Alexandre Vallée

Emmanuel Wiernik

Sofiane Kab

Cédric Lemogne

Marcel Goldberg

Marie Zins

Professor Jacques Blacher
email: jacques.blacher@aphp.fr

of depressive symptoms and socioeconomic status in determination of blood pressure levels and hypertension: The CONSTANCES population based study

Keywords: depressive symptoms, blood pressure, hypertension, CES-D, socioeconomic status

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

INTRODUCTION

Hypertension is a major risk factor for cardiovascular diseases [START_REF] Stokes | Blood pressure as a risk factor for cardiovascular disease. The Framingham Study--30 years of followup[END_REF] and could be more prevalent in persons with psychopathology [START_REF] Carroll | Blood pressure reactions to acute psychological stress and future blood pressure status: a 10-year follow-up of men in the Whitehall II study[END_REF][START_REF] Matthews | Blood pressure reactivity to psychological stress predicts hypertension in the CARDIA study[END_REF]. The World Mental Health Survey estimates that depression affects 350 million people worldwide (World Health Organization, 2012). Depression became the second global disease burden after ischemic heart disease since 2020. Recent large population studies have shown that psychiatric disorders were associated with hypertension [START_REF] Sandström | Psychiatric comorbidities in patients with hypertension--a study of registered diagnoses 2009-2013 in the total population in Stockholm County, Sweden[END_REF] and some studies have suggested that blood pressure (BP) may explain a part of the well-known association between psychopathology and cardiovascular diseases (CVD) [START_REF] Scuteri | Depression and cardiovascular risk: does blood pressure play a role?[END_REF].

Nevertheless, some studies which have investigated the association between depression symptoms and BP have reported positive [START_REF] Cuffee | Psychosocial risk factors for hypertension: an update of the literature[END_REF][START_REF] Jackson | Depression, anxiety and risk of hypertension in mid-aged women: a prospective longitudinal study[END_REF][START_REF] Maatouk | Association of hypertension with depression and generalized anxiety symptoms in a large population-based sample of older adults[END_REF], negative [START_REF] Hildrum | Anxiety and depression lowers blood pressure: 22-year follow-up of the population based HUNT study, Norway[END_REF][START_REF] Park | The relationship of depression with the level of blood pressure in population-based Kangbuk Samsung Health Study[END_REF][START_REF] Wiernik | Cardiovascular risk goes up as your mood goes down: Interaction of depression and socioeconomic status in determination of cardiovascular risk in the CONSTANCES cohort[END_REF] or nonexistent associations [START_REF] Grimsrud | The association between hypertension and depression and anxiety disorders: results from a nationallyrepresentative sample of South African adults[END_REF][START_REF] Yan | Psychosocial factors and risk of hypertension: the Coronary Artery Risk Development in Young Adults (CARDIA) study[END_REF]. The meta-analysis of Meng et al. has shown that depression is associated with increased risk of hypertension incidence suggesting that it is an independent risk factor of hypertension [START_REF] Meng | Depression increases the risk of hypertension incidence: a meta-analysis of prospective cohort studies[END_REF]. However, studies have observed a significant and negative association between levels of depressive symptoms and BP among large populations [START_REF] Hildrum | Anxiety and depression lowers blood pressure: 22-year follow-up of the population based HUNT study, Norway[END_REF][START_REF] Licht | Depression is associated with decreased blood pressure, but antidepressant use increases the risk for hypertension[END_REF] and among elderly people [START_REF] Liu | Depressive symptoms and metabolic syndrome components among older Chinese adults[END_REF]. Globally, transversal studies have suggested that depression was negatively associated with blood pressure whereas longitudinal studies have shown a positive association [START_REF] Nabi | Trajectories of depressive episodes and hypertension over 24 years: the Whitehall II prospective cohort study[END_REF].

The literature has accumulated some evaluating effects of psychosocial factors with depression [START_REF] Michal | Association of hypertension with depression in the community: results from the Gutenberg Health Study[END_REF]. Depressive symptoms varied considerably according to the role of contextual factors, including economic, environmental and demographic factors [START_REF] Kessler | The global burden of mental disorders: an update from the WHO World Mental Health (WMH) surveys[END_REF]. Socioeconomic status (SES) has come into focus as crucial determinant of depressive symptoms [START_REF] Dinardo | Variation of mechanical properties and quantitative proteomics of VSMC along the arterial tree[END_REF], showing that low SES-individuals presented higher odds of being depressed (V et al., 2007).

In parallel, many psychological factors, including depression, have been associated with increased risk of CVD, as has low SES [START_REF] Havranek | Social Determinants of Risk and Outcomes for Cardiovascular Disease: A Scientific Statement From the American Heart Association[END_REF]. Currently, the notion of social risk factors has been suggested to interact with psychological risk factors as etiology of CVD [START_REF] Lemogne | When Blue-Collars Feel Blue: Depression and Low Occupational Grade as Synergistic Predictors of Incident Cardiac Events in Middle-Aged Working Individuals[END_REF][START_REF] Wiernik | Cardiovascular risk goes up as your mood goes down: Interaction of depression and socioeconomic status in determination of cardiovascular risk in the CONSTANCES cohort[END_REF]. Different levels of SES indicators (e.g., education, occupational status, income) could modify the effects of psychological factors in incidence of CVD. Psychosocial changes have brought transformations in social organizations.

The relationship between depressive symptoms and blood pressure has been investigated in many epidemiological studies [START_REF] Jani | Relationship Between Blood Pressure Values, Depressive Symptoms, and Cardiovascular Outcomes in Patients With Cardiometabolic Disease[END_REF][START_REF] Kim | Depressive symptoms in elderly adults with hypotension: different associations with positive and negative affect[END_REF]. In parallel, hypertension was mainly associated with SES factors [START_REF] Cherfan | Unhealthy behavior and risk of hypertension: the CONSTANCES population-based cohort[END_REF][START_REF] Leng | Socioeconomic status and hypertension: a meta-analysis[END_REF].

Nevertheless, at our knowledge, no study has focused on the interactions between depressive symptoms, hypertension and SES. We hypothesized that depressive symptoms may have different associations with BP and hypertension according to the different levels of SES factors.

Main part of the studies investigating these associations are not representative of general population or country, and standardized measurements or definitions for SES and depression were lacking [START_REF] Freeman | The role of socio-economic status in depression: results from the COURAGE (aging survey in Europe)[END_REF]. The CONSTANCES cohort is a large prospective population based cohort designed as a research infrastructure and as a large random sample of the French adult population [START_REF] Goldberg | CONSTANCES: a general prospective population-based cohort for occupational and environmental epidemiology: cohort profile[END_REF]. The main strengths of the CONSTANCES cohort is that it provides standardized measurements for blood pressure, and standardized definitions of a broad scope of health conditions and determinants, occupational factors and outcomes, including participants living and working in either urban or rural neighborhoods and diversified in terms of jobs of socioeconomic status. In the CONSTANCES cohort, depressive symptoms were evaluated with de CES-D score, which was a self-report scale designed to measure depressive symptomatology in the general population. Validity was established by pat terns of correlations with other self-report measures, by correlations with clinical ratings of depression, and by relationships with other variables which support its construct validity [START_REF] Radloff | A self-report depression scale for research in the general population[END_REF][START_REF] Wiernik | Cardiovascular risk goes up as your mood goes down: Interaction of depression and socioeconomic status in determination of cardiovascular risk in the CONSTANCES cohort[END_REF].

Thus, the purpose of our study was to investigate, stratified by gender, the association between depressive symptoms, estimated by the CES-D score, with blood pressure levels and hypertension. Then, we investigated the extent to which the association between depressive symptoms, estimated by the CES-D score, and BP levels and hypertension might differ according to SES variables based on the CONSTANCES population.

METHODS

The CONSTANCES cohort

This ancillary study is a cross-sectional analysis using data from the CONSTANCES study.

The general aim of CONSTANCES is to establish a large population-based cohort to contribute to the development of epidemiologic research (www.constances.fr). Details about the study design and methods have been extensively discussed [START_REF] Zins | The French CONSTANCES population-based cohort: design, inclusion and follow-up[END_REF].

CONSTANCES is an ongoing prospective cohort that started in 2012. Adults aged 18-69 at inception were randomly selected from the National Health Insurance Fund (CNAMTS:

Caisse Nationale d'Assurance Maladie des Travailleurs Salariés) that covers salaried workers, professionally active or retired and their dependents (more than 85% of the French population) following a sampling scheme stratified on age, sex, socioeconomic status and region of France to ensure a representative sample of the CNAMTS.

Data collection

At enrollment, volunteer participants completed self-administered questionnaires where social, demographic, health information including personal and family history of diseases and events, and lifestyle behavior characteristics were gathered. In addition, they presented to the nearest of the 22-selected health-screening centers (HSCs) located throughout France, to benefit from a comprehensive health examination whereby medical, clinic exams, anthropometric measurements and biologic tests were performed. Furthermore, participants were linked through national social and health administrative databases, through which detailed information concerning health events and medical acts (medication, hospitalization) were noted.

Ethical considerations

All the participants included in the CONSTANCES cohort have signed an informed consent form. This research follows the tenets of the Declaration of Helsinki and was approved by the National Data Protection Authority (No. 910486) and the Institutional Review Board of the National Institute for Medical Research and the local Committee for Persons Protection.

Study population

Between February 2012 and January 2018, a total of 87,808 volunteers were recruited and linked to the French health insurance administrative database. Of them, we excluded 21,330 for missing data and not categorized variables and excluding participants with previous CV events. CV events were commonly recognize as cause of depression [START_REF] Hare | Depression and cardiovascular disease: a clinical review[END_REF]. We therefore analyzed data from 66,478 volunteers (Figure 1).

Hypertension and blood pressure

BP measurements were taken during the clinical examination at the HSC based on standardized operational procedures [START_REF] Ruiz | High quality standards for a large-scale prospective population-based observational cohort: Constances[END_REF]. SBP and DBP were measured in each arm at 2 min interval after 5 min of rest and using an automated oscillometric sphygmomanometer. The arm giving the highest SBP was considered the reference arm and a third BP measure was taken after 1 min of rest, the average of these two measurements was considered. Prevalent HTN was defined by a SBP at least 140 mmHg and/or a DBP at least 90mmHg or by individuals taking antihypertensive medications (Williams et al., 2018).

Depressive symptoms

Depressive symptoms were assessed using the validated self-administered Center of Epidemiologic Studies Depression scale (CES-D) [START_REF] Fuhrer | La version française de l'échelle CES-D (Center for Epidemiologic Studies-Depression Scale). Description et traduction de l'échelle d'autoévaluation. [The French version of the CES-D (Center for Epidemiologic Studies-Depression Scale)[END_REF][START_REF] Radloff | A self-report depression scale for research in the general population[END_REF].

This 20-item questionnaire has been designed for use in community studies. The CES-D score evaluates the frequency of depressive symptoms during the previous week (e.g., I felt depressed, I felt everything I did was an effort, my sleep was restless). Responses range from 0 (hardly ever) to 3 (most of the time). The CES-D score was used as a continuous variable with taking the interval between the 25 th and the 75 th percentile as unit, the meaning of onepoint increase in CES-D could be hard to figure out while one could more intuitively compare an individual in the middle of the upper half of the CES-D score distribution with an individual in the middle of the lower half.

Socioeconomic factors

Educational level was collected according to the International Standard Classification of Education [START_REF] Schneider | The International Standard Classification of Education 2011[END_REF] and was then classified into three levels: Low (High school diploma or less for 13 years of education), moderate (undergraduate degree for 14-16 years of education) and high (postgraduate degree for >17 years of education). Household monthly income was categorized into: low (less than 2100 Euros per month); moderate (2100-4199);

and high (at least 4200).

Occupational status was collected according to the French "Occupations and Sociooccupational Categories" [Professions et Categories Socioprofessionnelles (PCS)] classification system (INSEE, 2003) then categorized in three broad classes: high (e.g., managers), moderate (e.g., clerks or first-line supervisors) and low (e.g., plant and machine operators, cleaners).

Drugs treatments

Reimbursement of anti-hypertensive and antidepressant treatments were obtained by matching the individual data of the subjects included in the study with the data from the SNDS (Système national des données de santé). The names of the treatments and the reimbursement date in the year preceding the health examination were collected. Antihypertensive and antidepressant medications were determined based on the Anatomical Therapeutic Chemical (ATC) code assigned to respondents' medications. Codes indicative of anti-hypertensive medications were: beta blockers (ATC codes C07, excluding C07AA07, C07AA12 and C07AG02); agents acting on the renin-angiotensin system (ATC codes C09); thiazide diuretics (ATC codes C03, excluding C03BA08 and C03CA01); calcium channel antagonists (ATC codes C08); and miscellaneous anti-hypertensive medication (ATC codes C02, excluding C02KX01). Codes indicative of antidepressant medications were ATC codes N06A.

Covariates

Age, gender, couple status (couple life or single which included widowed or separated/divorced), alcohol consumption, dietary intake, physical activity, and smoking status (never, former, current smokers) were collected with a self-reported questionnaire.

Body mass index (BMI, kg/m 2 ) was measured at the examination. Alcohol consumption was defined in g/day of alcohol consumption. Dietary assessment was done through a validated 52-items food frequency questionnaire from which a DASH score was constructed based on food groups described by Fung et al [START_REF] Cherfan | Unhealthy behavior and risk of hypertension: the CONSTANCES population-based cohort[END_REF][START_REF] Fung | Adherence to a DASH-style diet and risk of coronary heart disease and stroke in women[END_REF]. Physical activity (PA) was assessed through three questions that considered the frequency of transferring, leisure time activity and sports. A score of 0-6 was calculated and physical activity level was classified as low (0-2), moderate(3-4) and high (5-6) [START_REF] Merle | Unhealthy behaviours and risk of visual impairment: The CONSTANCES population-based cohort[END_REF]. Diabetes mellitus status was based on either self-reported type II diabetes, receiving anti-diabetic medication or a fasting blood glucose concentration greater than or equal to 7mmol/l. Dyslipidemia was defined as having hypercholesterolemia and/or hypertriglyceridemia; either recorded by the health care practitioner at the HSC or by a fasting plasma total-cholesterol or triglycerides level of at least 6.61mmol/l or more than 1.7mmol/l, respectively.

Statistical analysis

Characteristics of the study population were described as the means with standard deviation (SD) for continuous variables. Categorical variables were described as numbers and proportions. Comparisons between groups were performed using Student's test for continuous variables. Pearson's χ 2 test was performed for categorical variables. SES factors were considered as ordinal variables. Statistical analyses were stratified on gender since hypertension differs between men and women [START_REF] Vallée | Patterns of hypertension management in France in 2015: The ESTEBAN survey[END_REF], as well as depression [START_REF] Van De Velde | Gender differences in depression in 23 European countries. Cross-national variation in the gender gap in depression[END_REF].

Associations between depressive symptoms and blood pressure levels were examined with gender linear regression models computing coefficients (b) and their 95% confidence intervals. Association between depressive symptoms and hypertension were examined with gender logistic regression models computing odds ratio (OR) and their 95% confidence intervals. Gender models were adjusted for age, antihypertensive and antidepressant medications, BMI, DASH score, alcohol consumption, diabetes, dyslipidemia, physical activity, tobacco habits and couple status.

First, we performed regression models including CES-D score with all covariates in same models to determine their significant impact on blood pressure and hypertension. Second, to assess possible effect modification, we stratified the CES-D score and blood pressure levels and hypertension analyses by each of the three SES variables, separately, and tested the statistical significance of these associations. Interactions were examined by including simultaneously CES-D score and one of the three SES factors and their interaction term. Statistics were performed using SAS software (version 9.4; SAS Institute, Carry, NC). A p value <0.05 was considered statistically significant.

RESULTS

A total of 66,478 volunteers without missing or not categorized data were included in the study, their characteristics are described in Table 1. The mean average CES-D score was 10.6 (8.7) for overall population, with a difference of 9 points between the 25 th and 75 th percentiles, mean CES-D score was 11.8 (9.3) for women and 9.2 (7.8) for men. 6.7% of the overall population had an antidepressant medication (8.7% for women, 4.4% for men). 28.6% of the overall population was hypertensive (20.9% for women, 37.4% for men).

The linear regression coefficient for the association between CES-D score and SBP was negative and significant in both women b=-0.64 95%CI [-1.08; -0.21] and men b=-1.12 95%CI [-1.55: -0.70]. SBP was decreased of 0.64 mmHg in women and of 1.12 mmHg in men between the 25 th and the 75 th percentiles of CES-D score (Table 2).

The linear regression coefficient for the association between CES-D score and DBP was significant neither in women b=-0.21 95%CI [-0.49; 0.07] nor in men b=-0.29 95%CI [-0.61: 0.03] (Table 2).

9

The association between CES-D score and hypertension was significant for men, OR=0.86 [0.80; 0.93], p<0.001 but not for women, OR=1.03 [0.96; 1.10], p=0.219 (Table 2).

Supplementary file presented the regression coefficient and OR for all covariates of adjustment (Supplementary file 1).

When considering CES-D score as continuous variable, after adjustment on covariates, the linear regression coefficient for the association between CES-D score and SBP was negative and significant in both women b=-0.04 95%CI [-0.06; -0.02], p<0.001 and men, b=-0.07 95%CI [-0.09; -0.05], p<0.001, but not for DBP (in women, b=-0.01 [-0.03; 0.01], p=0.401 and in men, b=-0.001 [-0.01; 0.01], p=0.937). In multivariate logistic regression, a significant association was observed between CES-D score, as continuous variable, and hypertension prevalence among men (OR=0.98 [0.97; 0.99], p<0.001), but not among women (OR=1.01 [0.99; 1.02], p=0.569). Among women, the interactions between CES-D score and educational levels were significant for both SBP (p=0.028) and DBP (p=0.036) (Figure 2). When women were categorized by income level or occupational status, the interactions were not significant for both SBP and DBP.

The association between CES-D score and SBP, which was not significant among participants with low educational level, became progressively more negative with increase educational level, being significant for high educational level. The mean SBP difference between the 25 th and the 75 th percentiles of CES-D score was -1.09 mmHg 95%CI [-1.76; -0.42] for high educational level (Figure 2). Likewise, the associations between CES-D score and DBP were not significant among women participants with low and moderate educational level but became significant for high educational level. The mean DBP difference was -0.46 mmHg 95%CI [-0.90; -0.02] for high educational level. Moreover, when the three factors of SES and their interactions with CES-D score were simultaneously included in the women model, only the interaction between CES-D score and educational level remained significant (p=0.045 for SBP and p=0.022 for DBP). No significant associations and interactions were observed between CES-D score and hypertension when women were categorized by SES factors (Figure 2).

Among men, none of the three analyses yielded significant interactions between SES factors and SBP. Only the interaction between income level and CES-D score was significant for DBP in men (p=0.010) (Figure 3). When introducing the three SES factors and their interactions with CES-D score simultaneously in the SBP model in men, none of the three were significant. When the three SES factors and their interactions were including simultaneously in DBP men model with CES-D score, only income level interaction was significant (p=0.010). No significant difference was observed among low and moderate income for DBP whereas high income level showed a significant difference b=-0.67 mmHg 95%CI [-1.11; -0.23]. No interactions were significantly observed among men between SES factors and hypertension although high income level presented the highest significant association, with OR=0.79, 95%CI [0.70; 0.88] (Figure 3).

Sensitivity analyses

When excluding from the analyses participants who received antihypertensive drugs When excluding participants who received antihypertensive and/or antidepressant drugs (N=10,891) from the models, CES-D score remained significantly associated with SBP among women (b=-0.63 95%CI [-1.07; -0.17] and among men but not for DBP among women (b=-0.20 95%CI [-0.49; 0.10]) and among men (b=-0.45 95%CI [-0.97; 0.07]).

When excluding participants who received antidepressant drugs (N=4,460) from hypertension prevalence models, CES-D remained significantly associated with hypertension among men (OR=0.85 [0.79; 0.91], but not for women (OR=1. 06 [0.97; 1.15]).

DISCUSSION

Our study investigated the association between CES-D score and BP levels and hypertension and then, how these associations could differ between participants according to their SES levels. Our main finding is that SBP was inversely associated with CES-D score in both genders. But, only men presented a negative association between CES-D score and hypertension prevalence, whereas women presented no significant association. For SBP, women, a significant interaction was observed between CES-D score and educational level whereas in men there was no significant interaction between SES factors and CES-D score.

For DBP, women presented a significant interaction between CES-D score and educational level whereas men presented a significant interaction between CES-D score and income level.

The association between CES-D score and SES factors was stronger in women with high educational level for SBP and DBP and for DBP of men with high income level. No interactions between CES-D score and SES factors for hypertension prevalence were observed in both men and women.

Studies examining the association between depression and blood pressure and hypertension yielded inconsistent results [START_REF] Trudel-Fitzgerald | Dysregulated Blood Pressure: Can Regulating Emotions Help?[END_REF] although many found a negative association [START_REF] Hildrum | Anxiety and depression lowers blood pressure: 22-year follow-up of the population based HUNT study, Norway[END_REF][START_REF] Lenoir | Relationship between blood pressure and depression in the elderly. The Three-City Study[END_REF][START_REF] Licht | Depression is associated with decreased blood pressure, but antidepressant use increases the risk for hypertension[END_REF][START_REF] Park | The relationship of depression with the level of blood pressure in population-based Kangbuk Samsung Health Study[END_REF][START_REF] Shah | Sex and age differences in the relation of depressive symptoms with blood pressure[END_REF][START_REF] Wiernik | Cardiovascular risk goes up as your mood goes down: Interaction of depression and socioeconomic status in determination of cardiovascular risk in the CONSTANCES cohort[END_REF], so that depression was associated with lower BP in cross-sectional studies. Longitudinal studies have suggested that depression may be a risk factor of incident hypertension [START_REF] Meng | Depression increases the risk of hypertension incidence: a meta-analysis of prospective cohort studies[END_REF]. Nevertheless, a follow-up conducted on over 20 years in the Nord-Trondelag Health Study (HUNT) showed that low BP was associated with increased prevalence of depression [START_REF] Hildrum | Anxiety and depression lowers blood pressure: 22-year follow-up of the population based HUNT study, Norway[END_REF].

Several possible mechanisms for low BP in depressive symptoms have been hypothesized. First, chronic low BP itself could be a cause of depressive symptoms, as fatigue and cognitive impairment [START_REF] Licht | Depression is associated with decreased blood pressure, but antidepressant use increases the risk for hypertension[END_REF]. This possibility has been shown in recent longitudinal studies, although with inconsistent results, that low BP at baseline could be considered as a predictive factor for depressive symptoms at follow-up but not the other way around [START_REF] Paterniti | Low blood pressure and risk of depression in the elderly. A prospective community-based study[END_REF], whereas other studies have found the opposite association [START_REF] Hildrum | Effect of anxiety and depression on blood pressure: 11-year longitudinal population study[END_REF].

Another explanation for the observed association does not assume causality but instead assumes a common underlying factor that independently enhances the risk for depression, as well as the factor to conserve a low BP level. The central monoamine system could be a possible cause of this factor [START_REF] Head | Central monoamine neurons and cardiovascular control[END_REF][START_REF] Stahl | Blue genes and the monoamine hypothesis of depression[END_REF]. For instance, depression is characterized by the alteration of neuropeptide Y levels, a major modulator of the norepinephrine signaling. Dysregulation in neuropeptide Y could decrease the sympathetic activity and BP [START_REF] Karl | Behavioral profiling of NPY in aggression and neuropsychiatric diseases[END_REF][START_REF] Michalkiewicz | Hypotension and reduced catecholamines in neuropeptide Y transgenic rats[END_REF]. More studies are required to unravel these underlying mechanisms implicated in the low BP of subjects with depression.

In our study, we have included participants with antihypertensive and antidepressant drugs.

Previous studies suggested that depression could be a side effect of some antihypertensive agents [START_REF] Prisant | Depression associated with antihypertensive drugs[END_REF]. Hypertension awareness may also induce depressive symptoms.

Moreover, antidepressant drugs may increase BP [START_REF] Razavi Ratki | Can Antidepressant Drug Impact on Blood Pressure Level in Patients with Psychiatric Disorder and Hypertension? A Randomized Trial[END_REF]. Regulation of the circulatory system and the autonomic vascular tone by serotonin and nitric-oxide may explain this mechanism. Nevertheless, sensitive analyses were performed in our study by excluding antihypertensive and antidepressant drugs and showed similar associations in our overall population and groups excluding these drugs.

Our results suggest that men had a somewhat stronger association between CES-D score and SBP than women. This result could be explained by many mechanisms. The prevalence of depression and hypertension differ between genders. Women had higher prevalence of depression and lower prevalence of hypertension than men. In the present study, SES interactions were observed in women but not in men. The association between depression and SES may result from several pathways that may differ to some extent between women and men. For instance, alcohol use, which is a risk factor of elevated BP, may mediate this association to a greater extent in men than women [START_REF] Chazelle | Explanations of educational differences in major depression and generalised anxiety disorder in the Irish population[END_REF]. Regarding, the association between hypertension and SES seems to be based mainly on dietary habits and especially salt intake. Individuals risk factors of hypertension could be influenced by individual behaviors depending on SES status [START_REF] Psaltopoulou | Socioeconomic status and risk factors for cardiovascular disease: Impact of dietary mediators[END_REF]. Salt consumption has been considered as one of the main cause of hypertension [START_REF] Gibbs | Salt and cardiovascular disease: clinical and epidemiological evidence[END_REF], and its use differed between gender [START_REF] Vallée | Relationship between Nutrition and Alcohol Consumption with Blood Pressure: The ESTEBAN Survey[END_REF]. The importance of salt consumption was mainly observed among SES underprivileged groups who usually consume snacks of fast type of food full of salt [START_REF] Psaltopoulou | Socioeconomic status and risk factors for cardiovascular disease: Impact of dietary mediators[END_REF]. Moreover, psychosocial processes could be additional pathways by which SES affects blood pressure. [START_REF] Pickering | Cardiovascular pathways: socioeconomic status and stress effects on hypertension and cardiovascular function[END_REF] However, these links remained unclear in literacy [START_REF] Grotto | Hypertension and socioeconomic status[END_REF]. Epidemiologic studies have shown that poor SES groups had more health problem than others [START_REF] Davari | Socioeconomic status, cardiac risk factors, and cardiovascular disease: A novel approach to determination of this association[END_REF]. Another study has shown that lowest education category was associated with a greater risk of hypertension [START_REF] Hoang | Risk factors for chronic disease among rural Vietnamese adults and the association of these factors with sociodemographic variables: findings from the WHO STEPS survey in rural Vietnam, 2005[END_REF]. Moreover, the lack of knowledge of hypertension as well as its predictive factors among less educated layers could result to an unawareness of hypertension prevention and a misunderstanding in detrimental health dietary lifestyle [START_REF] Fenech | Poor Awareness of Hypertension in France: The CONSTANCES Population-Based Study[END_REF][START_REF] Grotto | Hypertension and socioeconomic status[END_REF]. Difference in health behaviors between men and women can also affect SES status [START_REF] Ryu | Sex Differences in Cardiovascular Disease Risk by Socioeconomic Status (SES) of Workers Using National Health Information Database[END_REF]. Health status varies by gender and the different aspects of SES have varying degrees of impact on health status between gender.

Education and income levels are mainly associated with obesity, diabetes and hypertension and could explain the gender differences [START_REF] Zhang | Relation of socioeconomic status to overweight and obesity: a large population-based study of Chinese adults[END_REF].

Strengths and Limitations

The main strength of our study is the design of CONSTANCES, which ensure sufficient power; we adopted a population-based approach using a large nationwide randomly selected sample of participants. In addition, we used standardized protocols to collect anthropometric data including BP measurements; this ensures replication of data collection for all volunteers regardless of when, where and by whom they are performed and adds validity to our results [START_REF] Ruiz | High quality standards for a large-scale prospective population-based observational cohort: Constances[END_REF]. Furthermore, data were collected through different reliable methods, using national databases and validated questionnaires. Moreover, the CONSTANCES cohort randomly recruited its participants, this population may be representative of the general population [START_REF] Rothman | Why representativeness should be avoided[END_REF].

However, some our study presents some limitations. socio-economic data were collected by self-reporting. Medical history and comorbidities have been collected by self-reporting and physician assertion during medical examination in health centers. The cross-sectional design of the study may represent a limitation since reverse causation cannot be excluded.

CONCLUSION

Our study highlighted that increased CES-D score was associated with lower SBP in both genders but only with low rate of hypertension in men. Moreover, our current results show that in women, CES-D score was associated with lowered BP among high educational level.

Men present few interaction between CES-D score and SES factors. Thus, our results support an importance of considering depressive symptoms according to SES factors for blood pressure variation among women. Nevertheless, gender differences should be mainly explored in longitudinal cohorts to warrant the association between SES factors and depressive symptoms with hypertension.

Figure 1: Flow chart

Not categorized data refer to participants whose responses were not missing but could not be included in the ordered classification of each SES variable (e.g. "other diploma", "craftsman" or "farmer" and "don't know the answer", for educational level, occupation status and income level).

Table 1: Characteristics of the study population Table 2: Regression models for SBP, DBP and hypertension according to genders

Regression coefficients present the decrease or increase in BP (systolic and diastolic blood pressure) in participants between the 25 th and the 75 th percentile of CES-D. Odds ratio (OR) present the association between hypertension and the different covariates, and in participants between the 25 th and the 75 th percentile of CES-D. Models were adjusted for antihypertensive, antidepressant drugs, BMI, DASH score, Alcohol consumption, Diabetes, Dyslipidemia, Physical activity, Tobacco habits and couple status.

Figure 2 and

 2 Figure 2 and Figure 3 present the regression coefficients and OR and their 95%CI for the different interactions between CES-D score and SES factors for BP and hypertension according to gender. The regression coefficients correspond to the mean difference in mmHg between participants in the middle of the upper half and thus in the middle of the lower half of the CES-D score distribution.

(

  N=7,298), CES-D score remained significantly associated with SBP among women (b=-0.62 95%CI [-1.07; -0.18] and among men (b=-1.23 95%CI [-1.67; -0.80] but not for DBP analyses among women (b=-0.18 95%CI [-0.47; 0.10]) and among men (b=-0.53 95%CI [-0.70; 0.07]). When excluding antidepressant medications (N=4,460) from the analyses, CES-D score remained significantly associated with SBP among women (b=-0.62 95%CI [-1.05; -0.19]) and among men (b=-1.20 95%CI [-1.63; -0.77]) but not for DBP analyses among women (b=-0.63 95%CI [-1.27; 0.01]) and among men (b=-0.41 95%CI [-0.85; 0.03]).

Figure 2 :

 2 Regression coefficients and 95% confidence interval for the association between CES-D score interquartile and Blood Pressure and Odds ratio (OR) with 5% CI for the association between CES-D score interquartile and hypertension prevalence according to SES factors among women.

Figure 3 :

 3 Regression coefficients and 95% confidence interval for the association between CES-D score interquartile and Blood Pressure and Odds ratio (OR) with 5% CI for the association between CES-D score interquartile and hypertension prevalence according to SES factors among men.

Funding: none


Jean-François Bonnefon
email: jean-francois.bonnefon@tse-fr.eu

Iyad Rahwan
email: rahwan@mpib-berlin.mpg.de

Machine Thinking, Fast and Slow

Keywords: Artificial intelligence, machine behavior, dual-process, trust, algorithm aversion, machine ethics

Machines do not "think fast and slow" in the sense that humans do in dual-process models of cognition. However, the people who create the machines may attempt to emulate or simulate these fast and slow modes of thinking, which will in turn affect the way end users relate to these machines. Here we consider the complex interplay in the way various stakeholders (engineers, user experience designers, regulators, ethicists, and end users) can be inspired, challenged or misled by the analogy between the fast and slow thinking of humans and the Fast and Slow Thinking of machines.

Analogies between human and machine behavior

. For example, if machine behaviorists wished to understand the behavior of virtual assistants such as Siri or Alexa, they could run controlled experiments to see how the assistants react to different requests in different contexts. This approach does not assume that Siri and Alexa think the same way as human assistants, or that it would be useful to understand human assistants in order to understand virtual assistants. However, even though machine behaviorists would not draw such a naive analogy between human intelligence and machine intelligence, it would also be a mistake to completely forget that virtual assistants are inspired by human assistants.

First, if the analogy between human and virtual assistants guided the decisions of developers (engineers, user experience designers etc.), then it can be useful to understand how they, the developers, conceive of human assistants to better understand the virtual assistants they created. Second, if the analogy guides the behavior of users, then it can be useful to understand how they, the users, conceive of human assistants, to better understand how these expectations shape their interactions with virtual assistants -which can in turn shape the behavior of the virtual assistants themselves. Thus, folk theories of how humans think can powerfully shape how machines are developed and how these machines are ultimately perceived by users.

One folk theory in particular has permeated popular culture over the last decades: The idea that humans "Think Fast and Slow". Machines do not think fast and slow in the sense that humans do -but the way humans think fast and slow can inspire the people who create intelligent machines, just as they are inspired by other features of the human mind and brain [START_REF] Dehaene | What is consciousness, and could machines have it?[END_REF]. Furthermore, and more importantly for this article, people have many expectations about the way others Think Fast and Slow, and these expectations can shape their relations with intelligent machines as soon as these machines somehow convey or pretend that they are thinking fast and slow as humans do.

The folk theory of Thinking Fast and Slow

Our purpose does not require a state-of-the-art review of dual-process models, because we are not concerned about the way humans actually think fast and slow. What we are concerned with is the folk theory of Fast and Slow Thinking (capitalized, see below) -or maybe the folk theories of Fast and Slow Thinking: the theories that AI developers use as a rough analogy for the way their machines process information; the theories that come from exposure to bestsellers such as Blink [START_REF] Gladwell | Blink: The Power of Thinking Without Thinking[END_REF], Thinking, Fast and Slow [START_REF] Gladwell | Blink: The Power of Thinking Without Thinking[END_REF][START_REF] Kahneman | Thinking, Fast and Slow[END_REF], or Gut Feelings: The Intelligence of the Unconscious [START_REF] Gigerenzer | Gut Feelings: The Intelligence of the Unconscious[END_REF]; or simply the theories that come from a lifelong experience with the way other people think and act. Here we adopt the convention of using the terms Slow Thinking and Fast Thinking, capitalized, when we refer to the folk version of the dual-process model. We do not capitalize 'fast' and 'slow' when we talk specifically about decision speed, or when we refer to the dual-process model itself and not its folk version.

We do not know of any systematic work investigating the contents of the folk version of dualprocess theory. Note that the question here is not whether people have a correct folk theory of dual-process thinking. We have a reasonable consensus about how physics or biology work, and thus it makes sense to ask how accurate is folk physics or folk biology -but we do not have a similar consensus on dual-process thinking, and thus cannot really assess the accuracy of the folk dual-process theory. From a descriptive perspective, it seems a common enough assumption that "Folk psychology [...] may be tracking, obscurely, the same fundamental duality that scientific psychology has identified" or that "The core of dual-process theory is present in the everyday distinction between intuition and reason -the former immediate, quasi-perceptual, sensitive to subconscious cues and sometimes biased; and the latter slow, effortful, explicit and more cautious" [START_REF] Frankish | Dual-process and dual-system theories of reasoning[END_REF]. What is missing though, as far as we know, is an examination of how exactly the everyday distinction between intuition and reason maps onto the formal distinction(s) that psychologists make between intuitive and reflective processes. What we do have, though, is an empirical literature investigating how people respond to cues of intuition or reflection in others, and how these cues inform their perception of others. This is the literature we build on in the rest of this article. There is strong evidence that people use time, effort, and other metacognitive cues linked to dual-process theory to make inferences about humans and machines. In this article, we make the assumption that these inferences reflect a folk theory of the Fast and Slow Thinking of machines and humans -but the contribution we make does not entirely depend on this assumption. Indeed, the issues we review fall under the broader umbrella of the metacognition of machines, that is, the way people project human cognition on machines.

While we defer to later sections the detailed examination of the metacognitive cues that people attend to, and the effects these cues have on their perception of humans and machines, we can briefly summarize here some of the key differences we will discuss between Fast and Slow Thinking. First, Fast and Slow Thinking differ in speed and scope. Slow Thinking is, well, slow, and can only process a small amount of information at a time -whereas Fast Thinking can process large amounts of information without much effort. Second, Slow Thinking is based on explicit rules and transparent reasons -whereas Fast Thinking is implicit and based on opaque heuristics. Third, Slow Thinking plays a corrective role when Fast Thinking is led astray, since Fast Thinking is biased to rely too much on what is usual, normal, or familiar.

Our focus in this article is on mapping how people use the analogy of Slow Thinking and Fast Thinking on the machines they build and use. We distinguish between four groups of stakeholders: engineers; end users; user experience designers; regulators and ethicists. We argue that these groups focus on different facets of the analogy, as we shall explore below (see Figure 1 for a summary).

Engineering: Do Fast and Slow Thinking correspond to different programming techniques?

There is a long history of using the analogy of Fast and Slow Thinking in AI research. Even before the rise of machine learning, AI scientists made a distinction between heuristic programming approaches [START_REF] Cohen | Heuristic Reasoning about Uncertainty: An Artificial Intelligence Approach[END_REF] based on quick-fire rules [START_REF] Brooks | Cambrian Intelligence: the early history of the New AI[END_REF], and symbolic approaches that are based on carefully curated analytical rules [START_REF] Jackson | Introduction to Expert Systems[END_REF] subject to formal logic-based reasoning [START_REF] Lloyd | Foundations of Logic Programming[END_REF][START_REF] Van Emden | The Semantics of Predicate Logic as a Programming Language[END_REF]. This separation was never clear-cut, though, since even logic-based reasoning often relies on heuristic pruning of combinatorial search spaces, and is frequently applied over a combination of heuristic rules, thus performing a kind of hybrid of Slow and Fast Thinking. Similarly, models that penalize complexity, such as Lasso regression [START_REF] Tibshirani | Regression shrinkage and selection via the lasso[END_REF], can be seen as a form of Fast Thinking over simpler models. AI engineers can also use the nature of the task in order to distinguish heuristic and analytical reasoning. For example, one might consider automated theorem proving as an analytical task, while considering short-term motion planning as a heuristic task, even if one uses heuristics to speed up the former, and symbolic reasoning to conduct the latter.

Nowadays, when AI developers talk about machines Thinking Fast or Slow, they tend to agree that machine learning -and in particular, deep learning [START_REF] Lecun | Deep learning[END_REF] -corresponds to Fast Thinking [START_REF] Chen | Deep reasoning networks: Thinking fast and slow[END_REF][START_REF] Rossi | Preferences and ethical priorities: Thinking fast and slow in AI[END_REF], based on analogies of speed and scope, rules and reasons, and bias and correction. But often, this categorization fails to distinguish between the process of model learning itself -e.g. using backpropagation to train a convolutional neural network on millions of image-caption pairs to learn a high-dimensional distribution of image features [START_REF] Krizhevsky | ImageNet classification with deep convolutional neural networks[END_REF] -from the application of the learned model -e.g. feeding a new image to a pre-trained neural network. The learning process may indeed be a very slow process, but it still seems to correspond to Fast Thinking. Some argue that where machine learning operates on large amounts of data, Slow Thinking would only operate on a sparse network of knowledge [17,[START_REF] Bengio | The consciousness prior[END_REF]. Operating on such a sparse network would also help the machine to express its conclusions in terms of explicit causal models with rules and reasons, something that Fast Thinking can struggle with [START_REF] Weld | The challenge of crafting intelligible intelligence[END_REF][START_REF] Lage | An evaluation of the human-interpretability of explanation[END_REF]. These causal models would also help machines to overcome the problems that Fast Thinking has with out-of-distribution generalizations, that is, correct inferences about situations which are far from usual or familiar [START_REF] Bengio | The consciousness prior[END_REF]. While many researchers agree that machine learning stands for Fast Thinking in the dual-process analogy, there is no comparable agreement about what would stand for Slow Thinking. Some researchers argue that a hybrid approach is required, in which Slow Thinking is handled by a symbolic model, whereas others argue that Slow Thinking can be handled by an appropriately modified machine learning approach [START_REF] Chen | Deep reasoning networks: Thinking fast and slow[END_REF][START_REF] Rossi | Preferences and ethical priorities: Thinking fast and slow in AI[END_REF][START_REF] Dubois | Towards a Reconciliation Between Reasoning and Learning -A Position Paper[END_REF][START_REF] Lacroix | Learning from Learning Machines: Optimisation, Rules, and Social Norms[END_REF].

User Experience

Do people prefer machines to Think Fast or Slow?

People do not trust machines equally for all tasks. For example, people trust machines to solve complex numerical problems [START_REF] Logg | Algorithm appreciation: People prefer algorithmic to human judgment[END_REF] more than they trust them to recognise good jokes [START_REF] Yeomans | Making sense of recommendations[END_REF], hire good employees [START_REF] Diab | Lay Perceptions of selection decision aids in US and non-US samples[END_REF], or deal with emotions [START_REF] Waytz | Botsourcing and outsourcing: Robot, British, Chinese, and German workers are for thinking-not feeling-jobs[END_REF]. Generally speaking, it seems that people make a distinction between 'objective' and 'subjective' tasks. They see objective tasks as requiring rules and explicit reasoning; and subjective tasks as requiring intuitions, instinct, and implicit processing. In other words, they see objective tasks as appropriate for Slow Thinking, and subjective tasks as appropriate for Fast Thinking. And as it turns out, they spontaneously trust machines to perform objective tasks, but not subjective tasks [START_REF] Castelo | Task-dependent algorithm aversion[END_REF]. That is, they trust machines to Think Slow, but not to Think Fast (see Box 1 for a discussion of trust in machines beyond Fast and Slow Thinking).

However, we may be at the exact point in time when this pattern will begin to change. It is indeed possible that until recently, people were simply not accustomed yet to the idea of machines that would Think Fast -that is, machines that would engage in the implicit, holistic processing of a large amount of information, rather than on the sequential, explicit application of a set of rules. What people were accustomed to instead was the idea of machines that would Think Slow, apply logical rules or mathematical formulas in a rigid way, for predictable results. It is no longer rare, though, for discussions of intelligent machines in popular media, to reference so-called black-box algorithms, or to emphasise the impenetrability of deep learning techniques. Accordingly, people are getting more exposure to the idea that some machines may Think Fast. And as it turns out, when people get exposed to the idea that machines may Think Fast, they start trusting them with subjective tasks, instead of just trusting them for objective tasks [START_REF] Castelo | Task-dependent algorithm aversion[END_REF].

Accordingly, we may be at a turning point regarding the tasks people are willing to leave to intelligent machines. People used to have a restricted notion of what these machines were good for: objective, Slow Thinking tasks. But they are now getting used to the idea that machines can think in another way, a way for which they have the perfect analogy: Fast Thinking. People perceive a difference between Fast and Slow Thinking, and they believe that these two modes of thinking are good for different tasks [START_REF] Kupor | Thought calibration[END_REF]. As a result, when they have to trust a machine, they may not simply ask themselves 'Does the task require Slow Thinking?', but rather 'Can the machine think in whichever way is required by this task?'

Machines that look like they can think both ways, as humans do, would accordingly be more likely to be trusted, since they would seem to be flexible enough to handle both kinds of tasks. This raises at least two questions, though. First, what do people infer about a machine that is showing signs of Thinking Fast or Thinking Slow? And second, should we allow machines to pretend that they are Thinking Fast or Slow, if this pretense could improve their interactions with humans?

What do people infer about machines that Think Fast or Slow?

So far we have suggested that people may react differently to machines they perceive as Thinking Fast or Thinking Slow. If that is true, we need to consider the signals that people may attend to when deciding whether a machine is Thinking Fast or Slow. AI user experience (UX) designers may exploit these signals, in order to influence the way people interact with the AI. This is similar to the way UX designers exploit psychological quirks in their design of social media sites, online shopping sites, or smartphone applications [START_REF] Gray | The dark (patterns) side of UX design[END_REF].

When humans think, the main signals of Slow Thinking are time and effort. The longer it took to reach a response, and the harder someone seemed to think, the more likely that person engaged in Slow Thinking [START_REF] Mata | Using metacognitive cues to infer others' thinking[END_REF]. People make many inferences based on this perception. They believe that Slow Thinkers are more likely to be correct, at least for difficult questions [START_REF] Kupor | Thought calibration[END_REF]. They believe that Slow Thinkers have a more complicated moral character than Fast Thinkers -that is, they see a strong link between the actions of Fast Thinkers and their moral character, but they are not so sure about this link for Slow Thinkers [START_REF] Bonnefon | Reasoning Unbound[END_REF]. People also brace themselves when someone engages in Slow Thinking before talking, because they see this Slow Thinking as a harbinger of bad news -which are more delicate to phrase than good news [32].

We should not automatically assume that people will make any of these inferences about machines that they perceive as Thinking Slow. For example, when it takes a human a long time to generate a prediction, people trust that prediction more -but they trust the prediction less if it took a machine a long time to generate it [START_REF] Efendić | Slow response times undermine trust in algorithmic (but not human) predictions[END_REF]. One possibility is that people judge humans and machines using different benchmarks for decision time. Just as fifteen years is a short life for a human but a long life for a dog, fifteen seconds of thinking may be short for a human, but long for a machine. Accordingly, fifteen seconds may be a signal of Fast Thinking for a human, but a signal of Slow Thinking for a machine -and fifteen minutes could be a signal of Slow Thinking for a human, but a signal of malfunction for a machine. Thus, if we want to explore whether people react the same to humans who Think Slow and machines who Think Slow, we will have to carefully calibrate what counts as a signal of Slow Thinking for humans and for machines.

Another signal of Slow Thinking is the explicit correction of one's self-diagnosed mistakes or biases. This signal could play an important role in contexts where machines must make highstake decisions, for example in the moral domain. Machines can help make decisions with a large impact on the life outcomes of humans -for example, when approving bank loans, deciding whether a defendant will get parole, allocating kidneys, or make split-second choices when driving a car at full speed in a critical situation. In such situations, it is important to ensure that the decisions or recommendations of the machine meet appropriate ethical standards. For that purpose, the distribution of labor is usually that the machine Thinks Fast, and humans Think Slow. Either humans try to consider ethical dilemmas before they occur, in order to ponder them before the machine needs to solve them [START_REF] Bonnefon | The social dilemma of autonomous vehicles[END_REF][START_REF] Awad | The moral machine experiment[END_REF], or humans discover ethical issues with the Fast Thinking of the machine, after the fact, and then apply Slow Thinking to correct these issues [START_REF] Wong | Democratizing algorithmic fairness[END_REF][START_REF] Srivastava | Mathematical notions vs. human perception of fairness[END_REF]. But what if machines could use some form of Slow Thinking about their own Fast Thinking, in order to diagnose ethical issues with their own behavior, and self-correct to eliminate these issues? How exactly this could be implemented is a matter of debate [START_REF] Rossi | Preferences and ethical priorities: Thinking fast and slow in AI[END_REF][START_REF] Lacroix | Learning from Learning Machines: Optimisation, Rules, and Social Norms[END_REF], but our focus here is on how it would change the way people perceive intelligent machines that make high-stake decisions.

First, we would need to investigate whether people think that self-diagnosing and self-correcting ethical lapses is a job for Slow Thinking -and if they think this is equally true for humans and for machines. Second, we would have to investigate the inferences people would make about a machine that displays the ability to self-diagnose and self-correct in the moral domain. Consider a machine meant to help a judge to decide which defendant gets parole. Imagine now that after a few months of use, the machine tells the judge that it has diagnosed a racial bias in the recommendations it has made so far, and that it will now try to be more lenient to black defendants. How would the judge react? Would she be more likely or less likely to trust the recommendations of the machine from that point on? It is not at all clear that the admission of past mistakes might increase trust in the machine -insofar as we know that people lose trust in machines that make mistakes faster than they lose trust in humans who make mistakes [START_REF] Dietvorst | Algorithm aversion: people erroneously avoid algorithms after seeing them err[END_REF][START_REF] Prahl | Understanding algorithm aversion: When is advice from automation discounted?[END_REF]. While this aversion can be overcome if people can tweak the machine themselves [START_REF] Dietvorst | Overcoming algorithm aversion: People will use imperfect algorithms if they can (even slightly) modify them[END_REF], we do not know if it can be overcome by a promise by the machine to fix itself.

Law & Ethics: Should we allow machines to pretend they Think Fast and Slow?

We have argued that the trust that people have in machines which perform as advisors or social partners may depend on the kind of Thinking that machines signal to humans. Machines do not really think fast or slow, though, not as humans do. In a sense, people are being deceived, at least by omission, when they react positively to a machine because they have projected on this machine the kind of thinking that humans do.

This means that we have to be careful about where to draw the line when we allow machines to send signals of Fast or Slow Thinking in their interactions with humans. Consider for example the problem of explanation. Many argue that machines would be trusted more if they could articulate a rationale for their predictions or recommendations -instead of, e.g., simply stating these predictions or recommendations based on an opaque neural network computation [START_REF] Weld | The challenge of crafting intelligible intelligence[END_REF]. Providing an explicit reasoning for a conclusion (instead of framing it as an intuition) is a characteristic of Slow Thinking. In other words, the machine is displaying signals of Slow Thinking in order to be trusted more. Maybe that alone would not count as deception, if the machine provides an explanation that is a genuine and straightforward reflection of the reasons underlying its recommendations. It is perhaps unavoidable that in so doing, it will appear to Think Slow to human eyes -and if this appearance of Slow Thinking makes the machine more convincing, maybe this is just a positive but not explicitly pursued side effect of making the machine more transparent [START_REF] Stoyanovich | The imperative of interpretable machines[END_REF]. This is only possible, though, for machines that process information in a way that naturally lends itself to simple explanations -and this is itself an increasingly unlikely occurrence. In most cases, the explanation is only an approximate mapping of what actually went on under the hood. In a sense, the explanation is akin to a data visualization or an infographic. The data visualization aims at helping viewers to understand the gist of the results, but it does not aim at explaining the intricacies of the statistical modelling that allowed the results to be established. It is constrained by the data, but it is also a persuasion tool: Among the dozens possible ways of visualising the data, one was singled out, the one that seemed the most convincing. The same goes on when a machine produces an explanation of its deep computations. The explanation is the result of a complex trade-off between fidelity, simplicity, and persuasiveness [START_REF] Weld | The challenge of crafting intelligible intelligence[END_REF]. Consider for example a case where two explanations could be produced. The two explanations have the same fidelity to the actual computations of the machine. However, one of them will not be as convincing to humans, because of a known cognitive bias. In this case, it would seem best for the machine to show users the most convincing of the two explanations [START_REF] Miller | Explanation in artificial intelligence: Insights from the social sciences[END_REF][START_REF] Kim | Artificial Intelligence and persuasion: A construallevel account[END_REF]. After all, why be self-defeating and show humans an explanation that they are irrationally biased against? This is a path, though, that can easily lead to deception. Imagine again that two explanations could be produced. One explanation is slightly more faithful to the Fast Thinking of the machine, but it is also vastly less convincing, still because of a cognitive bias. Should it be eliminated in favor of the explanation that is slightly less faithful but vastly more convincing? Doing so would be deceptive if users had reasons to expect maximally faithful explanations. It would be less deceptive if users were warned that the machine may at times try to rationalize its recommendations, rather than explain them. It would be fascinating to see how much such an admission would change the trust that people have in machines. This change could be small, for psychological and practical reasons. From a psychological perspective, rationalization is a common use of slow thinking in humans [START_REF] Mercier | The Enigma of Reason[END_REF][START_REF] De Neys | Rational rationalization and System 2[END_REF], and it is accordingly possible that people would expect and tolerate some level of rationalization from machines, too, as soon as the machines pretend to Think Fast and Slow. From a practical perspective, we know that people are sometimes willing to be nudged toward a decision that serves their goals, even when the nudge can be construed as manipulative [START_REF] Sunstein | Human Agency and Behavioral Economics: Nudging Fast and Slow[END_REF]. Accordingly, it is possible that they may allow machines to be slightly manipulative, if such machine behavior is proven beneficial [START_REF] Ishowo-Oloko | Behavioural evidence for a transparency-efficiency tradeoff in human-machine cooperation[END_REF].

Concluding remarks

Intelligent machines have become so prevalent, so complex, and so intricately embedded with humans and other machines, that it is no longer possible to predict what they will do based on how they were designed. As a result, scientists have started to use the methods of behavioral science to study intelligent machines from the outside, as if they were humans or other animals. Citizens are engaging in their own version of this paradigm shift. Faced with machines whose capabilities and inclinations have become mysterious, people are recruiting the mental tools they use to assess other humans, and repurposing them for the assessment of machines. In this article, we speculated in particular about the way people relate to machines that display signs of Fast and Slow thinking.

As soon as machines display signs of Thinking Fast or Thinking Slow, people will make inferences about what they can trust the machines with, just as they make these inferences about humans. Accordingly (and see the Outstanding Questions for specific examples), we need to understand the signals of Fast or Slow Thinking that people pick up when they deal with machines; we need to compare the inferences they made about machines that Think Fast or Slow, to the inferences they make about humans; and we need to tackle the difficult ethical concerns that come with the potential for manipulation intrinsic to machines that learn to pretend they are Thinking Fast or Thinking Slow.

Text Box 1: Trust in Machines

This article focuses on how cues of Fast or Slow Thinking can influence people's trust in intelligent machines, but many other factors can affect this trust [START_REF] Glikson | Trust in Artificial Intelligence: Review of empirical research[END_REF]. For example, people trust intelligent machines more when there is evidence that they perform well on a given task, or when they are routinely used for this task [START_REF] Kramer | When do people want AI to make decisions[END_REF]. Anthropomorphism [START_REF] Waytz | The mind in the machine: Anthropomorphism increases trust in an autonomous vehicle[END_REF] and social behavior [START_REF] Traeger | Vulnerable robots positively shape human conversational dynamics in a human-robot team[END_REF][START_REF] Rahwan | Intelligent machines as social catalysts[END_REF] can help a machine build trust, although these effects can be complex. For example, while machines can learn behaviors that reliably elicit cooperation from humans [START_REF] Crandall | Cooperating with machines[END_REF], the mere fact that they are machines seems to penalize the trust they inspire -even when keeping their behavior constant, machines that reveal their true nature elicit lower cooperation than machines who pretend to be human [START_REF] Ishowo-Oloko | Behavioural evidence for a transparency-efficiency tradeoff in human-machine cooperation[END_REF]. People trust machines less for decisions which have a moral component [START_REF] Bigman | People are averse to machines making moral decisions[END_REF], although this distrust may be attenuated if they share the ethical values embedded in the machine [START_REF] Freedman | Adapting a kidney exchange algorithm to align with human values[END_REF]. If the ethical values embedded in machines are not aligned with the ethical values of users, there is a risk that users will simply opt-out of using these machines, and forfeit the potential collective benefit of their use [START_REF] Bonnefon | The moral psychology of AI and the ethical opt-out problem[END_REF]. Cultural and individual differences can affect the values that people want to see embedded in machines, which makes it important to collect data in large, multicultural samples in order to explore cultural and individual heterogeneity [START_REF] Awad | The moral machine experiment[END_REF][START_REF] Awad | Crowdsourcing moral machines[END_REF]. All the factors that affect trust in machines may interact with the way machines display signals of Fast or Slow thinking. Whether the machine Thinks Fast or Slow may affect expectations of performance on different tasks; anthropomorphism may amplify the effect of signals of Fast or Slow Thinking; machines that learn to display signals of Fast or Slow Thinking may be better able to pass as humans; Fast or Slow thinking may be perceived as more or less appropriate or desirable, depending on the moral component involved in the decisions of the machine. Cultural norms may change the preferences of users for machines that Think Fast or Think Slow, and individual differences may have a comparable impact. For example, people with a proclivity to process information reflectively may find it easier to trust machines who Think Slow.

Figure 1. Examples of the use of the 'Fast and Slow' analogy by stakeholders.

The folk theory of mind that people have about machines Thinking Fast or Slow impacts various stakeholders. These stakeholders may not use the analogy in the same way, as symbolized by the different arrangements of F and S in the thought bubbles. On the development side, engineers use the Fast and Slow analogy to select algorithmic solutions, while user experience (UX) designers use the analogy to shape how the machine is perceived by the user. On the user side, regulators might encourage Slow Thinking by machines for the purpose of producing explanations, while end user psychology ultimately determines how signals of Fast and Slow Thinking (e.g. hesitation, selfcorrection, explanation giving) shape the trust placed into the machine. Yet other examples are considered in the main text.

JFB acknowledges support from the ANR-Labex Institute for Advanced Study in Toulouse, the ANR-3IA Artificial and Natural Intelligence Toulouse Institute, and the grant ANR-17-EURE-0010 Investissements d'Avenir.