Emerging heterogeneities in Italian customs

Elena Agliari,1, 2 Adriano Barra∗,1 Andrea Galluzzi,3 Marco

Alberto Javarone,4, 5 Andrea Pizzoferrato,6 and Daniele Tantari1, 7

1Dipartimento di Fisica, Sapienza Universita di Roma, Italy2Facolta di Ingegneria, Campus Biomedico di Roma, Italy

3Dipartimento di Matematica, Sapienza Universita di Roma, Italy4Dipartimento di Matematica ed Informatica, Universita di Cagliari, Italy

5Dipartimento di Scienze Umanistiche e Sociali, Universita di Sassari, Italy6Mathematics Institute, University of Warwick, UK

7Centro E. De Giorgi, Scuola Normale Superiore, Pisa, Italy

Since its unification, more than a century ago, Italy has experienced strong social and economicaldiversities between its southern and northern regions. In the last decades, Italy has undergone asevere economical and political crisis reflecting corruption at various levels of social stratification aswell as a poor involvement of its population in the number of elections that occurred. This mightbe explained by a lack of confidence, or interest in the country as a whole, as if the primary socialand political focus of its citizens could still lay at smaller regional scales, possibly evidencing thepersistence of different cultural heritages. In order to shed lights on the possible existence of suchheterogeneities, we perform a statistical-mechanics-driven analysis focusing on key social quantifiers,namely the evolution of autochthonous marriages (as family still plays as a fundamental brick inthe edification of social aggregates) and of mixed marriages, namely those involving a foreign-bornand a native (as migrant integration takes place at the collective level of the host communities),in order to compare the Italian outcomes with those of nearest EU nations as Spain, France andGermany. Our theoretical framework, predicting a square-root growth for the number of marriagesversus the density of potential couples, nicely fits data for all considered countries. However, wefind a homogeneous outline in all cases but Italy, the latter exhibiting two clearly detached square-roots, naturally pertaining to northern and southern regions, respectively. These findings suggestthe existence of two culturally distinct communities, long-term lasting heritages of different, well-established cultures.

PACS numbers:

I. INTRODUCTION

Driven by the founding fathers Mazzini, Garibaldi and Cavour, the history of united Italy begins in 1861, when aconglomeration of city-states, republics, and other independent entities were merged into a single state. However, sinceits birth, strong inner diversities between local entities and, in particular between northern and southern regions, havebeen repeatedly pointed out and intensively studied by historians along the decades [8, 21, 22]. For instance, quotingthe Italian politician Antonio Gramsci [28] the newborn Italy had found in absolutely antithetical situations the twosections of the peninsula, the southern and northern, that gathered together again after more than a thousand years.(...) On the one hand (i.e. north) the tradition of a certain autonomy had created a bourgeoisie full of initiatives, andthere was an economic organisation similar to that of the other states of Europe, favourable to capitalism and industry.In the other (i.e. south), the paternal government of Spain and the Bourbon nothing had created: the bourgeoisie didnot exist, agriculture was primitive and it was not enough even to satisfy the local market; no roads, no ports, no useof the few waters that the region, for its special geological position, possessed. [23].

Beyond economical inequalities, the unification of Italy also implied the sudden convergence of cultural, ethical andbehavioural diversities. Indeed, as highlighted by the Italian historian and politician Giustino Fortunato [29] there areno doubts regarding the existence of a “meridional issue”, meant in economical and political terms. Between the northand the south of the peninsula, a great disproportion in the field of human activities, in the intensity of collective life,to the extent and in the kind of production, is present. Therefore, ultimately, the whole regards the close ties that exist

∗ Corresponding author’s email: adriano.barra@roma1.infn.it

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between the welfare and the soul of a population, and implies a profound difference between (northern and southern)customs and traditions, both intellectual and moral [17].

While we would agree only partially to these words, and just point out that the Royal Theater of Saint Charlesin Naples played as the oldest continuously active venue for public opera in the world (opening in 1737, decadesbefore both the Milan’s La Scala and Venice’s La Fenice theaters), these words -date back to more than one centuryago- may still capture the actual Italian scenario as local customs, dialects and traditions are still rooted along thepeninsula and a drastic gap between northern and southern regions (maybe sustained by the peculiar geography of thecountry) is currently reported (see e.g., [12]). Such diversification may justify the poor involvement of the populationin the political scene as if the Italian citizens could not identify yet with a unique national structure and their socio-economical interests lay at a smaller scale. In this paper we try to quantify these possible heterogeneities focusingon the evolution in the number of marriages contracted by its citizens. In fact, the attitude to marriage (and moregenerally to the family [24]) along with other variables such as religious faith and political identification, seems to bestrongly related to the cultural heritage of a nation and, as already evidenced in the past [25], its estimate throughoutthe peninsula can highlight that, despite rapid changes, a true convergence between northern and southern mores hasnot been achieved yet.

More precisely, under very minimal hypotheses, in the following we present a statistical-mechanics approach forderiving, under the hypothesis of homogeneity, a close-form expression for the evolution of the number of marriages asa function of the number of potential couples present in the territory. Its comparison with data is not fully satisfactoryfor Italy, yet it successfully holds for other neighboring countries (i.e., France, Germany and Spain). Remarkably,however, by treating Northern and Southern Italy as two distinct countries, the match between theoretical predictionsand data is plenty recovered, clearly highlighting the persistence of these heterogeneities. Finally, this picture is furthercorroborated by analyzing the evolution of the number of “mixed marriages”, for which analogous outcomes for allthe countries considered are found.

II. RESULTS AND DISCUSSION

The statistical mechanical approach to the investigation of social complexity consists in a bulk of stochastic tech-niques developed to model the underlying self-interacting network (whose nodes are single decision makers and linksmirror the existence of pair-wise interactions) in order to figure out its emergent features, being firmly grounded onthe law of large numbers, on the minimum energy and maximum entropy principles [15]. Although this perspectiveimplies a certain degree of simplification, its reward lies in its crucial ability to unveil robust collective behaviors. Infact, in the last decade, a massive usage of statistical mechanics, driven by quantitative sociology, has allowed extract-ing from available data-sets a big deal of descriptive as well as predictive information successfully applied in marketingand financial services [20], telecommunications [27], health-care and pharmaceutical [9], traveling optimization [19],migrant’s integration in host society [1, 5] and many other fields of social complexity [14, 16, 18].

Here, we develop a statistical mechanical model to describe the evolution in the number of marriages in a givencountry as a function of its population. By calibrating this model versus available demographic data, we aim tohighlight the possible persistence of different cultural traits among northern and southern regions of Italy. Therobustness of the result is checked by performing analogous analysis for nearest EU states, namely Spain, France andGermany.

In the following we provide a streamlined description of the outcomes of our model, while we refer to SectionMethods and to Ref. [1, 6] for more details.

First, we need to fix the degree of resolution at a certain territorial district, in such a way that different districtsare considered as independent realizations of the same system; this also implies that the number of marriages in agiven district is taken to depend only on the population within the district itself. We decide to fix the resolution atthe provincial level, as its extent is typically broad enough to justify the hypothesis of independence [1, 6], yet thenumber of provinces is large enough to get a reasonable pool for the statistical analysis.

We call NP the total amount of provinces for the country considered (NP = 110 for Italy, NP = 476 for Germany,NP = 53 for Spain, and NP = 96 for France, see also [26]), each labeled with an index α, namely α = 1, ..., NP . Also,

we call Mα and Fα the amount of males and of females, respectively, within the province α. Being N =∑NPα (Mα+Fα)

the total amount of citizens in the whole country, we can further define the relative percentages of males and femalesas γα = Mα/N and 1− γα = Fα/N , respectively.

Then, the amount of marriages LWα (i.e. local weddings) within the province α turns out [1, 6] to depend on thesquare-root of Γα ≡ γα(1− γα), and, under the assumption of homogeneity, the same holds for marriages LW at thecountry level

LW ∼√γ(1− γ) ≡

√Γ, (1)

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FIG. 1: From the top left proceeding clockwise plots regarding averaged local weddings LW versus the potential availablecouples Γ for Germany, Spain, Italy and France are presented. Raw data on both the y and x axis were normalized withrespect to the total number of weddings and total population size for each year taken into account. The error circles shouldbe understood with respect to the legend reported in each graph. In order to establish a direct comparison among the states,all the plots were realized dividing the interval of data in 30 bins. As it is clear from the plots, and numerically confirmed bythe tables presented in Figure Two, Italy is best fitted by two square root curves that, remarkably, naturally split the countryexactly into northern regions and southern ones as reported by Eurostat. The two-colored map shown at the bottom rightdepicts the definitions of Northern and Southern Italy as given by the European Union (Eurostat data) that perfectly matchesresults from our data analysis. The black circles, whose sizes mirror the amount of data they provided, represent examples ofcities whose marriages along the years 2000-2010 have been studied.

FIG. 2: These two tables show values of R2 coupled to the best fits as those reported in Figure One but obtained at differentbin divisions for each state data interval: as far as Italy is concerned, whatever the level of resolution we fix (i.e. whatever theamount of bins we use), the best fit considering the country as a whole is always significantly worst than considering Italy asthe superposition of southern and northern regions.

where γ =∑α γα and LW = (

∑NPα LWα)/NP .

Now, we proceed by extracting data series from the available sources (respectively ISTAT for Italy, DESTATIS forGermany, INE for Spain, and INSEE for France), and then, through a careful protocol for information extrapolationduring data analysis, we infer LW (γ) for comparison with Eq. 1. We refer to section Methods for an explanation ofthe theoretical and experimental routes followed, while here we directly discuss our findings.

As shown in Figure One, the predicted behaviour (1) successful matches data for all the European countriesconsidered but Italy. If analyzed as a single homogeneous set, data for Italy are too noisy to detect any clear

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trend; however, by treating data for Southern Italy and for Northern Italy separately (as if they were two differentcountries), the expected behaviour suddenly emerges, suggesting that, at least as far as this particular social quantifieris concerned, historical traditions have not mixed yet.It is worth noticing that, to obtain this result, we split Italy in such a way that the R2 of the related fits are maximal(as shown in Figure Two), and this division turns out to coincide with the definition of norther and souther Italy asreported in Eurostat.

III. METHODS

A. A theoretical reference framework

In this section we summarise the theory leading to Eq. 1; here we report only the key logical steps seeking forself-consistency, while we refer to [1, 6] for a detailed derivation.

We introduce an Hamiltonian (i.e., a cost function) H, describing the interaction pattern among males and females[30]. Each individual i is associated to a dichotomic variable or “spin” (referred to as σi = ±1 for males and asτi = ±1 for females) encoding a positive (i.e. +1) or negative (i.e. −1) attitude to marriage. Then, the “cost” of agiven configuration ({σ}, {τ}) is provided by the global Hamiltonian

H({σ}, {τ}) = − 1

N

NP∑α=1

(Mα∑i=1

Fα∑µ=1

σαi ταµ

), (2)

where α labels the various provinces, NP is the total number of provinces in the country, and N =∑α(Mα + Fα)

is the total population in the whole country. This Hamiltonian is the sum of terms like −σiτj over all the possiblecouples (i, j) of individuals belonging to the same province.

Intuitively, for the minimum energy principle (that tries to keep the numerical value of H({σ}, {τ}) at its minimum[15]), the function (2) tries to favor the configurations of citizens with the overall lowest possible frustration, that is,considering the couple (i, j) as an example, it favors the two states where the variables σi and τµ are aligned, thusσi = τj = +1 and σi = τj = −1, while misaligned couples σi 6= τj are unfavored. This assumption captures the trivialobservation that in these societies stable couples (σi = τj = +1) exist as well as, somehow less intuitive yet largelypredominant, stable not-couples (σi = τj = −1). On the other hand, the conflicting situation where one of the twopartners wants to get married (sat σi = +1) but the other does not (hence τµ = −1) is only transitory (hence notstable) as after a proper timescale, the pretender is expected to move toward another target.

Once the model is defined, that is we have an explicit expression for H({σ}, {τ}), we can automatically assign aprobabilistic weight (i.e., the Maxwell-Botlzmann distribution ρ ∝ exp[−H({σ}, {τ})]) to each possible configurationand therefore estimate the likelihood for the establishment of a given number of marriages.This allows to introduce the partition function ZN for the model is

Z =∑{σ}

∑{τ}

exp [−H({σ}, {τ})] , (3)

where the sum is performed over all possible∏NPα=1 2Mα × 2Fα configurations. By a direct calculation, it is straight-

forward to check that

ZN =∑{σ}

∑{τ}

exp

[1

N

NP∑α=1

(Mα∑i=1

Fα∑µ=1

σαi ταµ

)]∼∑{σ}

exp

{NP∑α=1

[1

2Mαγα(1− γα)m2

α

]}, (4)

where we highlighted the term mα = (∑Mα

i σi)/Mα, which measures the average propensity to marry for males withinthe province α. This quantity works as the “order parameter” of the model and it is expected to be proportional tothe experimental amount of marriages LWα within the province α (suitably normalized). Note that, in order to studythe joint evolution of males and females attitudes at wedding, the requirement of heterosexual weddings (constraintimposed by the Italian laws -as in Italy homosexual marriages are forbidden- and respected during data acquisition)implicitly allows to study the average propensity of only one of the two sex (male here, via mα).

Before proceeding it is worth stressing the social meaning of the last and crucial passage in eq. (4)[31]: thisequivalence is trivially obtained by performing the summation over the τ variables (i.e., by integrating over the“female degrees of freedom”), that returns a term ∼ cosh(

√MαΓαmα) due to the Eulero formula; the latter is then

written as cosh(x) = exp[ln cosh(x)] and then Taylor-expanded at the leading term as exp[ln cosh(x)] ∼ exp(x2/2).

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Remarkably, such an equivalence states that the initial model described by eq. (2), meant for males and females ininteraction and encoded by sums of terms ∝ −σαi ταµ , is statistically equivalent to a model accounting for imitative

interactions among males only encoded by the term ∝ −σαi σαj , that is −m2α. Otherwise stated, the phenomenological

rule described by the cost function (2), where males and females interact trying to satisfy their relationships, recoversthe Copy Model Theory, that is, the Discrete Choice with imitation [10, 11] -namely the extension of the McFaddeneconometric theory [7] to interacting decision makers- in Socio-Economic Literature or Hebbian Ferromagnetism inStatistical Mechanics Literature [2–4]. Of course, and in complete analogy, we could reach imitation among femalesonly, by summing over the σ variables first.

Now, Discrete Choices with imitation, where agents (here males) interact pair-wise in an imitative fashion, is wellknown in statistical mechanics (as the Curie-Weiss model [3]) as well as in quantitative sociology (as the Brock-Daurlauf theory [13]): for this model the expected behavior of the order parameter m versus the tuneable parameterΓ = γ · (1− γ) results in the following equation

m = tanh [aΓ ·m] , (5)

with a constant irrelevant to the present problem. By Taylor-expanding the above equation for small m we getm ∼

√Γ and, identifying trough the Law of Large Numbers the theoretical m with the experimental LW , namely by

writing LW ∝ m, we obtain the expected leading trend, namely

LW ∼ a√

Γ, (6)

with a another constant irrelevant to the purposes of the present work. This equation predicts, within each country(namely under the assumption of homogeneity among the σ as well as the τ variables), a square-root growth forthe expected number of marriages LW versus the density of potential couples Γ and can be compared directly withexperimental data.

B. An experimental reference framework

FIG. 3: Schematic representation of the procedure performed in data analysis. Entire datasets regarding marriages versustime and population density (amount of potential couples, thus males time females) versus time are extracted from Europeandatabases and stored in form of historical series (time series), as shown in the left panel. Each dot represents a province withina give year. After binning both the datasets we check that at least one of them, migrant’s density versus time, is monotonic soto allow the inversion that returns time versus migrant’s density (not shown). Then time is removed from our data by plotting-as raw data- marriages versus migrant’s density as shown in the central panel. Lastly we bin the latter to obtain the coarsegrained evolution of the phenomenon, whose spots (yellow circles) have been best fitted against the theory (red line).

We collected data for the number of marriages and for the female and male populations in Italy (source: ISTAT),France (source: INSEE), Spain (source: INE) and Germany (source: DESTATIS) over the time window 2000− 2010.We fixed the degree of resolution at the provincial level: this choice is determined by the empirical observation that

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marriages typically involve people living in the same province (i.e., the social interactions display a characteristicgeographic scale [1]); further, this in turn allows to treat each province independently from the others and thusimplies a statistical analysis over P different realizations.

Therefore, for each province α we collected the data series {Γα(y)} and {LWα(y)}, where data are sampled yearly,being y = 2000, ..., 2010. Data manipulation is a lengthy but simple protocol largely discussed in [1, 6] and summarizedin Figure Three. This allows getting the average evolution of LW versus Γ. Such values are then best-fitted againstEq. 6 as shown in Fig. 1.

As it appears evident even by direct visual inspection of Figure One, for France, Spain and Germany there is aremarkable agreement between the theory and the data, while Italian marriages behave substantially differently: twowell-separated square roots emerge and, quite remarkably, these are built by the northern and southern provinces,respectively. This is confirmed quantitatively by the fitting analysis reported in the tables of Figure Two.

FIG. 4: From the top left proceeding clockwise plots belonging to Germany, Spain, Italy and France are presented. Raw dataon both the y and x axis were normalised with respect to the total number of weddings and total population size respectivelyfor each year taken into account. The error circles should be understood with respect to the legend reported in each graph. Inorder to establish a direct comparison among the states, all the plots which are shown were realised dividing the interval ofdata in 30 bins. As it is clear from the plots, Italy is best fitted by two square roots curves.

C. A robust framework

Finally, in order to check robustness of our results, marriages between native and foreign-born citizens have beenanalyzed in a similar fashion. The theoretical framework underlying this kind of phenomenology is analogous to theone described above, but here the two parties are played by native and by foreign-born individuals (rather than malesand females, respectively); we refer to [1, 6] for a full treatment. The expected behavior for mixed weddings MW istherefore described by the function

MW ∼ tanh[bρ(1− ρ)MW ] ∼ b√

Γ, (7)

where ρ is the fraction of native people within the whole population, Γ = ρ ·(1−ρ) and b, b are two constant irrelevantto the present work.

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We checked the theoretical law (7) versus experimental data for the above mentioned four countries. The niceagreement for Spain, France and Germany suggests that the attitude toward a possible partnership with a foreign-borncitizen can be looked as the result of imitative mechanisms within native people only (as deepened in [6]). Moreover,the peculiar behavior outlined for Italian data corroborates the previous analysis, confirming strong discrepanciesbetween northern and southern regions even as for immigrant integration.

Acknowledgments

INdAM-GNFM (Progetto Giovani Agliari2014), EPSRC support and Sapienza Universita’ di Roma are acknowl-edged.AB is grateful to LIFE group (Laboratories for Information, Food and Energy) for partial financial support throughprogramma INNOVA, progetto MATCH.MAJ would like to thank Fondazione Banco di Sardegna for supporting his workAP acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC), Grant No.EP/L505110/1.

Additional information

Competing financial interests: the authors declare no competing financial interests.

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[28] The original statements are in Italian and read as: La nuova Italia aveva trovato in condizioni assolutamente antitetichei due tronconi della penisola, meridionale e settentrionale, che si riunivano dopo piu’ di mille anni. (...) Da una parte latradizione di una certa autonomia aveva creato una borghesia audace e piena di iniziative, ed esisteva una organizzazioneeconomica simile a quella degli altri Stati d’Europa, propizia allo svolgersi ulteriore del capitalismo e dell’industria. Nell’altrale paterne amministrazioni di Spagna e dei Borboni nulla avevano creato: la borghesia non esisteva, l’agricoltura eraprimitiva e non bastava neppure a soddisfare il mercato locale; non strade, non porti, non utilizzazione delle poche acqueche la regione, per la sua speciale conformazione geologica, possedeva.

[29] The original statements are in Italian and read as: Che esista una questione meridionale, nel significato economico e politicodella parola, nessuno piu mette in dubbio. C’e’ fra il nord e il sud della penisola una grande sproporzione nel campo delleattivita’ umane, nella intensita’ della vita collettiva, nella misura e nel genere della produzione, e, quindi, per gl’intimilegami che corrono tra il benessere e l’anima di un popolo, anche una profonda diversita fra le consuetudini, le tradizioni,il mondo intellettuale e morale.

[30] We considered only heterosexual couples as, over the time window considered, homo-sexual marriages where still forbiddenin the countries considered.

[31] Note that the equivalence is actually rather robust as it holds in the presence of general positive couplings between σ andτ , even in inhomogeneous and/or diluted networks [2], and for binary as well as real (i.e. Gaussian) variables [6]