Fabien Laurent

Aurélie Cébron

Christophe Schwartz

Corinne Leyval
email: corinne.leyval@limos.uhp-nancy.fr

Schwartz

Oxidation of a PAH polluted soil using modified Fenton reaction in unsaturated condition affects biological and physico-chemical properties

Keywords: Fenton, oxidation, PAH, soil, fertility, biological activity

come

Oxidation of a PAH polluted soil using modified Fenton reaction in unsaturated condition affects biological and physico-chemical properties

Introduction

The presence of pollutants in soils can affect soil functions (e.g. filter and exchange, support for plant growth and biodiversity) [START_REF] Smith | Effects of polycyclic aromatic hydrocarbons on germination and subsequent growth of grasses and legumes in freshly contaminated soil and soil with aged PAHs residues[END_REF][START_REF] Maxim | Driving forces of chemical risks for the European biodiversity[END_REF].

Although remediation treatments reduce or eliminate pollutant concentration, their potential effect on soil physical, chemical and biological properties, and soil functions is rarely considered. Polycyclic aromatic hydrocarbons (PAHs) are widespread contaminants in soil.

Their effects on human health and their carcinogenic potential is largely studied [START_REF] Bispo | Toxicity and genotoxicity of industrial soils polluted by polycyclic aromatic hydrocarbons (PAHs)[END_REF]Joe et al., 2004;[START_REF] White | Mutagens in contaminated soil: a review[END_REF]. Different remediation technologies were developed in the last decades to remove PAHs from contaminated soils [START_REF] Wang | Effect of bioremediation on polycyclic aromatic hydrocarbon residues in soil[END_REF][START_REF] Cajthaml | Bioremediation of PAH-contaminated soil by composting: A case study[END_REF][START_REF] Gan | Remediation of soils contaminated with polycyclic aromatic hydrocarbons (PAHs)[END_REF]. In situ chemical oxidation (ISCO) is a technology generally used to remediate organic contaminants in groundwater and saturated soil [START_REF] Rivas | Polycyclic aromatic hydrocarbons sorbed on soils: A short review of chemical oxidation based treatments[END_REF][START_REF] Huling | In-Situ Chemical Oxidation -Engineering Issue[END_REF]. This remediation technique based on the injection of different oxidant reagents does not require soil excavation and represents an alternative to conventional treatment (e.g. thermal desorption, venting). Fenton reagents (hydrogen peroxide and iron) are among the most commonly used and studied oxidizing agents [START_REF] Rivas | Polycyclic aromatic hydrocarbons sorbed on soils: A short review of chemical oxidation based treatments[END_REF] for pollutants such as petroleum hydrocarbons, BTEX, chlorinated ethenes and PAHs [START_REF] Huling | In-Situ Chemical Oxidation -Engineering Issue[END_REF]. In Fenton reaction, Fe (II) catalyzes the decomposition of hydrogen peroxide to generate hydroxyl radicals (OH . ) which are strong and non specific oxidants. However, some authors showed that OH . radicals preferentially attack the aromatic compounds [START_REF] Westerhoff | Relationships between the structure of natural organic matter and its reactivity towards molecular ozone and hydroxyl radicals[END_REF][START_REF] Mikutta | Review: organic matter removal from soils using hydrogen peroxide, sodium hypochlorite, and disodium peroxodisulfate[END_REF] and can also react with sorbed and aqueous PAHs. Fenton oxidation generally includes acid addition since a low pH (2-3) is required for optimum reaction, but modified Fenton reaction at near neutral pH using ferric ions and chelating agents was also performed [START_REF] Nam | Enhanced degradation of polycyclic aromatic hydrocarbons by biodegradation combined with a modified Fenton reaction[END_REF].

Fenton reaction was mainly studied in saturated conditions (Jonnson et al., 2006;[START_REF] Sirguey | Impact of chemical oxidation on soil quality[END_REF][START_REF] Sun | Influence of pyrene combination state in soils on its treatment efficiency by Fenton oxidation[END_REF]Valderrama et al., 2009) with large liquid/solid ratios. Further, the amounts of oxidant used in many studies [START_REF] Nam | Enhanced degradation of polycyclic aromatic hydrocarbons by biodegradation combined with a modified Fenton reaction[END_REF]Palmroth et al., 2006a;Valderrama et al., 2009) were very high for field treatment. Chemical oxidation in unsaturated conditions was also applied, although fewer studies were reported (Palmroth et al. 2006a, Huling and[START_REF] Huling | In-Situ Chemical Oxidation -Engineering Issue[END_REF]. The addition of chemical oxidants could impact other soil characteristics than organic pollutant concentration and for surface soils this could lead to a global loss of fertility. Chemical oxidation of PAHs was shown to induce a decrease of organic carbon, total nitrogen and phosphorus contents in soils [START_REF] Leifeld | Organic carbon and nitrogen in fine soil fractions after treatment with hydrogen peroxide[END_REF][START_REF] Mikutta | Review: organic matter removal from soils using hydrogen peroxide, sodium hypochlorite, and disodium peroxodisulfate[END_REF][START_REF] Sirguey | Impact of chemical oxidation on soil quality[END_REF]. Microorganism populations were negatively affected following ISCO but the impact seemed to be temporary with a rebound of cell numbers after a few weeks [START_REF] Sahl | The effects of in situ chemical oxidation on microbiological processes: A review[END_REF]. After oxidation treatment, PAH biodegradation was enhanced, suggesting the possible combination of both chemical oxidation and biodegradation of organic pollutants [START_REF] Lee | A hybrid Fenton oxidation-microbial treatment for soil highly contaminated with benz(a)anthracene[END_REF][START_REF] Nam | Enhanced degradation of polycyclic aromatic hydrocarbons by biodegradation combined with a modified Fenton reaction[END_REF]Palmroth et al., 2006a;2006b;Valderrama et al., 2009) The present study was conducted to assess the impact of chemical oxidation to surface soil using modified Fenton reaction on PAH removal and on soil physico-chemical and biological parameters. Since surface soils are mostly unsaturated, we performed the oxidation in unsaturated condition. An industrial PAH contaminated soil was treated with a volume of reagents calculated to keep the soil at water holding capacity. We used a modified Fenton reaction without acid addition to the soil to avoid a strong pH decrease that may drastically affect biological activity. Two concentrations of reagents were tested. Analyses of PAH concentration, soil characteristics (pH, cation exchange capacity, organic carbon, nitrogen, phosphorus), microbial density and activity and seed germination and plant growth using ryegrass (Lolium perenne) were performed with oxidized and control soil.

Materials and methods

Soil sampling and analysis

An industrial soil sample was collected from a former coking plant site (Neuves-Maisons, France) [START_REF] Biache | Effects of thermal desorption on the composition of two coking plant soils: Impact on solvent extractable organic compounds and metal bioavailability[END_REF][START_REF] Monsérié | Technosol genesis: identification of organo-mineral associations in a young Technosol derived from coking plant waste materials[END_REF]. The soil is a sandy loamy soil (11.9% clay, 21.5% silt and 66.6% sand). The soil presents a high content of organic carbon (50g kg -1 ), a neutral pH (7.3) and the contamination by the 16 US-EPA priority PAHs reaches 1200 mg kg -1 . Large amount of soil was excavated and homogenized by quartering. Subsamples were sieved at 2 mm and air dried at 25°C. Soil analyses were performed by INRA laboratory (Arras, France) according to international standard methods: water holding capacity (WHC) (ISO 11464), pH, total organic carbon (ISO 10694), total nitrogen (ISO 13878), extractable phosphorus (ISO 11263), cation exchange capacity (CEC, NF X 31-130).

Oxidation experiment

The modified Fenton reaction was performed with two levels of reagents corresponding to 6 g kg -1 (low, L) and 65 g kg -1 (high, H) of H 2 O 2 . Three glass containers were filled with 1500 g of 2 mm sieved soil at 5 % humidity. In two of them, the soil sample was mixed with 7 (L) or 82 (H) g of solid ferrous sulfate (FeSO 4 , 7H 2 O, 99.5% purity) to catalyse the decomposition of H 2 O 2 without increasing the volume of solution added. Then, 450 mL of a solution of H 2 O 2 at either 0.54 (L) or 6.3 M (H) were added gradually to reach water holding capacity. The third one was a control with addition of 450 mL of water and no reagent addition. After 48 h, the soil sample in each container was homogenized and sub-sampled for further analysis. The soil was then air dried and sieved to 2 mm again. For microbial analysis, sub-samples were directly used for quantification of culturable heterotroph bacteria and incubation. For DNA extraction sub-samples were stored at -20°C.

Measurement of microbial activity (carbon mineralization) in soil after oxidation

Fenton oxidized and control soil samples (20 g), with five replicates each, were incubated at 100% WHC in 150 mL serum bottles with a Teflon septum for 5 weeks at 24°C to measure microbial activity by CO 2 production. To avoid anaerobic conditions during incubation, bottles were aired out every week. Carbon dioxide (CO 2 ) release was measured every day by infrared spectrophotometer (Binos, absorption at 2325.6 cm -1 ) [START_REF] Quantin | PAH dissipation in a contaminated river sediment under oxic and anoxic conditions[END_REF]. After 5 weeks, five replicates were taken for microbial and PAH analysis as described hereafter. An abiotic control of each modality (autoclaved twice at an interval of 48 h) was performed for a week in order to evaluate the abiotic release of CO 2 .

MPN counts of heterotroph microorganisms

Soil (1 g fresh) was suspended in 10 mL sterile ultra-pure water with 6 g sterile glass-beads and soil suspension was shaken during 1 h. Serial dilution of soil suspension (10 -2 to 10 -7 ) was prepared in NaCl (0.85%). The most-probable-number (MPN) was counted in 96-well microplates. A volume (25 µL) of dilution was added with 200 µL nutrient broth liquid medium (1 g L -1 ) in each well with 40 replicates by dilution. Microplates were incubated for 48 h at 28°C then absorbance was measured at 620 nm and MPN counts calculated by a computer program using McCrady table [START_REF] Binet | Dissipation of 3-6-ring polycyclic aromatic hydrocarbons in the rhizosphere of ryegrass[END_REF].

Quantification of bacteria, fungi and PAH-degrading bacteria

DNA extractions were performed independently for each biological replicate. DNA was extracted using the FastDNA © Spin kit for soil according to manufacturers recommendations (MP Biomedicals) from 1 g of soil. Bacteria, fungi and PAH-degrading bacteria were quantified by targeting 16S rDNA, 18S rDNA and PAH-RHD α genes using real-time PCR quantification of gene copy number, with the primer sets 968F/1401R [START_REF] Felske | Quantification of 16S rRNAs in complex bacterial communities by multiple competitive reverse transcription-PCR in temperature gradient gel electrophoresis fingerprints[END_REF], FF390R/Fung5F [START_REF] Lueders | Stable isotope probing of rRNA and DNA reveals a dynamic methylotroph community and trophic interactions with fungi and protozoa in oxic rice field soil[END_REF], PAH-RHD α GN F/R and PAH-RHD α GP F/R [START_REF] Cébron | Real-Time PCR quantification of PAH-ring hydroxylating dioxygenase (PAH-RHD[alpha]) genes from Gram positive and Gram negative bacteria in soil and sediment samples[END_REF], respectively. Real-Time PCR experiments were conducted in triplicate with an iCycler iQ (Bio-Rad), associated with iCycler Optical System Interface software (version 2.3). The final volume used (20 µL) contained 10 µL of iQ SYBR GREEN SuperMix (Biorad), 0.4 µM each primer, 0.06% bovine serum albumine (BSA), 0.2 µL DMSO, 0.08 µL T4gp32 (MP Biomedicals) and 1 µL of DNA as described in [START_REF] Cébron | Real-Time PCR quantification of PAH-ring hydroxylating dioxygenase (PAH-RHD[alpha]) genes from Gram positive and Gram negative bacteria in soil and sediment samples[END_REF].

Quantitative calibrations of Real-Time PCR assays were performed with 10 times dilution series (from 10 8 to 10 3 target gene copies µL -1 ) of standard linearized plasmids (pCR2.1 vector from Invitrogen) with target gene fragment inserted [START_REF] Cébron | Real-Time PCR quantification of PAH-ring hydroxylating dioxygenase (PAH-RHD[alpha]) genes from Gram positive and Gram negative bacteria in soil and sediment samples[END_REF].

Germination and plant growth test

Fenton oxidized and control soil samples (100 g) with five replicates were placed in 200 mL pots. Soil was watered with deionised water to 70% WHC and soil moisture was daily adjusted. Twenty seeds were sown on each pot, thinned to 5 plants after germination. The pots were placed in a growth chamber at 24°C/20°C, 16 h day light, 250 µmol m -2 s -1 intensity.

The germination rate was recorded every day and conducted over a period of 2 weeks. After 4 weeks, plants were harvested, and roots gently rinsed in water. Shoot and root dry weights were measured after drying at 105°C for 24 h.

PAH analysis

PAHs were extracted from soil samples in triplicates using ASE 200 (Accelerated Solvent Extraction Dionex). Anhydrous sodium sulfate (1 g) and 1 g of Florisil® was added to each sample (1 g) in the extraction cell to purify the extract. The extraction solvent was composed of 50% acetone and 50% methylene chloride and extraction was run at 100°C and 130 bars for 5 min [START_REF] Ouvrard | In situ assessment of phytotechnologies for multicontaminated soil management[END_REF]. After evaporation of most of the solvent, samples were diluted in 5 mL of acetonitrile and evaporated to obtain exclusive acetonitrile extracts.

Analysis of 16 US-EPA priority PAHs concentrations was performed by high-performance liquid chromatography (Varian) [START_REF] Monsérié | Technosol genesis: identification of organo-mineral associations in a young Technosol derived from coking plant waste materials[END_REF]. Results were reported for dry soil for comparison between treatments.

Statistical analysis

Statistical analyses were performed using XLSTAT© Software. Comparisons were made by ANOVA after verification of applicability conditions. A multiple post hoc comparison (Tukey) test was applied to determine the difference per pair. Gene quantification data were log transformed for statistical comparisons. To test time effect of bacteria recolonization a Student t-test was applied. For seed germination a Fisher test was applied to calculate LSD (least significant difference).

Results

Effect of Fenton oxidation on soil PAH concentration and physico-chemical characteristics

Total PAH concentration was significantly lower in Fenton oxidized than in control soil with 22% and 14% decrease with H and L oxidant concentration, respectively (Table 1). The same result was found for the individual PAHs except for the three low molecular weight PAHs naphthalene, acenaphtylene and acenapthene where the concentration decrease was not significant (Table 1). No clear difference was observed for the degradation rate between the 3 (18 to 36% decrease with H oxidant concentration), 4 (20.3 to 24.3%), 5 (16 to 22.1%) and 6

(24.3 to 24.6 %) ring PAHs. No further significant PAH concentration decrease occurred during the 5 weeks incubation (data not shown). Although no replicate analysis was performed for organic carbon and nitrogen content, the carbon content tended to be lower in oxidized than control soil, while nitrogen content was not affected. After Fenton H treatment, several parameters were strongly affected: a CEC decrease of 2 units, a pH decrease of 2.5 units and a decrease of available phosphorus (77% of the initial content) were measured.

Effect of Fenton reaction on microbial density and activity

No production of CO 2 was observed in the abiotic controls (data not shown). The Fenton H treatment significantly and rapidly increased carbon mineralization rate, while mineralization rate was not significantly different with Fenton L treated and control soil (Figure 1). After oxidation (T0), the number of culturable heterotrophs, the 16S, 18S rDNA and PAH degrading (PAH-RHD α ) gene copy numbers were significantly lower in Fenton H treated than in control soil (Figure 2). After 5 weeks of incubation (T5), these numbers were significantly higher than at T0 in Fenton H treated soil (Figure 2), while they did not significantly differ between T0 and T5 for control and Fenton L treated soils. After 5 weeks the number of culturable heterotrophs and of 18S rDNA gene copies were even significantly higher in Fenton H treated than in control soil. However, in Fenton L treated soil there was no significant difference in culturable heterotrophs, 16S, 18S and PAH-RHD gene copy number with the control soil at T0 and five weeks after incubation (T5).

Effect of treatment on germination and growth

Ryegrass germination rate reached 75-80% in Fenton treated and control soil after 14 days.

However, a 3-days significant delay in seed germination was observed for the Fenton H treated soil (Figure 3). Root and shoot biomass was significantly lower in Fenton H treated soil (35% and 43% decrease) than in the control soil, but it was not affected in Fenton L treated soil (Figure 4).

Discussion

The modified Fenton reaction applied in unsaturated conditions significantly reduced the amount of PAHs in soil. The degradation concerned the different PAHs except the lower molecular weight ones. Similar degradation rates of PAHs regardless of the number of aromatic rings or lower degradation rates of higher molecular weight PAHs were previously reported depending on the H 2 O 2 /Fe 2+ ratio [START_REF] Tran | Comparison between Fenton oxidation process and electrochemical oxidation for PAH removal from an amphoteric surfactant solution[END_REF]. However, our degradation rate, obtained with 5-56 g oxidant added for 1 g PAHs, was lower than observed in other studies where higher concentrations of oxidants were applied in saturated conditions (100 to 4000 g oxidant for 1 g PAHs) for spiked [START_REF] Nam | Enhanced degradation of polycyclic aromatic hydrocarbons by biodegradation combined with a modified Fenton reaction[END_REF][START_REF] Kulik | Degradation of polycyclic aromatic hydrocarbons by combined chemical pre-oxidation and bioremediation in creosote contaminated soil[END_REF] or aged contaminated soils [START_REF] Nam | Enhanced degradation of polycyclic aromatic hydrocarbons by biodegradation combined with a modified Fenton reaction[END_REF][START_REF] Jonsson | Comparison of Fenton's reagent and ozone oxidation of polycyclic aromatic hydrocarbons in aged contaminated soils[END_REF][START_REF] Jonsson | Degradation of polycyclic aromatic hydrocarbons (PAHs) in contaminated soils by Fenton's reagent: A multivariate evaluation of the importance of soil characteristics and PAH properties[END_REF]. In soil, the non specific action of hydroxyl radicals could oxidize the targeted molecules as well as the organic matter, which increases the quantity of oxidant needed to degrade PAHs. The soil contains more than 50 g kg -1 of organic carbon and PAHs represent only 2% of it [START_REF] Monsérié | Technosol genesis: identification of organo-mineral associations in a young Technosol derived from coking plant waste materials[END_REF]. The apparent lower C org content in both oxidized treatments than in the control soil, could be due to the action of hydroxyl radicals, but this should be confirmed by further investigations. Moreover, the soil used in this study had a high carbonate content which can limit the efficiency of Fenton reaction. At the same time, this reaction lead to a decrease of pH, probably due to the injection of an acidic H 2 O 2 solution and to the reaction between Fe (III) and H 2 O 2 [START_REF] Huling | In-Situ Chemical Oxidation -Engineering Issue[END_REF]. Carbonates can also buffer the environment of hydroxyl radicals which present a higher efficiency in acidic conditions [START_REF] Huling | In-Situ Chemical Oxidation -Engineering Issue[END_REF]. Another explanation could be the low accessibility of aged pollutants in this historically contaminated soil [START_REF] Katayama | Bioavailability of xenobiotics in the soil environment[END_REF][START_REF] Ouvrard | In situ assessment of phytotechnologies for multicontaminated soil management[END_REF]. Contrary to other studies, the contact between PAHs and the reagent was not enhanced by the use of a high volume of solution. The fact that hydroxyl radicals have a short half life [START_REF] Sies | Strategies of antioxidant defense[END_REF] added to the difficulty to access PAHs located in newly formed aggregates specific to the industrial soil [START_REF] Monsérié | Technosol genesis: identification of organo-mineral associations in a young Technosol derived from coking plant waste materials[END_REF] can be another limitation for the degradation by such chemical processes.

Soil fertility was affected by the Fenton oxidation with the higher concentration of oxidant added. The main effect was a decrease of soil pH, a negative effect on plant growth, as previously observed by [START_REF] Sirguey | Impact of chemical oxidation on soil quality[END_REF] and a decrease of CEC and available P. The decrease in CEC could be explained by the consequence of the pH drop on the charge of the organic matter carboxyl groups, which partly turned to COOH instead of COO - [START_REF] Sirguey | Impact of chemical oxidation on soil quality[END_REF]. Moreover, it can result from the ionisation in acidic conditions of mineral OH groups. Cation exchange capacity reflects the mobility and the availability of ions which are important components of soil fertility. The decrease of available phosphorus content could result from the formation of ferric phosphate in acid condition which is an insoluble form of phosphorus. The pH decrease, the low available phosphorus content and the decrease of cation exchange capacity could explain the decrease of biomass and root elongation. Soil fertility and plant growth could possibly be restored by addition of ameliorants (lime, fertilizer) [START_REF] Séré | Soil construction: A step for ecological reclamation of derelict lands[END_REF].

Besides decreasing soil fertility, the oxidation treatment affected microbial density and activity. The decrease in bacterial, fungal, and PAH degrading bacteria population densities could be explained by the toxicity of hydroxyl radicals strongly reacting with biological membranes [START_REF] Slater | Free-radical mechanisms in tissue injury[END_REF]. Moreover, the heat produced by the exothermic Fenton reaction and the decrease of pH could contribute to the decreased microbial number and activity just after chemical oxidation. The decrease of the number of microorganisms after Fenton reaction as well as the rebound have been previously observed [START_REF] Ferguson | A field trial of in situ chemical oxidation to remediate long-term diesel contaminated Antarctic soil[END_REF]Palmroth et al., 2006b;[START_REF] Sahl | The effects of in situ chemical oxidation on microbiological processes: A review[END_REF]. The increased microbial activity, estimated by the increased CO 2 release, and the increased number of cultivable and total bacteria and fungi during incubation after oxidation indicated that recolonization occurred. Cultivable bacteria which are heterotrophic preferentially use the most available organic carbon. The dead bacterial cells (Palmroth et al., 2006b) as well as the organic carbon affected by the oxidation treatment [START_REF] Leifeld | Organic carbon and nitrogen in fine soil fractions after treatment with hydrogen peroxide[END_REF][START_REF] Mikutta | Review: organic matter removal from soils using hydrogen peroxide, sodium hypochlorite, and disodium peroxodisulfate[END_REF] could potentially provide a supplementary available amount of organic carbon. Contrary to other studies, no further degradation of PAHs occurred in our experiment following oxidation, and no variations in PAH-degrading populations were observed. However, it was previously shown that PAH availability in this historically contaminated soil was low and limited natural attenuation [START_REF] Ouvrard | In situ assessment of phytotechnologies for multicontaminated soil management[END_REF].

Conclusion

Partial removal of PAHs (14 and 22%) in a historically contaminated soil was possible in unsaturated conditions using Fenton reagents with the low and high doses of H 2 O 2 (6 and 65 g kg -1 ). The impact of chemical oxidation on PAH concentration and soil physico-chemical and biological parameters differed with the level of reagent used. PAH degradation was not proportional to the quantity of reagent added. With the highest oxidant level applied, soil parameters were highly impacted, especially pH value and biological parameters such as the quantity of microorganisms, seed germination and plant growth. The impact on microbiological parameters was temporary and disappeared rapidly. Specific microbial functions could be investigated to further check whether soil microbial functioning was affected. Reduction of soil pH was a major limiting factor for plant growth at high level of oxidant. Further investigations could be performed with different concentrations of reagents to optimize PAH degradation without impact on vegetation. Otherwise, chemical oxidation could be combined with soil restoration strategies.

Figure captions Figure 1 :

 captions1 Figure captions

Figure 2 :

 2 Figure 2: Density of cultivable bacteria, 16S rDNA, PAH-RDHα and 18s rDNA gene copy numbers in oxidized (Fenton L and H) and control soil (Control) at the start (T0) and after 5 weeks (T5) of incubation. As the evolution of PAH-RHD α GN and GP populations was not significantly different, the two populations were added to represent the global population of degraders. Mean ± SE (n=3). LD: detection limit. Different letters within category data indicate significant differences between treatments; stars indicate significant differences between T 0 and T 6 by Mann and Whitney test.

Figure 3 :Figure 4 :

 34 Figure 3: Germination rate (%) of Lolium perenne seeds in oxidized (Fenton L and H) and control soil. Mean ± SD (n=5). Stars indicate a significant difference between Fenton H treated and Control soil

  Figure 2

Table 1 :

 1 Physico-chemical characteristics of the soil after Fenton treatment at low (L) and high (H) concentration of oxidant. Concentrations of PAHs, given as mean, followed by the same letter are not significantly different at the 5% level (one-way ANOVA, Tukey test)

			Control	Fenton L Fenton H
		Units
	Org C	(g kg -1 )	61,7	57.7	57.1
	N	(g kg -1 )	2.4	2.4	2.3
	Olsen P	(g kg -1 )	0.049	0.068	0.011
	CEC	(cmol kg -1 )	10.3	10.5	8.7
	pH		7.3	7.4	4.9
	Naphthalene		24.8 a	26.4 a	22.0 a
	Acenapthtylene		0.7 a	0.6 a	0.8 a
	Acenaphthene		57.9 a	54.8 a	52.7 a
	Fluorene		25.9 a	22.9 b	20.4 b
	Phenanthrene		89.1 a	80.9 ab	72.9 b
	Anthracene		36.8 a	26.2 b	23.6 b
	Fluoranthene		235.5 a	206.1 b	186.9 c
	Pyrene Benzo(a)Anthracene	( µg kg -1 )	128.8 a 101.2 a	111.4 b 87.0 b	102.6 c 78.4 c
	Chrysene		56.7 a	47.4 b	42.9 c
	Benzo(b)Fluoranthene		96.7 a	83.5 b	77.3 b
	Benzo(k)Fluoranthene		30.8 a	26.6 b	24.5 b
	Benzo(a)Pyrene		108.8 a	91.5 b	84.7 b
	Dibenzo(a.h)Anthracene		13.1 a	11.3 b	11.0 b
	Benzo(g.h.i)Perylene		64.2 a	52.7 b	48.4 b
	Indeno(1.2.3-cd)Pyrene		90.9 a	75.4 b	68.8 b
	Total PAHs		1161.9 a	1004.9 b	917.9 c

Acknowledgments

This work was funded by the ANR-Precodd Oxysol project, the French Government and the Lorraine Region (GISFI project, www.gisfi.fr). The authors thank Prof. Marie-Odile Simonnot and Jean-Christophe Renat (Valterra Company) for fruitful discussions and advices.


Thomas Boyer-Kassem
email: thomas.boyer.kassem@univ-poitiers.fr

Sébastien Duchêne
email: sebastien.duchene@umontpellier.fr

On discrimination in health insurance

Keywords: discrimination, health profiling, health insurance, ethics, responsibility

In many countries, private health insurance companies are allowed to vary their premiums based on some information on individuals. This practice is intuitively justified by the idea that people should pay the premium corresponding to their own known risk. However, one may consider this as a form of discrimination or wrongful differential treatment. Our goal in this paper is to assess whether profiling is ethically permissible in health insurance. We go beyond the existing literature in considering a wide range of parameters, be they genetic, non-genetic, or even non-medical such as age or place of living. Analyzing several ethical concerns, and tackling the difficult question of responsibility, we argue that profiling is generally unjust in health insurance.

Introduction

In many countries, private health insurance companies are allowed to vary their premiums, or to reject applicants, based on some information they collect on individuals. This is the case in the United States, United Kingdom, Switzerland and France among others.1 For instance, the companies can propose higher premiums for people with higher cholesterol rates. The intuitive justification for this practice is that people should pay the premium corresponding to their own known risk. If having a high cholesterol rate increases the risk of a cardio-vascular disease, and hence expected health care costs, then the premiums should be adapted accordingly. Such linking of risk factors and health care costs (for short: health costs) is known as "health profiling" (or "health risk adjustment"). Risk factors may be as diverse as: medical history, smoking habits, alcohol consumption, age, or even genetic factors.2 Note that health profiling can be implemented without assuming that correlation means causation, and an instrumental use of correlation is sufficient. For instance, the place of living may be used to profile if a correlation is observed with health costs, even if the company is aware that there may be some confounders. Health profiling can be considered as a "statistical" discrimination if it is based on scientifically established statistical correlations, and we shall assume this here.

Health bills and premiums are a major issue for people in many countries. For instance, nearly 2 million people a year in the US declare bankruptcy because of unpaid medical bills [START_REF] Mangan | Medical bills are the biggest cause of US bankruptcies: study[END_REF]. Moreover, health profiling can lead to denial of insurance altogether to people whose risks are so high that insuring them is unprofitable. Note also that profiling in health insurance is not a concern for optional insurances only. In Switzerland for instance, profiling on age and on place of living is implemented for the compulsory basic health insurance. So, assessing the ethical permissibility of health premiums is a pressing issue. Health discrimination is wrongful for a broad range of parameters, one may argue, because it makes people pay more on the basis of characteristics over which they have no control ("I can't be blamed for this"), which are group characteristics only ("judge me, not my group") and because it amounts to a double punishment ("I'm already ill, and now I have to pay more").

Our goal in this paper is to assess the above arguments in order to evaluate whether profiling in health insurance, wheter compulsory or optional, is ethically permissible. Discrimination refers to the "acts, practices, or policies that impose a relative disadvantage on persons based on their membership in a salient social group" [START_REF] Altman | Discrimination. The Stanford Encyclopedia of Philosophy[END_REF]; see also Lippert-Rasmussen 2013), which can be morally wrong when this differential treatment is based on irrelevant factors so that people are differentially treated for no good reason. The question then becomes whether statistical facts about a group (for instance, people with a specific medical history) have relevant justificatory force in treating members of that group differently than others (requiring them to pay higher premiums).

In the literature so far, the debate on discrimination in health insurance has been mainly on whether insurances should be allowed to use genetic information [START_REF] Hellman | What makes genetic discrimination exceptional?[END_REF][START_REF] Hellman | When is discrimination wrong?[END_REF][START_REF] Moreau | What is discrimination?[END_REF][START_REF] Lippert-Rasmussen | Genetic discrimination and health insurance[END_REF]. Our scope is wider, and for instance we shall consider that the information which the insurance company may used can be genetic or not, medical or not. More precisely, the list of parameters we shall consider here consists in: present diagnosed illness (such as diabetes or heart failure), medical history, body mass index, smoking habits, alcohol consumption, genetic information, gender, age, race, sexuality, place of living. Overall, a health insurance company might want to rely on scientifically established statistical correlation between any of the parameters from the above list and health costs. For instance, if parameter X is observed to be correlated with higher health costs per year, for whatever reason, then health profiling entails that the premium for people with parameter X increases.

When it comes to fairness in health insurance, an important parameter which is not in that list is undoubtedly the income of agents: should an agent with a higher income pay more than an agent with a lower income? We choose not to enter this debate here, not because it is an uninteresting question, but because we think that the kind of arguments that may be used for it are radically different from the ones that may be used for all other parameters from our list [START_REF] Fleurbaey | Fair utilitarianism[END_REF]. So, we choose not to include the parameter "income" in the list. That is, we only ask in this paper whether varying health insurance premiums according to parameters from our list is fair, all else being equal, and in particular assuming equal incomes. In other words, when we argue that premiums should not vary with, for instance, medical history, the reader should remember that this position is implicitly for agents of equal incomes; if agents do have different incomes, the reader is free to use the theory of her own, on which we don't take stand here (our view on the parameters from our list is compatible with any view the reader may have on whether agents with higher incomes should pay more or not).

Another question we don't address in the paper is whether profiling in health insurance is economically justified for an insurance company, and whether and why it should profile3 . We just note that, when profiling is not forbidden by law, companies have generally seized the opportunity. This suffices to pose the question of its ethical character.

Our thesis is twofold. First, profiling on parameter X is ethically acceptable only in case agents are responsible for the costs associated with X (and not only for X). This condition can be further specified in requiring that (i) the agent is responsible for X, (ii) X is causally linked to health costs, and (iii) the agent knows that (ii). If at least one of these conditions is not met, the same premium should be offered regardless of the person's value of this parameter. Second, no parameter from our list actually fulfills these conditions. So, we conclude that profiling in health insurance is a form of unfair discrimination in all the cases we discuss. Note that our thesis is ethical only. We are not concerned with its practical implementation in policy -this question would need another paper. Therefore, we do not discuss any practical implications resulting from our ethical conclusions whether for optional or compulsory health insurance.

The scope of our conclusion is new in the literature. In his no-profiling thesis, Lippert-Rasmussen (2015b) also discusses choices and responsibility. However, that paper only considers medical information, and relies on a luck egalitarian view (Lippert-Rasmussen 2015a). Here, we take a broader perspective, including non-medical information that is correlated with health costs, and not restricting ourselves to a luck egalitarian view. We start in Section 2 by a tour of ethical theories to guide our discussions. In Sections 3 and 4, we tackle the question of responsibility.

Ethical concerns with health profiling

This Section considers various ethical concerns with health profiling. Which reasons can one have to object to health profiling? Doesn't it maximize total utility? Does it violate equality of opportunity? Does it harm the worst-off? Can't it be justified behind a Rawlsian veil of ignorance? We raise these concerns, and connect them to dominant ethical theories. Methodologically, we choose not to endorse here one particular ethical theory, but show how health profiling raises various valid -utilitarian, egalitarian, prioritarian and contractualist -concerns. Our pluralist approach analyzes the various ethical concerns raised by health profiling, each of which can plausibly claim to have normative weight. For reasons of space, we limit ourselves to the most central concerns and do not claim to capture all relevant subtleties of different ethical theories. Before reviewing in some details the various ethical concerns mentioned above, let us briefly consider libertarianism. Because libertarians insist on freedom of choice and on the idea that people are morally entitled to their resources, in particular the money they own, it is hard to see how they could support a no-profiling thesis which compel agents to some form of risk sharing and money redistribution. For libertarians, agents have the right to accept, and companies to offer, health insurance contracts which any terms, in particular with some profiling. Libertarianism seems to be the only moral theory which clearly opposes no-discrimination positions.

Utilitarian concerns

In a utilitarian framework, one should maximize the total sum of individual utilities. Let us compare a world, called NP, in which only companies which do not profile exist, and a world called P in which only companies which profile exist. If an agent's utility depends exclusively on the money she gains and loses, the sums of expected utilities are the same in both worlds, if the insurance companies are assumed to simply redistribute the same total health costs. In other words, health profiling seems to raise no specifically utilitarian worries. 4Now, total utility plausibly does not depend only on the monetary gains and losses of individual agents but also on that of insurance companies. Profiling itself can be extremely costly to the insurance companies. Collecting private data on individuals and making statistical analyzes require significant technical and human resources. Also, profiling can generate costly disputes about whether there were pre-existing conditions that made people ineligible for the insurance they chose. Therefore, profiling is costly to the insurance company, and in fine to the agents.

In addition, money is not all that matters. People who have to pay more as the result of profiling may feel discriminated against and stigmatized. Such emotional costs plausibly lower total utility. Also, whether people are happy with paying specific premiums depends on what they get in return. Imagine two people paying the same premium: A falls ill but B does not. Does it make sense to assume that the utility loss of A's sickness is compensated for perfectly by the reimbursement from the insurance? And what about B who pays the premium but never gets reimbursed because she does not fall ill? She loses money but does get a sense of security.

Let us therefore extend our simple framework and assume that three factors matter for well-being (or utility for that matter):

1. money (which you lose when paying premiums and health care costs, but the latter can get reimbursed);

2. health (which can be lost but also restored when health care costs are made);

3. psychological and emotional costs (such as a sense of security, or feelings of unfairness and stigmatization).5

In this extended framework, the only difference between NP and P worlds will lie in the third factor. Assume for simplicity that agents are either sick or healthy. The sick may feel stigmatized in the P world (negative utility), while the healthy will have a sense of security (positive utility) and may have a feeling of unfairness (negative utility) since they pay for the sick. Overall, it is not clear where the total sum of utility will head, unless we make specific assumptions about the values and we do not enter this complication here.

of the utilities associated with psychological costs. The value of this extended framework, however, is to reveal the uneven distribution of utility losses and gains. In a P world, the sick will suffer from utility losses that are not only health-related (obviously) but also money-related and stigmatization-related. In a sense, health profiling triples the harm inflicted on the sick, who are worse off not only in terms of health but also money (their premiums are higher in a P world than in an NP world) and psychology (they feel stigmatized). Conversely, in an NP world, the healthy basically sponsor the treatments of the sick, more evenly distributing utility. However, such distributional concerns are best expressed not in utilitarian but in prioritarian and egalitarian terms, to which we turn below. These approaches have the advantage that they do not require us to make a hypothetical guess of the above values of the utilities associated with psychological costs.

To summarize the utilitarian approach, if we only consider money (item 1) and health (item 2), the overall cost remains the same in both worlds, and NP and P are morally equivalent. The only difference is in the redistribution of the total utility within the population at the individual level. Now, if psychological and emotional costs (item 3) are included, it is essential to precisely and quantitatively define this notion. Note that the definition and the scope of these costs are quite subjective, since individuals may feel different emotions or costs depending on their medical histories, psychological profiles and health status [START_REF] Finkelstein | Approaches to estimating the health state dependence of the utility function[END_REF]. However, the addition of this third item does not help us to rule on the issue of health profiling within utilitarianism. This is why we now turn to other ethical concerns.

Prioritarian concerns

A second set of concerns with health profiling is that it makes the worst-off even worse off. If everyone has the same amounts of money (as indicated in the end of the Introduction, we do not consider differences in incomes here for simplicity), people in poor health are the worst-off, and it would be unjust if they were made even worst off.

Leximin prioritarians believe that inequalities -e.g. paying different premiums -are just only if they improve the situation of the worst off. Take Rawls's Difference Principle, which states that "social and economic inequalities are to be arranged so that they are [. . . ] to the greatest benefit of the least advantaged" (Rawls 1999, p. 95). In our problem, the least advantaged are those in poor health. Since inequalities should be arranged to their benefit, they should at least not be charged more than people in good health, which speaks against health profiling.

Other prioritarians argue that the same incremental well-being gains should be given more moral weight when they go to the worst off than when they go to the better off (e.g. [START_REF] Adler | Well-Being and Fair Distribution[END_REF]). Here too, health profiling is unjust because it further worsens the situation of the worst off while benefiting the better off. In a P world, those in poor health will see both their wealth and health decrease. In an NP world, at least the worst-off (in terms of health) are not made worse off (in terms of money, compared to the healthy). If any differential treatment is called for on prioritarian grounds, it is a form of inverse profiling, with the sick paying lower rather than higher premiums, which would improve their situation compared to a P world.

The idea that health profiling constitutes an unfair treatment of the worst-off is basically a reformulation of the idea that it constitutes a double (or even triple) punishment on the sick. First, agents in poor health already pay a penalty by being in poor health. Second, they are charged more because of profiling (compare this with people in jail, who are not charged for the cost of their prison stay). Third, they suffer emotional costs through stigmatization.

Contractualist concerns

Contractualists like Rawls and Scanlon argue that ethical concerns arise from a (hypothetical) contract between agents. Rawls uses his famous "veil of ignorance" thought experiment to argue that rational parties in the original position would agree on justice principles that ensure the best possible situation for the worst off. If you do not know which situation you will end up in (e.g. whether you will be in poor or in good health), you will only favor inequalities (1) that arise from fair equality of opportunity (see Section 2.4) and ( 2) that improve everyone's situation, including the worst-off. As such, we would all see the injustice of requiring those in poor health to pay more, because we might as well end up in that situation (once the veil of ignorance is lifted and the distribution of health benefits is known). Health profiling would not pass this contractualist test of justice. It would indebt the sick and likely turn them into a permanent underclass. Trapping them into poverty, health profiling would generate a vicious cycle of bad health and less wealth, which besides obvious utilitarian (2.1) and prioritarian (2.2) worries, will not be consented to from the impartial point of view of Rawls' original position.

Now take the contractualist approach by Thomas Scanlon, according to which acts and policies are to be judged by moral principles, and these principles only hold if no one could reasonably reject them. "In order for a principle to be reasonably rejectable there must be some relevant standpoint from which people typically have good reason" to refuse that this principle be used by themselves or by others (Scanlon 1998: 218). Consider health profiling, i.e. adapting premiums according to the agents' risk profiles. People in poor health could reasonably object to this principle, for reasons mentioned before: it amounts to a triple punishment. Conversely, it would not be reasonable for healthy people to oppose a no-profiling principle on the basis that they are paying slightly higher premiums. Scanlon's contractualism thus seems to conclude that the sick have legitimate grounds for complaint, which adds to the conclusion that health profiling is ethically impermissible.

A general feature of contractualism is that individual benefits and burdens should not be aggregated and that utilitarians neglect what Rawls (1999) calls the "separateness of persons". [START_REF] Ashford | Contractualism. The Stanford Encyclopedia of Philosophy (Fall 2012 Edition)[END_REF] express this as saying that contractualism "does not allow a number of lesser complaints to outweigh one person's weightier complaint". Compare this with the utilitarian approach in Section 2.1. If we assume that agents' utility functions are convex, then high premiums have comparatively less weight than low ones. When all individual utilities are added, profiling gives a higher collective utility than no profiling. Contractualists disagree: the fact that some persons have to pay an excessively high premium is sufficient to reject profiling, even though others benefit from paying a low premium with a relatively higher individual utility. This corresponds to the prioritarian insight that gains (and conversely, burdens) for the worst off have more moral weight than gains (and burdens) to those better of.

Since the rejection of a principle can be based on reasons not related to well-being or utility, contractualist concerns are not consequentialist. "I might reject a principle that arbitrarily exempts some people from a burden borne by everyone else, on the grounds that such a principle treats me unfairly -even if the alternative is a principle that places that burden on everyone." [START_REF] Ashford | Contractualism. The Stanford Encyclopedia of Philosophy (Fall 2012 Edition)[END_REF] The relevance to health profiling should be clear: paying more can be considered unfair to those in poor health because of consequentialist reasons (it amounts to a triple punishment on the part of the sick), and non-consequentialist reasons (the sick are not responsible for being ill; more on this in Section 3).

Egalitarian concerns

Egalitarian concerns about health profiling are diverse, basically because of the variety of egalitarian theories, each of which provides a different answer to the question: equality of what? Utilitarian or more broadly welfarist theories can be understood as egalitarian (each unit of utility or welfare is taken into equal consideration) and so can contractualist theories (each person is given equal respect, an equal position in the contractualist scheme). Or one could favor equalizing health, but we are already assuming that insurance companies reimburse all health costs. Or one could favor equalizing access to health care, which obviously speaks against health profiling, which makes access to health care depend straightforwardly on health risks. Or one could favor equalizing wealth, which holds that the situation in which people's wealth (or spent money) are more equal should be preferred. Again, profiling goes against such an egalitarian theory.

A widespread egalitarian theory is resourcist and stresses that justice requires equalizing everyone's resources (rights, liberties, primary goods but also wealth and opportunities). Such responsibility-sensitive luck egalitarian theories argue that what people do with these resources is up to them. We will treat them, and their relevance to health profiling, more extensively in Section 3.

Closely related is capability theory, according to which everyone should have (equal or at least basic) capabilities or effective opportunities to do and be what one wants to [START_REF] Robeyns | The capability approach: a theoretical survey[END_REF]. In a P world, the sick do not benefit from the redistribution that would characterize an NP world and ultimately end up with substantially less capabilities than the rich, even to the extent that their most basic capabilities (like bodily health; Nussbaum 2006) are no longer met.

Another promising theory is social egalitarianism, which stresses that in a just society, everyone can relate to each other 'as equals'. Instead of trying to equalize a specific 'currency of justice' (like utility, welfare, resources or capabilities), authors like Samuel Scheffler and Jonathan Wolff see equality in social or relational terms. Again, health profiling seems hardly defensible, as it is stigmatizing to those in poor health. Also, as the abovementioned vicious cycle between health inequalities and economic inequalities traps (a lot of) sick people into poverty, they are increasingly marginalized and effectively inhibited from relating to others as equals.

Finally, one can, like [START_REF] Scanlon | The Diversity of Objections to Inequality[END_REF], refer to multiple reasons to object to inequality, none of which assume that such inequality is in-trinsically bad. The inequalities arising from health profiling can be objected to because they ultimately result in suffering (with some sick people no longer able to pay their health costs), because they give rise to problematic relationships of superiority and inferiority (with sick people being stigmatized), because they give rise to unequal playing fields and thus unequal opportunities in multiple domains (like the job market) and undermine the procedural fairness of procedures in important basic institutions (like equal access to basic health care).

The conclusion that health profiling raises serious egalitarian concerns thus holds across the board. Regardless whatever should be equalized, a P world raises ethical worries that an NP does not.

3 What about responsibility?

One might object that the analysis of the previous Section is too rough: all parameters X that could be used in profiling have been treated equally, whereas they are not equal from an ethical viewpoint. Some cases of poor health seem to result from deliberate choices, for which people bear responsibility. For instance, as the health risks of smoking are common knowledge nowadays, someone who smokes can be held responsible for this behavior and can thus be required to bear its consequences. It would be unfair to have others pay for one's choices. If someone chooses to take a risk, she should be prepared to pay for it. So, the objection goes, ethical considerations regarding responsibility not only allow but even require profiling on those parameters for which people bear responsibility. This objection is in line with moral theories for which a core distinction should be made between what results from pure bad luck and what results from an agent's choice (e.g. along Dworkin's 2000 line). Depending on the specific distributive principle endorsed, this can give theories such as luck egalitarianism or luck prioritarianism. For instance, luck egalitarianism (Lippert-Rassmussen 2015a), considers that inequalities (e.g. paying a higher premium) are just when they arise from choices (option luck). Luck egalitarians generally argue that resources (such as money) should be distributed equally at first but that inequalities may legitimately arise through people's choices (such as people with unhealthy lifestyles paying more for their health care).

We agree that responsibility is indeed crucial in assessing fairness, and we are ready to grant the point made by luck egalitarians, luck prioritarians, or other luck sensitive theories. What we want to point at, however, is that the question of responsibility in health insurance is more complex than the above objection seems to assume. As a starting point, let us specify what is meant by "responsibility" with the following classical definition: an agent is responsible for Y if Y is a result, foreseeable by the agent, of a free choice of hers. This definition can be refined by acknowledging that forseeability and freedom of choice come in degrees, and hence responsibility too. In our problem, a first distinction is that responsibility can bear on two things: the value of a parameter X (e.g. I smoke), and the associated health costs (e.g. the cost of my chemotherapy in case I have a lung cancer). We consider responsibility for X in this Section, and responsibility for the costs in the next Section.

Recall the list of factors we consider in this paper (cf. Section 1): present diagnosed illness, medical history, body mass index, smoking habits, alcohol consumption, genetic information, gender, age, race, sexuality, place of living. Few people would consider that one is responsible for one's genes, gender, age, race, or sexuality. The most plausible candidates to pertain to one's responsibility are then four: body mass index (BMI), smoking habits, alcohol consumption, and place of living (plus diagnosed illness and medical history insofar as they are linked to these parameters). According to the responsibility objection presented above, profiling on these parameters is fair because agents can be held responsible of them and of related health costs. A general theme of our answer is that the responsibility problem is more complex than sketched above. In particular, not all of these four parameters should be dealt with in the same way. We group together the first three -BMI, smoking habits and alcohol consumption -as they involve addictive behaviors, and we discuss them in this Section, distinguishing between theoretical (Section 3.1) and pragmatic (Section 3.2) issues. Place of living is discussed in Section 4.

A theoretically complex issue

One should start by acknowledging a theoretical complexity. Smoking, drinking, and food habits that can increase your body mass index, are unhealthy lifestyles which are addictive. And it is scientifically wellestablished that (i) genetic predispositions (Agrawal and Linskey 2008[START_REF] Kreek | Genetic influences on impulsivity, risk taking, stress responsivity and vulnerability to drug abuse and addiction[END_REF], Rankinen et al. 2005[START_REF] Stice | Relation between obesity and blunted striatal response to food is moderated by Taq1A A1 allele[END_REF][START_REF] Wang | Similarity between obesity and drug addiction as assessed by neurofunctional imaging: A concept review[END_REF][START_REF] Bochukova | Large, rare chromosomal deletions associated with severe early-onset obesity[END_REF][START_REF] Grimm | Genetics of eating behavior: Established and emerging concepts[END_REF] and (ii) environmental factors play an important role in these three points. It has been clearly shown that a wide variety of environmental factors, such as social, cultural, physical and familial environments, have a strong and significant impact on drug addictions [START_REF] Rhodes | Risk factors associated with drug use: the importance of 'risk environment[END_REF]) and body mass index [START_REF] Bishop | Childhood obesity[END_REF][START_REF] Borengasser | High fat diet and in utero exposure to maternal obesity disrupts circadian rhythm and leads to metabolic programming of liver in rat offspring[END_REF]. For example, [START_REF] Whitesell | Familial, social, and individual factors contributing to risk for adolescent substance use[END_REF] highlight how familial risk factors -such as childhood maltreatment, level of parental education, familial socio-economic status -can increase risk of drug consumption for adolescents. Physical and sexual abuse, emotional abuse, but also social influences or deviant peer relationships are non-exhaustive factors that explain drug use (for reviews, see [START_REF] Hawkins | Risk and protective factors for alcohol and other drug problems in adolescence and early adulthood: implications for substance abuse prevention[END_REF][START_REF] Whitesell | Familial, social, and individual factors contributing to risk for adolescent substance use[END_REF]. Concerning the BMI and obesity, [START_REF] Christakis | The spread of obesity in a large social network over 32 years[END_REF] show that the risk of being, or even becoming obese, is significantly higher for subjects with "obese family members or peers in their social networks". This phenomenon is known as "social clustering" and could be explained by "similar social norms" and by an induction process between individuals that favor the spread of obesity. Genetic, psychological and environmental factors greatly influence the BMI and food habits (for a review, see [START_REF] Richter | Understanding and addressing food addiction: A science-based approach to policy, practice and research[END_REF] Genetic and environmental factors are clearly out of the scope of people's responsibility -one doesn't choose one's genes, nor the socioeconomic status of one's parents. The importance of these factors is not anecdotal. For instance, the genetic predisposition is estimated to account for around 50% of alcohol addictions (Gierski et al. 2013) and between 50 and 80% of the BMI (Allison et al. 1996, Bell et al. 2005). 6 There are also some vicious circles and reinforcement processes. For example, drinking a lot can affect one's abilities, such as memory, impulsivity, or decision-making and increases the need to drink [START_REF] Cabé | Troubles cognitifs dans l'alcoolodépendance : intérêt du dépistage dans l'optimisation des prises en charge[END_REF]. Studies on neuronal and hormonal functioning have also shown some addictive processes in the appearance and maintenance of obesity and in addictive-like eating behaviors [START_REF] Gearhardt | Neural correlates of food addiction[END_REF][START_REF] Murray | Hormonal and neural mechanisms of food reward, eating behaviour and obesity[END_REF]. These processes are close to drug addictions [START_REF] Volkow | How can drug addiction help us understand obesity?[END_REF] and affect subjects' behaviors and emotions [START_REF] Parylak | The dark side of food addiction[END_REF], generating reinforcement processes. Then, an initial responsibility can only diminish as time goes. In addition, some psychiatric disorders, for which people cannot be held responsible, do have some effects on health. For instance, schizophrenic persons in acute delirious episodes can become disinterested in topics considered relevant for "living a healthy life", or put themselves into physical danger. Note finally that the knowledge of the causal influence of each factor is not sufficient to assess someone's responsibility. Interactions between the various factors are known to be crucial in triggering an addiction (for instance, a genetic predisposition requires some environmental factor to be active). So one needs to know much more to attribute individual responsibility.

Overall, this gives several theoretical reasons why it is not possible to simply consider that an individual is fully responsible for a parameter related to addictions on which profiling could be implemented, and hence that it would be fair to do so. Free will is just not the only ingredient there. 7 One might reply that the causal influence of genetic and environmental factors can be assessed, and that the premiums should vary according to what remains of one's responsibility. Unfortunately, this suggestion raises important pragmatic difficulties, that we discuss next.

Pragmatic difficulties

We now want to argue that assessing the causal influence of genetic and environmental factors for smoking, drinking, and BMI, in order to remove that part from the responsibility of agents, is not pragmatically feasible for health insurance companies.8 First, consider genetic factors. Current knowledge of the causal influences of genetic factors is only at its beginnings, and is not very precise yet. For example, the influence of genetic factors on alcoholic addiction is known with large uncertainties: "between 40 and 60%" (Gierski et al 2013) and between 50 and 80% for the BMI [START_REF] Allison | The heritability of body mass index among an international sample of monozygotic twins reared apart. International journal of obesity and related metabolic disorders[END_REF][START_REF] Bell | The genetics of human obesity[END_REF]. Which rate would it be fair to consider for profiling? Second, identifying the causal influence of environmental factors (e.g. of having an alcoholic father or an obese mother) is even much more complex, and existing data are even less precise. Third, assessing the level of interaction between genetic and environmental factors adds a high degree of complexity. Fourth, these studies on environmental factors are epidemiological and concerned with averages, whereas the responsibility argument requires the assessment of individual responsibility. A precise individual responsibility cannot automatically be inferred from (imprecise) averages. For instance, even if we knew that having an alcoholic father (an obese mother) accounted for alcoholism (obesity) at the rate of 30% on average, this would not imply that Mr. Y's responsibility is reduced of 30% because of his alcoholic father (his obese mother). Perhaps, in his particular situation, related to personal circumstances and history, his responsibility is actually reduced of 10%, or of 50%. It is not enough that the insurance company is fair on average, because the argument of responsibility is precisely made at the individual level.

One might suggest that the insurance company could go beyond epidemiological medical studies, and launch studies of environmental factors of their would-be clients to assess their individual responsibilities. But this would be very difficult if not impossible (how assess the precise influence of Mr. Y's alcoholic father, or obese mother?) and very costly. Furthermore, these individual inquiries could be opposed on privacy grounds. For instance, egalitarians could argue that inquiring in great detail into people's intimacy would fail to treat them with the respect that is equally due to all human beings.

If implemented, profiling can raise premiums dramatically and this can have dire consequences on individuals. Given our previous point about the financial and emotional harms of health profiling on those who are already in poor health, we believe a cautious attitude should be adopted: without high-standard proofs of someone's individual responsibility about parameter X, profiling on X should not be implemented. A kind of presumption of innocence should prevail.

This cautious approach can be re-expressed as a value judgment between two possible kinds of errors: either charging high fees for individuals who are not responsible for the value of parameter X, or charging only slightly higher fees for all individuals, some being responsible and some being not. We believe the latter situation is preferable when knowledge is sparse and responsibility cannot be assigned with enough confidence. It would be morally wrong to charge someone very high fees without being sufficiently sure that she is responsible. As we have argued above, the knowledge that health insurance companies can reasonably hope to have on individual responsibilities is very low and imprecise on many parameters. As a consequence, the cautious approach we embrace recommends that profiling should not be implemented for these parameters

To sum up, we have argued that for three over four parameters, there are theoretical problems in considering that agents are responsible for the values of the parameters, or pragmatic problems in assessing these values. We discuss the fourth parameter, that of place of living, in the next Section, within a more general consideration.

Responsibility and causality

The previous section has discussed the responsibility of an agent towards the value of a parameter X. As indicated, this is not the whole story of responsibility: what matters in the end (according to the objection mentioned at the beginning of Section 3) is her responsibility for the health costs. It is because the agent is responsible for increased health costs that it would not be fair for others to pay for these extra costs. This leads us to consider now the relation between X and associated health costs.

So that the responsibility of the agent extends to health costs, and not just to X (e.g. so that the responsibility of the agent extends to the cost of her chemotherapy, and not just to her being a smoker), health costs need to be forseeable by the agent, according to the classical definition adopted in Section 3 (an agent is responsible for Y if Y is a result, foreseeable by the agent, of a free choice of hers). This forseeability requires two things: that there is a causal connection between X and the costs (so that choosing X does make a change in the costs), and that the agent is aware of this connection. So, correlations between X and costs are not enough for a profiling to be fair, and this is in stark opposition with current profiling practices, which are just based on the identification of correlation patterns.

In other words, if someone is responsible for some X, but that X is not what makes health costs be higher, then it is unfair to charge the person more for the increased health costs. The responsibility of the person just bears on something irrelevant for health costs. For instance, suppose that there is a correlation between soccer match attending and increased health costs in one's life. Attending to soccer matches (=X) can be considered as a deliberate choice, on which one's responsibility makes no doubt. But would it be fair to profile on this parameter in health insurance? No, because there is no causal relation between attending a soccer match and having a poorer health. I'm not suddenly changing my health when attending a soccer match; instead there are some confounders, like belonging to some social class. Now, causal relations are not always of an all-or-nothing nature, as the presence of a parameter can only increase the chance of an illness, and of related health costs. So, a better version of our point about causality is that profiling on X is all the fairer than the causal link between X and health costs is strong. Summing up with previous Section 3, we can now claim that there are three necessary conditions for a profiling on X to be fair: (i) the agent is responsible for X, (ii) X is causally linked to health costs, and (iii) the agent knows that (ii). This can be summed up in the formulation that a profiling is fair only if the agent is responsible for the health costs. Since each condition admits degrees, this transmits onto the final judgment on fairness, producing a more nuanced thesis: a profiling on X is all the fairer than (i) the agent is all the more responsible for X, (ii) X is all the more causally linked to health costs, and (iii) the agent all the more knows that (ii). This is the final general thesis about fairness for profiling in health insurance on which we settle. Note that according to our thesis, it would not have been fair to profile on smoking before mid-twentieth century for this reason, and it would not be fair to profile on the use of many products today for that same reason.

Note that some parameters satisfy condition (ii) and not condition (i). For instance, age is one of the causes of many illnesses, but it is not the result of deliberate choice. So our thesis forbids profiling on age, and requires that newborns pay as much as grownups or elderly people. This might be seen as a weird position. Does it signal that our thesis, and arguments, are wrong? We think it rather signals that the limits of our methodological choice of setting aside differences in income, have been reached. One might have the intuition that profiling on age is fair, and for instance that it is not unfair for an insurance company to offer discounts for children. It seems to us that such an intuition largely depends on the fact that children don't have income of their own, and that charging them a full premium would place too huge a financial burden on their parents, whereas our western societies are accustomed to public policies in favor of birth and families. In other words, our no profiling thesis on age should be complemented with the reader's own fairness views on social policies regarding families and elderly people, a question that we have deliberately chosen not to address in this paper. This shouldn't be considered as a counterargument against our thesis.

Let us now come back to our initial question, and investigate whether some parameters satisfy the three necessary conditions we have stated above. The previous section has excluded all parameters except the place of living (e.g. a neighborhood, a town, a county). Suppose that there is some correlation between the place of living and health costs, of which the insurance company would like to take advantage. Either this correlation comes from a causality relation (the place of living causes some increased health costs), or it does not come from one. Suppose there is a causality relation (i.e. condition (ii) is met). It must be because there is some form of pollution in the area which must cause some illness to the inhabitants, or something similar. Then it is very unlikely that some people might voluntarily choose to live there -you generally live in a polluted area because you are not rich enough to live elsewhere. So, no responsibility in this case, and condition (i) is actually not met when condition (ii) is. Suppose now there is no causality relation between the place of living and the increased health costs (condition (ii) is not met). Then it is very possible that people chose to there (since for instance there is no pollution), and condition (i) might well be met. But overall, conditions (i) and (ii) are never met together. So, we conclude that it is unfair to profile on any parameter from our list in health insurance.

Conclusion

We have argued that profiling in health insurance raises substantial ethical concerns for egalitarians, prioritarians, contractualists, and possibly for utilitarians, especially if they are concerned with luck and responsibility issues. Only libertarians would not oppose profiling. We have argued that the no-profiling conclusion holds for a large range of parameters: present diagnosed illness, medical history, body mass index, smoking habits, alcohol consumption, genetic information, gender, age, race, sexuality, place of living (with a nuance regarding age in relation with social policies, as discussed in Section 4). As mentioned in the introduction, we do not take stands here on whether it would be fair for agents with higher incomes to have a higher premium. The reader may combine her own view on that question with our thesis. Because insurance companies are generally interested in health profiling, it seems to us that the only way for practice to be in accordance with our ethical principles is that the law forbids profiling in health insurance, as is already done in some countries for some parameters. However, discussing precisely how to implement this ban in policy would need another paper, and we shall not attempt it here.

Some further generalization might be considered. We have assumed that the reimbursement rate is identical for everyone. What if some people would like a lower or higher coverage? Our no-profiling thesis can be reproduced for any level of reimbursement. However, the various levels of reimbursement should vary uniformly, and not be specialized on some specific illness. Otherwise, for instance, smokers would choose the special reimbursement for lung cancer, while non-smokers would avoid it, and this could lead to a de facto profiling.

Our general thesis might be nuanced for some voluntary (possibly punctual) practices, such as the practice of extreme sports like bungeejumping or climbing, or traveling to dangerous countries. These practices involve higher health risks and thus higher expected health costs. Given that responsibility is clearly involved in these choices (although extreme sports may to some extent be addictive), health profiling could be ethically permissible in such exceptional cases. Rather than allow health profiling, however, the already current practice to require people to take additional insurances when practicing specific sports or when traveling serves the same purpose. In sum, we believe that on any plausible account of what matters ethically, profiling in health insurance is objectionable.

There is, however, an ethical viewpoint which has not been considered in this paper: paternalism, the idea that when agents are not fully rational, and their choices are not optimal, an authority (here: the State or the insurance company) can limit agents' autonomy so as to improve their choices for their own good. In the case of health insurance, paternalism could try to justify higher premiums for smoking addicts, for instance, so as to give them an additional incentive to quit smoking. But paternalism is not without raising ethical concerns of its own (e.g. could States, and even more private companies, be paternalistic?) and more fundamentally, the problem would be changed: the question would become to find which amount of increase in health premiums would best incentivize agents (as opposed to: whether the fixed increase in health premium corresponding to the fixed increase in risk is fair), and for which parameters.

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France has exceptions: "mutuelles", which are not-for-profit health insurance companies, are not allowed to implement some profiling based on medical criteria. However thay can profile on age or place of living. French for-profit health insurance companies are allowed to profile on medical

criteria. 2 Profiling on genetic information has been forbidden in the US since 2008. Cf. https://www.genome.gov/24519851/ In Australia, profiling is illegal for "health status, age or claims history". Cf. http://www.health.gov.au/internet/main/publishing.nsf/Content/Frequently+Asked+Questions-1

Most economic analyzes consider that insurance premiums must be risk adjusted mainly when purchasing insurance is not mandatory, since risk adjustment is necessary to prevent adverse selection causing either the bankruptcy of insurance companies or the collapse of insurance markets.

This depends on the assumption that individual utilities are linear with premiums. If the aggregated utility function were convex or concave, utilitarianism would side respectively for or against profiling. However, empirical data on the shape of the utility function for losses are not consensual: in experiments, some individuals display concave functions, others display convex or linear, and there seems not to be a "typical" profile[START_REF] Kahneman | Prospect theory: An analysis of decision under risk[END_REF][START_REF] Abdellaoui | Loss aversion under prospect theory: A parameter-free measurement[END_REF][START_REF] Abdellaoui | A tractable method to measure utility and loss aversion under prospect theory[END_REF][START_REF] Abdellaoui | Do financial professionals behave according to prospect theory? An experimental study[END_REF]. So, it is not clear which function we should consider here,

A feeling of stigmatization can occur for people in poor health, like in "I'm pointed at because of my obesity". On the other side, some people in good health may have a feeling of unfairness, like in "I shouldn't be paying for those people in bad health".

One may object that in criminal law for instance, the responsibility of alcoholics is not discounted in this way. To this, we reply first that the law in many countries may not have adapted quickly enough to recent scientific findings, second that the moral responsibility in which we are interested here may not correspond to the legal responsibility (and it is a matter of ongoing debate whether it should).

In the philosophical literature on addiction, the position we are defending here might actually seem like a truism. For instance,[START_REF] Wallace | Addiction as defect of the will: some philosoph-ical reflections[END_REF] needs to write a whole paper to argue that volition plays at least some role in the actions of an addicted person, against those who hold a mechanistic conception of addiction, where actions are determined by desires.

Note that we are actually considering a form of genetic profiling that is the opposite of the kind discussed in the literature: we use genetic factors to argue that premiums should not be raised.

Acknowledgments

Many thanks to Bart Engelen for his valuable contribution. We would like to thank also Marlène Guillon, Julien Cabé, Nicolas Cabé, Tom Juille, as well as participants at the 13th conference on the International Network for Economic Methodology (San Sebastian, 2017), and audiences in Poitiers (MAPP and MSHS, 2018) for useful comments and suggestions. This work has benefited from an AXA postdoctoral fellowship and support from GREDEG Nice.