase-transitions found in Physics: the Ginzburg-Landau theory (henceforth referred to as "the GL theory") which we describe later.

THE $-GAME

The $-Game was inspired by the Minority Game (MG) introduced in 1997 by Ye-Cheng Zhang and Damien Challet (Challet and Zhang (1997), Challet and Zhang (1998) as an agent-based model proposed to study market price dynamics [START_REF] Zhang | Modeling market mechanism with evolutionary games[END_REF], [START_REF] Johnson | Crowd effects and volatility in markets with competing agents[END_REF], [START_REF] Lamper | Predictability of large future changes in a competitive evolving population[END_REF] at the expense of trying to describe all aspects in detail. Similar to the Minority Game, the $-Game should be considered as a "minimal" model of a financial market. Formally, N players (or agents) simultaneously take part in a one-asset financial market over a horizon of T periods. At each period, t ≤ T , each player i chooses an action a i (t) ∈ {-1, 1}, where action "1" is interpreted as "buy" and action "-1" as "sell". Players are assumed to be boundedly rational, in the sense of using only a limited information set upon which to base decisions. In the version of the $-Game presented in this paper, the agents use two different types of investment strategies, technical analysis strategies and fundamental analysis strategies. Concerning the decision making related to technical analysis, each player observes the history of past price movements, which is limited to the size of their memory, m ∈ N. Each player has at his/her disposal a fixed number of s strategies which are randomly assigned at the beginning of the game. It follows that player i's, j'th strategy, a j i , is a mapping from the set of histories of size m to {-1, 1}. We denote by h(t) ∈ {0, 1} m the history vector that agents observe in period t before taking the action of either buying or selling an asset. We interpret "1" to represent an up move of the market (an increase in the asset price) and "0" corresponds to a down move of the market (a fall in the price of the asset). These assumptions are equivalent to having agents behave as technical analysts who use lookup tables to determine their next move. Table 1 shows an example of a strategy for m = 3:

A strategy therefore tells an agent what to do given the past market behavior. If the market went down over the last three days, the strategy represented in Table 1 suggests that now is a good moment to buy (000 → 1) in Table 1. If instead the market went down over the last two days and then up today, the same strategy suggests that now is a good moment to sell (001 → -1) in Table 1. While a single strategy recommends an action for all possible histories (of length m), we also allow for agents to adopt different strategies over time. Namely, agents keep a record of the overall payoff each strategy would have yielded over the entire market history (i.e. not limited to m periods prior) and use this record to update which strategy is the most profitable. In every time period agent i therefore choses the best strategy (in terms of payoff, see definition below) out of the s available. This renders the game highly non-linear: as the price behavior of the market changes, the best strategy of a given agent changes, which then can lead to new changes in the price dynamics. The action of the best strategy of agent i at time t, is denoted by a * i (t). We denote by (a * (t)) i ∈ {-1, 1} N ×T the action profile of the population, where a * (t) = (a * 1 (t), ..., a * N (t)) ∈ {-1, 1} N corresponds to the action played by the N agents in period t. The payoff π of the ith agent's jth strategy, a j i , in period t is determined as follows:

π[a j i ] = a j i (t -1) N k=1 a * k (t) (1)
The return r(t) of the market between period t and t + 1 is assumed to be proportional to the order imbalance N k=1 a * k (t):

r(t) = N k=1 a * k (t)/λ (2)
with λ a parameter describing the liquidity of the market. Therefore the payoff of a given strategy (1) can be expressed in terms of the return of the market in the next time period as: From (1) one can see that the payoff depends on two different times: the individual decision at time t -1 and the aggregate "decision" at time t. Such a feature of the payoff function is illustrative of real financial markets, where traders decide to enter a position in a market at time t -1, but do not know their return until the market closes the next day (time t). This is especially clear from (3) where it can be seen that the $-Game rewards a given strategy that at time t -1 predicted the proper direction of the return of the market r(t) in the next time step t. The larger the move of the market, the larger the gain/loss depending on whether the strategy properly/improperly predicted the market move. Therefore in the $-Game, agents correspond to speculators trying to profit from predicting the direction of price change.

π[a j i ] = a j i (t -1) λr(t) (3
In addition to technical analysis strategies that try to profit from price changes, we also consider strategies that try to profit from information of the fundamental value of an asset P f (t). P f (t) is determined entirely from future expectations about the dividends d(t) attributed to the asset at the end of the experiment. Whenever P (t) > P f (t) a fundamental strategy therefore gives the recommendation to sell, whereas if P (t) < P f (t) it recommends buying. Furthermore in order to take into account a diminishing use of such strategies in a purely speculative phase when the price P (t) >> P f (t), the probability to use a fundamental strategy is taken from a Poisson distribution γ exp (-γ) with γ = P (t)-P f d . To sum up, the $-Game as described in this article can be described in terms of just five parameters:

• N -The number of agents (market participants).

• m -The memory length used by the agents.

• s -The number of strategies held by the agents. It should be noted that the s strategies of each agent is chosen randomly (corresponding to a random column of '0's and 1's in table 1) in the total pool of 2 2 m strategies at the beginning of the game.

• λ -The liquidity parameter of the market.

• d(t) -The future expectations about the dividends paid at the end of the experiment. To simplify, d(t) will be taken constant in time t in this paper.

The dynamics of the $-Game are driven by nonlinear feedback because each agent uses his/her best strategy at every time step. As the market changes, the best strategies of the agents change, and as the strategies of the agents change, they thereby change the market. Formally one can understand such dynamics by representing the price history h(t) = m j=1 b(t -j + 1)2 j-1 as a scalar where b(t) is the bit representing the direction of price movement at time t (see table 1). The dynamics of the $-Game can then be expressed in terms of an equation that describes the dynamics of b(t) as:

b(t + 1) = Θ( N i=1 a * i (h(t))), (4)
with Θ a Heaviside function. The nonlinearity of the game can be formally seen from:

a * i (h(t)) = a {j|maxj=1,...,s{Π[a j i (h(t))]} i (h(t)), Π[a j i (h(t))] = t k=1 a j i (h(k -1)) N i=1 a * i (h(k)) (5)
Inserting the expressions (5) in expression (4) one obtains an expression that describes the $-Game in terms of just one single equation for b(t) depending on the values of the variables (m, s, N, λ, d) and the random variables a j i (i.e. their initial random assignments). A major complication in the study of this equation happens because of the non-linearity in the selection of the best strategy. For s = 2 however the expressions simplifies because one only need to know the relative payoff Marsili (1999), Challet, Marsili (2001) ). For this special case it was shown in Roszczynska-Kurasinska et al. ( 2012) that the Nash equilibrium for the $-Game with only technical analysis strategies (with no cash nor asset constraints) is akin to that of Keynes' "Beauty Contest" where it becomes profitable for the subjects to guess the actions of the other participants. The optimal state is then one for which all subjects cooperate and take the same decision (either buy/sell). Documents de Travail du Centre d'Economie de la Sorbonne -2012.83

q i ≡ π[a 1 i ] -π[a 2 i ] between two strategies (Challet,

GINZBURG-LANDAU THEORY

To describe further the competition between technical analysis trading strategies and fundamental analysis trading strategies as used in the $-Game, we suggest to borrow a description from Physics where different states of a system can be characterized via a so-called free energy F . F in that case plays a central role, since its minimum determines how the state of the system will appear. F can be written as F = E -T S with E the energy of the system, T the temperature and S the entropy which one can think of as representing how much disorder there is in a given system. From the definition of F we can see that the state of a system is determined by a struggle between two different forces, one representing "order", this is the E term, and the other term representing "disorder" given by the T S term. We suggest a similar struggle of "forces" to be present in the trading experiments.

The competition between order and disorder as described by F , can be understood in more detail by considering the example given by the Ising model, which is a model of ferromagnetism. For the Ising model the energy E = -J <i,j> s i s j with s i , s j representing the atomic "spins" of a material. The <>-notation in the summation indicates that the sum is to be taken over all nearest neighbors pair of spins. Each spin itself can be thought of as a mini magnet. In the two-dimensional Ising model the spin s i = 1 if the spin is "up" and s i = -1 if the spin is "down". Taking the coupling strength between spins J positive, the minimum energy E min of the system is simply given by either all spins up (s i ≡ 1), or all spins down (s i ≡ -1). For temperature T = 0 the minimum of the energy E is therefore also the minimum of the free energy F . However as soon as T > 0, the finite temperature will introduce fluctuations of the spins introducing thereby a non-zero contribution to the entropy S. The larger the temperature T the larger this tendency, until at a certain temperature T c above which order has completely disappeared -the system is in a disordered state. Order in the case of the Ising model is measured by the magnetism, which is just the averaged value of the spin m = E(s i ).

GL theory introduces the idea that we can in general understand such order-disorder transitions mentioned above by expanding the free energy in terms of the order parameter m. Specifically write:

F = C + am + αm 2 + bm 3 + β/2m 4 + ... (6)
Using now the symmetry argument that there should be no difference in the free energy between the two states with respectively either all s i ≡ 1 or s i ≡ -1, all odd order terms in m disappear in (6). Taking furthermore the derivative (in order to find its extreme) we end up with the equation at a minimum of F :

0 = m(α + βm 2 ) (7)
(7) has the trivial solution of the magnetization m = 0, this is the high temperature solution and describe the disordered state. Taking β positive, the other non-trivial solution happens for negative α, m 2 = -α/β. By writing α = (T -T C ) one sees that the magnetization scales as (T -T c) 1/2 for temperatures below T c . The exponent of 0.5 is the so called "mean field" or GL exponent of the transition. We now propose to consider in similar terms the competition in the trading experiments between profit from speculation obtained through trend-following, versus the tendency to destroy such trends due to mean reversion towards the fundamental price [START_REF] Andersen | Detecting anchoring in financial markets[END_REF]. The general tendency to create either a positive/negative price trend corresponds to "order" whereas either the lack of consensus or the mean reversion to the fundamental price value will destroy such order. To make the analogy with our discussion above, we introduce what one could call the "free profit" given by two terms F P = P -T S. P is the profit of the ordered state which for T = 0 corresponds to a continuous up/down trend of the market. S is an entropy term that destroys the ordered state, and T is the "temperature" which will be introduced below.

As discussed beforehand, the payoff of a strategy in the $-Game describes the profit for the given strategy. Agents in a Nash equilibrium are characterized by using the same strategy over time, therefore such a strategy has to be optimal. We can then write the total profit P for the system of traders in a Nash equilibrium of the $-Game as: We note the resemblance of ( 9) to the Ising model described above. One major difference with respect to the Ising model however is the "interaction" between traders, since (9) says that trader j's action at time t has an impact on trader i's profit from the action he/she took at time t -1. Therefore the "interaction" is seen to be "long-ranged" in ( 9) whereas the interaction is local (it only concerns nearest-neighbors) for the Ising model. Similar to (6) we can introduce an order parameter and expand the "free profit" in terms of this parameter. In the case of the Ising model the order parameter is given by the spatial average of the local order (the magnetization).

P (t) = i π[a * i ] (8) = N i=1 N j=1 a * i (t -1)a * j (t) (9
In the trading setup we suggest to consider the local order o expressed in terms of the order imbalance: o = 1/N N i=1 a * i which from ( 2) is seen to be proportional to the return. The parameter o varies between -1 (all agents decide to sell) and 1 (all agents decide to buy). In the case where one can neglect the dividends (the experiment described in Roszczynska-Kurasinska et al. ( 2012) o → ±1 so this corresponds to the complete ordered outcome. For the experiments performed under the assumptions of rational expectations the price converges to the fundamental price in the end of the experiments and we get o → 0 for t → t n with t n the duration of the experiment.

Applying now the GL idea and expanding F p in terms of o, one ends up with the very same conditions (7) to determine o, except that the extreme (extremes) now describes a maximum (maxima) instead of a minimum (minima) as was the case for F . Note that all odd order terms of o disappear since there is no difference in the profit that traders obtain in shorting the market compared to going long. Figure 1 illustrates the expansion of F p (y-axis) as a function of o (x-axis) for the two cases: i) the T > T c solution (i.e. the disordered state corresponding to no trend in the experiments o = 0) can be seen as the maximum of the solid line, whereas the two T < T c solutions (i.e. the ordered state corresponding to a certain trend in the experiments o = 0) can be found as the maxima of the dashed line.

One of the main implications of the GL theory is the existence of a nontrivial transition from a high "temperature" disordered state in the trading experiments where traders don't create a trend over time, to a low 'temperature" state characterized by trend following. A "temperature" can now be defined via the randomness of the model as will be explained in the following. Randomness enters the $-Game through the initial conditions in the assignments of the s strategies to the N traders in the game. In order to create a given strategy one has to assign randomly either a 0 or a 1 for each of the 2 m different price histories. Therefore the total pool of strategies increases as 2 2 m versus m. However many of these strategies are closely related -take e.g. table 1 and change just one of the 0's to a 1, this thereby creates a strategy which is highly correlated to the one seen in table 1. In Challet, Zhang (1997), Challet, [START_REF] Zhang | Modeling market mechanism with evolutionary games[END_REF], it was shown how to construct a small subset of size 2 m of independent strategies out of the total pool of 2 2 m strategies. As suggested in [START_REF] Savit | [END_REF] and Challet, Marsili (2000)) , a qualitative understanding of the MG can then be obtained by considering the parameter α ≡ 2 m N . However as pointed out in Zhang (1998) the ratio α ′ = 2 m N ×s seems intuitively to be more relevant since this quantity describes ratio of the total number of relevant strategies to the total number of strategies held by the traders. Taking into account the presence of a fundamental value strategy we therefore introduce the ratio T = 2 m +1 N ×s to describe the temperature in the simulations of the $-Game presented in the following. The relation of T to the fluctuations of the system becomes clear when one consider that when sampling the variance of a small sample is larger than the variance of a large sample (a fact called "the law of small numbers" in Psychology/Behavioral Finance [START_REF] Tversky | Judgment under uncertainty: heuristics and biases[END_REF], [START_REF] Kahneman | Prospect theory: an analysis of decision under risk[END_REF], [START_REF] Tversky | Loss aversion in riskless choice: A reference-dependent model[END_REF] ). Therefore when the sample of strategies held by the N traders is small with respect to the total pool of relevant strategies, this corresponds to the large fluctuations, large temperature case. Vice versa a large sample of strategies held by the N traders therefore corresponds to a small temperature case as seen from the definition of T .

RESULTS

Figure 2 shows three different results representing typical market behavior corresponding to fundamental price behavior, as well as speculative behavior in an increasing/decreasing market. Figure 3-4 show histograms representing respectively speculative behavior (blue) or fundamentalist behavior (red) as outcomes in a setup of the $-Game corresponding to a trading experiment with given realizations of the 5 parameters (N, m, s, λ, d). The histograms in figure 2 represents simulations performed with s = 2 whereas the histograms in figure 3 were done for simulations with s = 18. The different histograms were obtained from an ensemble average of 200 simulations of the $-Game where each realization of the game were run for up to 200 * 2 m time steps. A speculative state was determined whenever m successive price changes had occurred whereas a fundamental state was characterized by Documents de Travail du Centre d'Economie de la Sorbonne -2012.83 the price fluctuation within a 50 percentage range of the fundamental value P f . White in the figures represents the cases where neither a definite speculative nor fundamental state could be defined.

We first notice the somewhat surprising fact that the dividends d as well as the liquidity of the market λ, only seem to have a quite limited impact on the final state of the market. In particular for the smallest m values (m = 3, 5) increasing dividends appear to have a somewhat stabilizing effect allowing for slightly more fundamental value states. The same stabilizing trend appears to be at play as one increases the liquidity of the market, but again, this tendency appear to be very weak. A much clearer tendency is seen with respect to increasing speculation when increasing the number of traders N , respectively decreasing the amount of information m used in the decision making of the technical analysis trading strategies. A larger number of strategies s assigned to the traders is also seen to enhance speculation (compare figure 3 and figure 4).

One of our main results is that a qualitative behavior of a trading experiment can be predicted depending on the given value of T . In particular with respect to expectations about the outcome in an experimental setup of the market model, such an understanding is important (Bouchard et al. 2012). The fact that T determines the outcome of trading behavior can be seen by changing the nominator and denominator by the same factor, which then should lead to invariant behavior in terms of trading decisions. This means that for example the (m = 3, N = 11) (i.e. T = 0.72/s) trading behavior for a given λ and s should fall in between the (m = 5, N = 101) (i.e. T = 0.32/s) and (m = 8, N = 101) (i.e. T = 1.27/s) cases. From figure 2 and figure 3 this is seen indeed to be the case. Similarly comparing figure 3-4 it is seen that increasing (/decreasing) N and decreasing (/increasing) s by the same amount leads to two systems behaving similarly in terms of investment profile (compare N = 101 rows in figure 3 to N = 11 rows in figure 4) . These results underscore the importance of the parameter T when it comes to the understanding of the aggregate decision making in the model.

CONCLUSION

A general framework has been suggested to describe the human decision making in a certain class of experiments performed in a trading laboratory. Our framework allows us to predict the outcome of such type of trading experiments in terms of when to expect a fundamental versus a speculative state. We have shown how a qualitative understanding could be found depending on just one parameter, representing the fluctuations of the model. Our findings give certain guidance with respect to the implementation of trading experiments performed in a trading laboratory (Bouchard et al. (2012)).

)

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.83

)

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.83

  FIG.1: Illustration of the "Free Profit" Fp as a function of the order parameter o for two different "temperuatures" corresponding to T > Tc (solid blue line), and T < Tc (dashed green line) respectively.

  ). The MG was introduced following a leading principle in Physics, that in order to solve a complex problem one should first identify essential factors Documents de Travail du Centre d'Economie de laSorbonne -2012.83

	history, h(t) action, a j i (t)
	000	1
	001	-1
	010	-1
	011	1
	100	-1
	101	-1
	110	1
	111	-1
	Example of a strategy


Kristel Jacquier
email: kristel.jacquier@univ-paris1.fr

Public Support for European Integration: A comparative analysis

Keywords: European integration, political economy, globalization, survey research Intégration européenne, économie politique, mondialisation, données d'enquêtes. JEL Classification: P16, F55, C25

This paper proposes to study how socio-economic characteristics shape preferences in European matters. It is assumed that social groups threatened by liberalization tend to be more euro-skeptical than others. This hypothesis is tested using individual-level data from two rounds of the European Social Survey. Controlling for national fixed effects and income, we focus on variables of occupational status (International Standard Classification of Occupations ISCO-88, and current occupation). Finally, we include a variable of subjective partisan affiliation to make sure that our results are not concealing a left/right positioning. We argue that the economic status of agents plays a crucial role in explaining crosssectional variations in public support for the European process in each member state. Additionally, the partisan affiliation confirms that in European matters, socio-economic forces are not a mere reflection of the left/right spectrum.

Soutien à l'intégration européenne: une analyse comparative

Résumé:

Le présent article propose une étude des déterminants socio-économiques du soutien à l'intégration européenne. A l'aide des données Enquêtes Sociales Européennes, nous testons l'hypothèse selon laquelle les groupes sociaux qui craignent les effets de la libéralisation auront également tendance à être méfiants vis-à-vis de l'intégration européenne. Nous nous focalisons sur les variables d'emploi (CSP, statut d'emploi actuel, syndicalisation) en contrôlant par le revenu et le pays d'origine. Une variable de positionnement subjectif sur l'échelle gauche/droite est introduite afin de s'assurer que nos résultats ne dissimulent pas une affiliation partisane. Les résultats obtenus prouvent que le statut économique des agents est une variable déterminante pour expliquer les préférences des européens et souligne l'importance de l'intégration européenne comme dimension politique.

Introduction

A vast literature in political science has attempted to identify the main deterrents of public support for the European Union. This goes from economic benefits at the macro or micro level [START_REF] Eichenberg | Europeans and the European Community: The Dynamics of Public Support for European Integration[END_REF][START_REF] Anderson | The Dynamics of Public Opinion toward European Integration, 1973-1993[END_REF][START_REF] Gabel | Understanding Variation in Public Support for European Integration[END_REF] to purely cultural factors [START_REF] Mclaren | Public support for European integration: cost/benefit analysis or perceived cultural threat?[END_REF][START_REF] Medrano | Framing Europe: Attitudes to European Integration in Germany, Spain, and the United Kingdom[END_REF] or contextual variables [START_REF] Brinegar | Location, Location, Location: National Contextual Factors and Public Support for European Integration[END_REF] ; Sánchez-Cuenca, Ignacio, 2000). The question has never been settled; therefore it is reasonable to think that several influences work together. As a contribution to the existing literature, this paper proposes to study how socio-economic characteristics shape preferences in European matters. Using individual-level data from two rounds of the European Social Survey, a cross-country analysis is conducted on two samples: the fifteen original EU members, and post communist countries.

In international economic relations, integration is defined as « the gradual elimination of economic frontiers between independent states. As a result the economies of these states end up functioning as one entity » (W. [START_REF] Molle | The Economics of European Integration: Theory, Practice, Policy[END_REF]. This theoretical framework makes clear that European integration is an on-going process.

During the 1950s and the 1960s, a permissive consensus [START_REF] Lindberg | Europe's Would-Be Polity[END_REF] existed in Europe. A large majority of citizens displayed a tacit support for the European process.

Because of such public disinterest, political elites have been able to pursue their own policy interests. After the signing of the Single European Act (SEA) in 1986, citizen support for European integration started to rise and reached a peak in 1991. By then the European integration was considered a purely economic arrangement that brought about macro-economic stability and -to some extent-prosperity.

In the aftermath of the Maastricht Treaty, public opinion was confronted to a more complex situation. The political jurisdictions of the European Union (EU) were extended; the Union now had a word to say in social policy, environmental and defense matters. The year 1992 witnessed a sharp drop in public support. Since then, public opinion on European membership has stabilized to a sizeable minority of supporters (the rest being hostile or indifferent 1 ). In the present day, further integration of the Union boils down to reinforcing constraints. As for development plans, the European Council focuses mainly on deepening competition and liberalization, and calls for structural reforms (see [START_REF] Amable | The Lisbon strategy and structural reforms in Europe[END_REF] about the Lisbon strategy).

The free market is constantly re-enforced while social objectives are relegated to the background [START_REF] Amable | Changing French Capitalism: Political and Systemic Crises in France[END_REF].

In this study, we focus on two motives of distrust towards the EU: the economic liberalization process and the loss of sovereignty [START_REF] Beckfield | Remapping Inequality in Europe: The Net Effect of Regional integration on Total Income Inequality in the European Union[END_REF][START_REF] Beckfield | European integration and income inequality[END_REF]; [START_REF] Kvist | The Europeanisation of social protection[END_REF] de [START_REF] Vries | Interests, identity and political allegiance in the European Union[END_REF]. It can be argued that the political agenda of the Union has become more and more detrimental to the low skilled workers on the labor market 2 , which leads them to be decreasingly supportive of further integration. Adopting a political economy viewpoint we focus on the distributive consequences of European integration. The paper is organized as follows. Section 2 presents the literature. In Section 3, we describe the methodology. Section 4 exposes the empirical results and section 5 concludes the analysis.

Literature

"Citizens are at the core of the European construction: the Union has the imperative to respond concretely to their needs and concerns", as evidenced by this declaration of The European Council in 1996, further integration requires a strong political support. Thus analysts (especially political scientists) attempt to identify what are the main deterrents of public support for the European Union [START_REF] Keohane | Conclusion: Community politics and institutional change[END_REF].

Several studies make the case that citizens evaluate the EU based on macroeconomic performances [START_REF] Eichenberg | Europeans and the European Community: The Dynamics of Public Support for European Integration[END_REF][START_REF] Anderson | Economic Benefits and Support for Membership in the E.U.: A Cross-National Analysis[END_REF][START_REF] Gabel | Understanding Variation in Public Support for European Integration[END_REF]. This is far from surprising since the founders of the European Union justified the integration in terms of welfare gains from trade. The economic performances are still essential today through the ability of the Union to provide price stability. Nevertheless the explanatory power of macro-economic predictors have largely decreased over time, and will not be considered in the present analysis.

Another field of research focuses on micro economic calculations. Gabel (1998) models the personal potential to gain from trade liberalization. He measures the relative competitiveness of individuals based on their occupation. And so does the present article. Bruno Cautrès and Gérard Grunberg (2007) also emphasize an "elitist bias", they demonstrated that more educated and higher-income individuals are more in favor of European integration. As previously introduced, the signing of the Maastricht Treaty coincides with the drop in Public Support for the EU. [START_REF] Eichenberg | Post-Maastricht Blues: The Transformation of Citizen Support for European Integration, 1973-2004[END_REF] argue in favor of a causal relationship and document it. Before Maastricht, the Union was limited to economic purposes. The treaty expands the number of policy areas for which the EU has some responsibility and strengthens the powers of the European Parliament. It is a political shift. They consider Maastricht as a "system transforming event that dramatically altered the nature of the integration process". The authors emphasize that many citizens want to preserve their national arrangements, notably social protection. Indeed Eurobarometer data show that the higher the social expenses, the least citizens support EU action on health and social security. They also insist on the influence of the Economic and Monetary Union (EMU) and its budgetary implications. Citizens dependent on state generosity could fear further integration. They argue that, since Maastricht, the politics of European integration are animated by distributive concerns. The present study is in line with this view. Indeed, even though total income inequality in the EU has declined, within-country income inequalities have increased (Beckfield 2009 3 ), suggests that there are winners and losers of further regional integration. [START_REF] Beckfield | European integration and income inequality[END_REF] provides three arguments to explain why regional integration (both economic and political) should raise income inequality: workers are exposed to international competition, labor unions are weakened and market-oriented EU polities should drive welfare state retrenchment. [START_REF] Kvist | The Europeanisation of social protection[END_REF] precisely investigate the constraining effect of European integration on national welfare states (notably through the EMU). We use the political allegiance argument to assume that support for Europe is low when citizens see the EU as preventing their national regimes from providing the expected level of social protection (de Vries and Kersbergen 2007, 313).

Labor market or social protection policies are at the very root of socio-political compromises that funded post-war European economies. The convergence towards the median redistribution level in Europe would unsettle institutional arrangements. According to Hall and Soskice varieties of capitalism (2001), in liberal market economies (LMEs) more redistribution would cause a raise in taxation and job losses, whereas in coordinated market economies (CMEs) less redistribution would decrease job protection, and lessen investment in specific skills [START_REF] Iversen | An Asset Theory of Social Policy Preferences[END_REF]. As a result European integration might be destabilizing within both types of capitalism.

A more recent field of research focus on contextual variables and especially how national variables can reinforce or mitigate the impact of previously cited determinants. [START_REF] Brinegar | Location, Location, Location: National Contextual Factors and Public Support for European Integration[END_REF] intend to comprehend what they call the "socio-tropic evaluations of the effects of European integration on national capitalism". In their study, the skill level is taken into account through the frame of national factor endowments and varieties of capitalism. They follow Scheve (2000) and use the Heckscher-Ohlin model of factor endowment to predict that in countries relatively well endowed with skilled workers, skilled workers should support integration while less-skilled workers should oppose it. [START_REF] Scheve | Comparative Context and Public Preferences over Regional Economic Integration[END_REF], focus on the degree of wage bargaining centralization. He argues that centralized wage bargaining tends to reduce wage inequality. Thus the distributive consequences of integration are mitigated and individuals are less threatened by European Integration. Finally, we use the cleavage theory [START_REF] Lipset | Cleavage Structures, Party Systems and Voter Alignments: An Introduction[END_REF] in order to draw a multidimensional analysis (both cross national and cross sectional variations are taken into account). This theory distinguishes two types of cleavages. The national level that results from the country economic context (i.e. historical and cultural factors mainly) and the socioeconomic level: social divides, class conflicts or some new subdivisions (post-materialism 4 , age, education or access to information). According to Inglehart, post-materialist people should support Europeanization. Such an hypothesis won't be tested here because of the lack of empirical validation in previous studies [START_REF] Janssen | Postmaterialism, Cognitive Mobilization, and Support for European Integration[END_REF]Gabel, 1998a). Furthermore the decline in left/right partisanship announced by post-materialists has no empirical foundation (Amable 2007). J. [START_REF] Janssen | Postmaterialism, Cognitive Mobilization, and Support for European Integration[END_REF] and [START_REF] Anderson | Economic Benefits and Support for Membership in the E.U.: A Cross-National Analysis[END_REF] both criticize the idea that the nation state represents materialist value. Following [START_REF] Anderson | Economic Benefits and Support for Membership in the E.U.: A Cross-National Analysis[END_REF] we assume that the European Union is a purely economic enterprise. The nation state tends to consider noneconomic goals when the European Union does not.

All of the studies previously mentioned focus on western Europe, the preferences of postcommunist countries are far less documented. In a study of five transitional countries (Czech Republic, Estonia, Hungary, Poland, and Slovenia) Cichowski (2000) emphasizes three main determinants of public support for EU membership: satisfaction with democracy, promotion of free market and party cues. [START_REF] Tucker | Transitional Winners and Losers: Attitudes toward EU membership in Post-Communist Countries[END_REF] confirms that free market supporters welcome European integration. They also use individuals' self-assessments of economic progress to ascribe "winner" and "loser" statuses, and regard it as the best predictor of support for EU membership.

Empirical strategy

Data

The analysis is based on the European Social Survey (ESS) dataset. The program was launched by the European Science Foundation (ESF) and designed to compare social attitudes and values across European countries. We focus on the last two rounds of the cross-sectional survey: ESS3 (2006) and ESS4 (2008), merged together into one dataset. The ESS provides a large data sample (at least 1,500 respondents per country) and employs the most rigorous methodologies. [START_REF] Kohler | Surveys from Inside: An Assessment of Unit Nonresponse Bias with Internal Criteria[END_REF] describes the ESS as the most reliable data for international comparisons. We use the question survey below as a proxy to measure public support for the European Union:

* "Unification" refers to further integration rather than further enlargement

Even though the scale is not a straightforward response, we expect the respondents who support further integration to give a number between 7 and 10, and those reluctant to the EU to answer under 4. That's why we reduced the variable to three ordinal categories. Using such dependent variable it is assumed that further integration reveals support for the political agenda of the Union when the survey was made. I argue that some individuals might consider unification of Europe as a positive step but are dissatisfied with the course of negative integration5 (Scharpf, 1999).

Two groups were defined in order to capture national characteristics 6 . The EU 15 states (the members of the EU prior to the eastern enlargements in 2004 and 2007) the new member states (also called post-communist countries). Among the EU 15 states, the study encompasses Germany, Austria, Belgium, Denmark, Spain, Finland, France, Great Britain, Greece, Ireland,

The Netherlands, Portugal and Sweden. As far as post communist countries (2004 enlargement and afterwards) are concerned, Bulgaria, Czech Republic, Hungary, Estonia, Latvia, Poland, Romania, Slovenia and Slovakia are included. The appendix provides descriptive statistics.

Econometric specification

Because the dependent variable of the model encompasses discrete choices that can be ordered we run an ordered logit regression. As we have seen in the previous section, the eleven original categories (from 0 to 10) were re-coded to three.

The estimated equation can be defined as:

* D + C i i i i i i y         
 ,  ,  ,  and  are parameters to be estimated and * i y is the latent variable, i.e. the intensity of the support for the European integration. D is a vector of individual sociodemographic characteristics (age and gender). E measures the socioeconomic position of individuals (ISCO classification, employment status and employment relation). C is a country dummy which accounts for any omitted country-specific influence. P stands for partisanship and  is the error term.

We do not observe * i y , but a variable i y that goes from 0 to 10 and rises when public support for the European Union rises:

8 if * 1 j i j y     

For

Where j  are thresholds, with and Only the sign and the significance of the coefficient can be interpreted [START_REF] King | Making the Most of Statistical Analyses: Improving Interpretation and Presentation[END_REF].

To facilitate the interpretation of the results, odd ratios are provided instead of coefficients. Odd ratios allow to compare dummy variables in a meaningful way (within the same regression, the magnitude of coefficients is comparable). For example, an odd ratio of 0.5 for the dummy variable "female" means that, holding all other variables constant, the odds of having more negative attitudes toward European integration are half as large for women as for men.

Assumptions

Citizens consider (or experience) distinct benefits from the European Union membership.

As mentioned before, two motives of distrust towards the EU can be suggested: the economic liberalization process and the loss of sovereignty. The second motive is linked to the EMU. Its implementation exacerbated worries about European issues. From then on, not only was the European Central Bank delegated the sole authority to conduct monetary policy, budgetary policy would be constrained by the Stability and Growth Pact. Thus countries which adopted the EMU have to bear constraints on both monetary and budgetary policies. And for the others, "more integration" might stand for the adoption of the common currency; so citizens who fear a loss of sovereignty are unlikely to call for more European integration.

Considering those issues, it is reasonable to expect less competitive citizens to fear both a cut in government spending and a surge in labor market flexibility. worker. Opportunities exist for those skilled enough to compete in the European market so we expect the manual laborers to be less supportive of the European integration. In the end we test whether social groups threatened by liberalization tend to be more euro-skeptical.

Then we focus on particular statuses: being unemployed, self-employed, or part of a trade union. We expect the unemployed to be hostile to liberalization as they rely on social transfers.

However, Esping-Andersen (1999) emphasize that some outsiders are interested in economic policies that maximize their likelihood of finding a job. Some unemployed people might picture the EU as a land of opportunity. We intend to figure out whether or not unemployed people express distinct preferences from the other respondents. On the opposite self employed should welcome a liberal market and low levels of social transfers [START_REF] Iversen | An Asset Theory of Social Policy Preferences[END_REF][START_REF] Guillaud | Preferences for redistribution: an empirical analysis over 33 countries[END_REF]. We use a three-category variable to assess whether or not the employment relation has an impact on European preferences: wage earners are the reference category and the others are self employed and employed in a family business. Using a dummy variable we test trade union membership. Trade union members are supposed to be more informed about the risks of liberalization for low-skilled workers and should be opposed to it.

Finally, a variable of subjective partisanship is included. We do not have any strong prior expectations regarding the effects of such variable; we use it as a control. Socioeconomic characteristics determine partisanship (Gabel, 1998) so we want to make sure that the previous results are not concealing a left/right positioning.

Some usual controls are included: gender, age, country dummies. A dummy for the round of the European Social Survey is added in order to make sure that the fusion of rounds 3 and 4

does not bias the estimators. The education level is not presented here because the ISCO classification already provides such information. However we run the estimates with the education level instead of the ISCO variable and we find the same result as in the literature: The more educated individuals are, the more they favor European integration (with a few exceptions among new member states, like Bulgaria for example). The main assumptions hold for post-communist countries (the literature suggests that in those countries, the most successful individuals promote EU membership. [START_REF] Tucker | Transitional Winners and Losers: Attitudes toward EU membership in Post-Communist Countries[END_REF] evaluate winners and losers thanks to a self-assessment variable while socio economic characteristics are used here). However it is useful to separate the two groups so as to capture specific traits. There are good reasons to believe that the variables take on a different meaning in new member states, and that some variables stand out more sharply. First the factor endowment model predicts that individuals whose factor is abundant welcome liberalization while scarce factors oppose it, and it appears to us that the skill endowment in eastern Europe is different from western countries. Secondly we expect the partisanship variable to work differently. Indeed euro skeptical political parties are nationalist parties in both western and eastern countries, but in eastern Europe they are traditionally close to the communist party. Consequently, euro skeptical individuals in post-communist countries are likely to self-position to the very left of a left-right scale.

Estimation results

Cross-sectional analysis

To facilitate the interpretation of the results, odd ratios are provided instead of categorical variable estimates. Table 1 and 2 display the results. Column [START_REF] Amable | The Lisbon strategy and structural reforms in Europe[END_REF] corresponds to the model without partisanship, column [START_REF] Amable | Changing French Capitalism: Political and Systemic Crises in France[END_REF] involves the same variables but partisanship is included. The estimates confirm that pro-EU preferences are significantly and robustly correlated with an individual's level of human capital.

First we observe that the wealthier the individuals claim to be, the more they support further European integration in both samples (the former and new member states). This is all the more interesting that we control for the education level. The lowest incomes are notably reluctant to the EU, their odds of having more positive attitudes toward European integration are 29 per cent smaller than our reference category ("Coping on present income") for post-communist member states, and 24 per cent for the original member states. Cross national differences also seem to reflect the country education level. Skilled individuals in coordinated market economies (where the education system invests on specific skills) are thus expected to be less supportive of integration than their counterpart in countries with more general education systems [START_REF] Brinegar | Location, Location, Location: National Contextual Factors and Public Support for European Integration[END_REF]. Indeed country dummies reveal that countries where, ceteris paribus, negative attitudes towards European integration are most widespread are Austria, Finland and Sweden. In the end, estimates demonstrate not only that cross national variations are considerable but also that individual skills may work differently in different institutional contexts.

In line with our assumptions, right wing parties are strong supporters of further integration. As mentioned above, nationalist parties are close to the communist party in eastern Europe 7 . Euro-skeptical political factions are far left individuals while right wing parties are expected to support market liberalization.

In order to complement the cross national analysis, separated country estimates are run.

Table 3 presents the results in four major countries: France, Germany, Great Britain and Sweden.

They confirm our findings and some national characteristics stand out.

In the case of Sweden the baseline model is highly relevant. First, occupational variations are marked. Secondly self employment is significantly and positively correlated with public support (41 per cent superior from wage earners) while union members are 27 per cent less supportive of the European Union. The lowest income categories do not significantly differ from the reference category ("coping on present income"), however the highest income display a strong support for further integration. The same can be said about France where medium and low incomes have similar preferences, but very high incomes heavily support European integration.

The opposite can be observed in Great Britain, where only the last income category is negatively correlated with the support. High income individuals do not support the European Union. There are two straightforward reasons: first euro skepticism is widespread in Great Britain, regardless of the socioeconomic background, secondly the level of redistribution is higher in the rest of Europe so rich people might fear convergence towards the other countries.

The distrust among poor British respondents is consistent with the variety of capitalism hypothesis that citizens in LMEs fear a raise in taxation and job losses. Indeed, unemployment in Great Britain is historically lower than the European average. Poor workers do not want more taxes or lose their jobs. However it has to be noticed that unemployed people in Great Britain are 37 per cent more supportive of the EU than paid workers (significant at 0.1). It appears that people who do not have a job might support a raise in unemployment benefits.

Concluding remarks

Using individual-level data from two rounds of the European Social Survey, a crosscountry analysis was conducted on two samples: the fifteen original member states, and the post communist member states. We argued that the European political agenda promotes liberalization and budgetary constraints which leads the less competitive citizens to dread a surge in labor market flexibility and cuts in government spending.

The estimates are consistent with the literature. They tend to prove that social groups reluctant to further European integration are the same who traditionally fear liberalization, i.e. manual workers. Conversely, managers and professionals promote integration in both samples.

Even though occupational clusters are taken into account, the highest income categories remain significantly more in favor of the European process than medium or low income ones.

Unemployed people do not have distinct preference from workers in our analysis. Union membership is significant and as predicted, unionized workers are less supportive of further integration than their non-unionized counterparts. Respondents in education were heavily supportive of the European Union in both samples.

We focused on cross national variation comparing former member states to new ones. We found that in countries without a comparative advantage in skill-intensive sectors, the skillspreference link is attenuated. Indeed the distributive consequences of European integration are distinct from one institutional setting to another.

In former member states it sounds clear that since the Maastricht treaty was signed, European integration plays a crucial role in shaping national political preferences 8 . The economic policies implemented by the European Union (notably budgetary orthodoxy or liberalization policies) are unlikely to favor manual workers or people dependent on state generosity. Social democratic countries like Sweden best illustrate theses social divides. The distributive consequences of European integration appear to us as an important aspect to consider for European policy makers. The loss of sovereignty is a burning issue when European authorities decide to adopt the Treaty on Stability, Coordination and Governance in the Economic and Monetary Union to overcome the sovereign-debt crisis.

It has to be noted that when European issues are concerned, preferences are not aligned to traditional partisanship, or well-known dimensions such as economic or cultural drivers.

Although changes in party system have not occurred until now, European integration appears increasing like a political cleavage.

The study emphasizes that the preferences of managers across Europe are similar while preferences of managers and manual workers within the same country are distinct, indicating that transnational dimensions are strong. Nevertheless, some social groups stand out more or less sharply from one country to another. Indeed, we argue that European citizens perceive the European Union in a roughly similar manner; but integration has different implications depending on the institutional characteristics of the country of residence. As an example, for British people European integration might stand for more redistribution, whereas Swedish people expect the opposite from the EU. Identifying this contextual preference formation is an important tasks for future research.

Firstly, we intend

  to show that social groups reluctant to further European integration are the same who traditionally fear trade liberalization, i.e. manual workers. International trade models have documented the distributive consequences of trade and individual attitudes towards trade (see Rodrik (1995) for a review of the literature). Most of the studies are based on the factor endowments model (a combination of the Heckscher-Ohlin model and Stolper-Samuelson theorem), and predict that trade liberalization benefits individuals who own the factors with which the economy is relatively well endowed and hurts the others (Rodrik and Mayda 2005). Scheve and Slaughter (2000) find that in the United-States a two-factor model is a powerful predictor of public opinion about trade.

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Figure 3 -Figure 4 -

 34 Figure 3-UE 15 states: Main survey question (frequency)

Figure 5 -

 5 Figure 5-EU 15 states: average support by ISCO

Figure 6 -

 6 Figure 6-Post communist countries: average support by ISCO

"Now thinking about the European Union, some say European unification* should go further. Others say it has already gone too far. Using this card, what number on the scale best describes your position?"

	Unification								Unification
	has already								should go	(Don't
	gone too far								further		know)
	00	01	02	03	04	05	06	07	08	09	10	88

  FollowingGabel (1998) we expect support for the EU to be positively correlated with an individual's level of human capital. Income is used as a proxy of such competitiveness. We also use the International Labor Classification (ISCO-88) as it reflects the education level of individuals. The nine groups are the following: Manager, Professional, Associate professional, Clerk, Service worker, Agricultural worker, Craftsman, Machine operator, and Elementary

Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Table 1 : Ordered logit: Original member states

 1 Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

	[1]	[2]

Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Table 2 : Ordered logit: Post communist countries

 2

	[1]	[2]

Documents de Travail du Centre d'Economie de la Sorbonne -2012.88 Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Table 3 : Ordered logit: Separated Country Regressions

 3

	France	Germany	Great Britain	Sweden

Documents de Travail du Centre d'Economie de la Sorbonne -2012.88 Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

See Van Ingelgom V, (2012) for a detailed analysis on indifference Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

In France for example, the European Constitution was rejected by referendum in 2005 because a large part of the French electorate feared the Constitution would enforce a neoliberal economic model Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Beckfield runs estimates of panel models of within-country income inequality using data from 1972 to 1997 Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

The idea was introduced by R.Inglehart in 1971. The theory of modernization argues that, social development and economic prosperity drives political changes in advanced economies. These political changes correspond to the rise of post-materialism values among individuals. Materialist values are security, fight against inflation; whereas post-materialist values are selfdevelopment, cosmopolite views...Post-materialist theories predict a decline of the traditional left-right cleavage (Giddens, 1994). Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Deregulation of national norms rather than new institutions or programs

A pooled regression was carried and provides evidence that our main assumptions hold. We choose to create two group of countries to obtain more details on each group and because the literature usually do not include eastern Europe. In addition, separating the countries in two groups allows to reduce the extent of country fixed effects Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

For an analysis of political demand in France see Guillaud and Palombini (2006) and Grunberg and Schweisguth (1997) Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Source: ESS question survey: Some say European unification should go further, others say it has already gone too far. Using this card, what number on the scale best describes your position? Documents de Travail du Centre d'Economie de la Sorbonne -2012.88

Among the former member states, the gap from one ISCO category to the other is wide, the likelihood to support European integration is 0.55 (45 per cent) inferior for elementary workers compared to professionals. The gaps are much less pronounced among eastern member states (a 22 per cent drop in the support for elementary workers compared to professionals). The issue is addressed in the next section.

Unemployed people do not stand out as a distinct category compared to paid workers; this might be due to heterogeneity among the individuals in the group. In table 1 (the EU 15 states), the estimates also point out that people in education strongly support integration compared to paid workers (the support goes up by 46 per cent). The employment relation does not predict preferences of individuals in European matters.

Data on union membership are missing for Romania and Latvia, consequently the variable was excluded. However tested on the other new member states, union membership is insignificant. Concerning the original fifteen member states, union membership is significant at 10 per cent and as predicted, unionized workers are less supportive of further integration than their non-unionized counterparts (by 4%).

Finally, comparing column [START_REF] Amable | The Lisbon strategy and structural reforms in Europe[END_REF] and [START_REF] Amable | Changing French Capitalism: Political and Systemic Crises in France[END_REF] confirms that socioeconomic characteristics do not operate through a left/right positioning. The inclusion of the variable does not distort the previous results: the variables remain significant and the coefficients remain globally unchanged.

The present analysis weights in favor of the emergence of a new political cleavage around

European integration [START_REF] Kriesi | West European Politics in the Age of Globalization[END_REF].

Cross-national analysis

Two groups were isolated in the study in order to capture national characteristics. The factor endowment model predicts that individuals whose factor is abundant welcome liberalization while scarce factors oppose it. But in countries without a comparative advantage in skill-intensive sectors, the skills-preference link should be attenuated, or even reversed [START_REF] Scheve | Comparative Context and Public Preferences over Regional Economic Integration[END_REF]. In line with this assumption skilled workers in the former member states strongly support integration compared to unskilled workers while the situation is attenuated in post-communist states. We notice for example that the support of machine operators is only 16 per cent less than professionals in those countries while the support drop by 52 per cent (the odd ratio is 0, 48) in the fifteen former member states.