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Crowdsourcing the Robin Hood effect in citiesThomas Louail, Maxime Lenormand, Juan Arias, José Ramasco

To cite this version:Thomas Louail, Maxime Lenormand, Juan Arias, José Ramasco. Crowdsourcing the Robin Hoodeffect in cities. Applied Network Science, Springer, 2017, 2 (11), pp.11. �10.1007/s41109-017-0026-3�.�hal-01535480�

Crowdsourcing the Robin Hood effect in cities

Thomas Louail,1, ∗ Maxime Lenormand,2, ∗ Juan Murillo Arias,3 and Jose J. Ramasco1

1Instituto de Fısica Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB),Campus UIB, 07122 Palma de Mallorca, Spain

2Irstea, UMR TETIS, 500 rue Francois Breton, FR-34093 Montpellier, France3BBVA Data & Analytics,Avenida de Burgos 16D, E-28036 Madrid, Spain

Socioeconomic inequalities in cities are embedded in space and result in neighborhood effects,whose harmful consequences have proved very hard to counterbalance efficiently by planning policiesalone. Considering redistribution of money flows as a first step toward improved spatial equity, westudy a bottom-up approach that would rely on a slight evolution of shopping mobility practices.Building on a database of anonymized credit card transactions in Madrid and Barcelona, we quantifythe mobility effort required to reach a reference situation where commercial income is evenly sharedamong neighborhoods. The redirections of shopping trips preserve key properties of human mobility,including travel distances. Surprisingly, for both cities only a small fraction (∼ 5%) of trips need to bealtered to reach equity situations, improving even other sustainability indicators. The method couldbe implemented in mobile applications that would assist individuals in reshaping their shoppingpractices, to promote the spatial redistribution of opportunities in the city.

The growth of economic inequality has raised con-cern and attention in recent years [1, 2]. In cities,entangled processes such as location choices of house-holds and businesses, daily mobility, segregation andclosure attitudes, central planning, or global economicrestructuring contribute to these inequalities becom-ing embedded in space. Over the course of severaldecades their joint actions have given rise to spatiallysegregated cities, characterized by uneven distribu-tions of capital among their neighborhoods. While theintensity of socioeconomic inequalities vary from onecity to another, the general observation that ”someneighborhoods are poorer than others” has been madefor cities with different age, in every continent, and fordifferent periods in urban history [3–6]. An abundantliterature has long depicted the neighborhood effect[7], and highlighted its societal costs and enduringconsequences [8–12].

Over the last decade, increasing volumes of digitalgeographic footprints have been passively producedby individuals using mobile ICT devices, and thesefootprints have been increasingly analyzed by scien-tists as well. These data are not free of biases [13]or privacy concerns [14], but they undeniably consti-tute an important asset for understanding social phe-nomena in detailed spatio-temporal contexts [15–20].They also have the potential to reveal the informa-tion required to coordinate individuals’ actions, sothat large groups of people can tackle issues whichare distributed and spatial by nature. This is par-ticularly true in the case of mobility networks, whichalready integrate such footprints in feedback mecha-nisms: people produce data when moving, and theirtravel decisions are partly guided by the data pro-duced by others. Examples include GPS navigationusing real-time traffic data, local search and discovery

∗ Corresponding authors (thomas.louail@ifisc.uib-csic.es,maxime.lenormand@irstea.fr) who contributed equally tothis work.

of new places, or location-based dating applications.So far these footprints have been mainly used in ap-plications intended to enhance individual satisfaction(time savings, discovery of a location, encounter ofa partner), but they have also fostered spontaneousand large-scale solidarity movements during disasters(e.g. Facebook’s safety check, or the use of dedicatedTwitter hashtags). An important question thus con-cerns the possibility to scale up the use of such per-vasive data, in order to address complex social issueswith distributed and coordinated approaches, issuesfor which improvements would necessarily occur onlonger timescales. There is a need to relate smarttechnology with sustainability and spatial justice incities [21], and this implies building upon the existingpractices of individuals. Here we develop further thisidea by focusing on a complex problem: the reductionof spatial inequality in large cities.

The “Robin-Hood effect” refers to a process throughwhich capital is redistributed to reduce inequality. Aspatial and city-scale implementation would then con-sist in taking from the rich neighborhoods to give tothe poor. This role is normally played by the city’sgovernance, and is essential to mitigate spatial in-equality. However, studies in cities worldwide havedemonstrated that top-down planning and fiscal poli-cies alone are inefficient in significantly counterbal-ancing the consequences of the neighborhood effect[22, 23]. It has also been long emphasized that devel-oping economic activity in disadvantaged regions in-directly benefits the surrounding populations, by fos-tering job opportunities, transport facilities and in-creased safety [24]. Here we study an original ap-proach to rebalance economic activity among a city’sneighborhoods, that would not incur any additionalenvironmental or monetary costs, but would insteadrequire a slight evolution of shopping mobility prac-tices. According to surveys, shopping and leisure tripsaccount for 15% to 20% of the individuals’ daily trips[25]. Such trips virtually move money from one partof the city to another, and directly contribute to shape

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Figure 1. Rewiring urban shopping trips. (a) Average income per business in the neighborhoods of Barcelona resulting fromindividual transactions. The average income has been normalized by the maximum value among neighborhoods. The datacorrespond to 2011 and is displayed by zip code in the metropolitan area. From this perspective, some neighborhoods are fivetimes richer than others. (b) The general principle common to the iterative rewiring methods. At each step a transactionis randomly selected, along with the possible alternative businesses (highlighted in bold). If rewiring the transaction to oneof them (randomly selected) decreases inequality between neighborhoods and matches the other constraints, then rewiring isperformed.

the distribution of wealth across neighborhoods. Byconnecting areas, shopping trips foster metropolitanintegration and social cohesion [26], and the resultingmoney flows are a key component of the developmentof territories [27]. In large cities there are businessesof various types in most of the neighborhoods, and ev-ery time one has to buy usual products such as food,gas or clothes, one can actually choose among sev-eral stores and several neighborhoods, even withoutincreasing the distance traveled.

In the following we demonstrate that more evenlybalanced cities are reachable by the cumulative ad-dition of small and reasonable changes in a limitedfraction of individuals’ shopping destinations. Whilethere exists various spatial indicators for quantifyingterritorial inequalities, static indicators fail to providea clear picture of the collective effort required to reacha certain level of redistribution. This in mind, wequantify the proportion of individual shopping tripsthat should be redirected to evenly share the com-mercial income between neighbourhoods, a conceiv-able path toward the spatial redistribution of oppor-tunities in the city. We show that alternative shoppingmobility scenarios not only allow to distribute moneymore evenly in space, but also to enhance the spatialmixing of city residents through their shopping mo-bility, without increasing the total distance traveled,nor changing the effective purchases and the mobilityroutines of individuals.

RESULTS

Data

We use a dataset containing one year of credit cardtransactions for more than 150 000 anonymous users inover 95 000 businesses of Barcelona and Madrid. Eachtransaction is time-stamped and contains the informa-tion collected by the bank on both the cardholder andthe business. It also includes the customer’s age andresidence neighborhood, the business category and itsgeographical coordinates (see the Appendix for de-tails). From these data there are two obvious waysto estimate inequality among neighborhoods: first, inmeasuring the income of their residents – indirectlyestimated through the total amount of money spentduring the year; second, in measuring the total incomeresulting from the commercial activity of businesseslocated in these neighborhoods. The map on Figure 1ashows the latter for Barcelona, and reveals that someneighborhoods are indeed five times “richer” than oth-ers. This measure is particularly interesting because itresults from the spatial organization of shopping trips,which may be much easier to alter than any other typeof our daily trips, notably commuting.

Rewiring the shopping trips networks

From the data for both cities we construct the bi-partite spatial network whose nodes are individuals

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Number of rewiring operations Xx 105)

XkX0

WSDρ

Rewiringheuristic

Figure 2. Decreasing spatial inequality in the city by adapting daily shopping destinations. (a) Decrease of wealth inequal-ity among neighborhoods as a function of the fraction of transactions rewired, for various rewiring methods. Four combinationsof choice heuristics are considered, ”Uniform-Uniform” (U-U in the legend), ”Uniform-Weighted” (U-W), ”Weighted-Uniform”(W-U) and ”Weighted-Weighted” (W-W). (b) Decrease of wealth inequality (W /W0) while preserving the spatial mixing index(S/S0), the total distance traveled (D/D0) and the exploration rate (ρ/ρ0), as a function of the number of rewiring operations.Values have been averaged over hundreds of replications. The bars represent the minimum and the maximum values obtainedbut in most cases are too close to the average to be seen (see Figure S9-S10 in Appendix for Madrid).

and businesses, and whose edges stand for transac-tions (see Figure S2 in Appendix). We then per-form rewiring experiments, in which randomly se-lected transactions are redirected toward alternativebusinesses of the same category, but located elsewherein the city. The purpose of each rewiring operation isto incrementally decrease inequality in the spatial dis-tribution of business income W (see Figure1a). Fur-thermore, we consider three key properties of urbanmobility: the distance traveled D, the individual mo-bility routines ρ (measured as the tendency to returnto already visited businesses), and finally the spatialmixing of residents of different neighborhoods S. Wand S are defined as distances to homogeneous spatialconfigurations. At each step, an individual transac-tion is selected along with all the candidate businessestoward which it could be reasonably redirected. Oneof them is randomly chosen, and if rewiring the trans-action results in distributing money more evenly inspace while matching the other constraints, then thechange is accepted. The purchases and the amountof expenses of each individual are preserved, and thisiterative process is run until the rewiring rate fallsbelow a given threshold. Since the rewiring processis stochastic, all the results have been averaged overhundreds of replications (see Methods for more detailsabout the four metrics and constraints considered inthe rewiring process).

Numerous rewiring methods fulfilling these con-ditions could be proposed. In particular, besidesthe random selection of transactions (’Uniform’ sam-

pling), we can choose them according to a probabilityproportional to their amount and/or inversely pro-portional to the income of the target neighborhood(’Weighted’ sampling). Even more informed methodsmight be proposed, but for the sake of simplicity, onlybasic random procedures are considered in the follow-ing.

Reachability of even spatial distributions

We first investigate the reachability of an even spa-tial distribution of the commercial income resultingfrom individual purchases, while the variables S, Dand ρ remain in the range of their empirical values.To address this question, we apply the method withthe four constraints of Equation 5 such as αW = 0,αS = 1, αD = 1 and αρ = 1. This constitutes the Ref-erence experiment. Figure 2a shows the evolution ofinequality in the urban area of Barcelona as a func-tion of the fraction of rewired transactions, accord-ing to various methods. Surprisingly, even with basicrandom methods, it is possible to reduce spatial in-equality by more than 80% while reassigning only 20%of individual transactions. All the methods producethe same qualitative behavior – an early regime ofvery fast decay, followed by a regime of slower decay.Weighted methods are naturally more efficient, andallow to reach spatial equity by redirecting a smallerfraction of transactions. In particular, a reduction of80% in W /W0 can be obtained by rewiring only 5%

4

of the transactions if the method is double weighted.The state of the other variables S, D and ρ is also

monitored along the process, as shown in Figure 2bfor a Uniform-Uniform method. What makes the pre-vious results remarkable is in fact that income redis-tribution is achieved without increasing the distancetraveled by individuals (D), nor changing their mo-bility routines (ρ). Moreover, a positive side-effect isto increase the frequency of encounters of individualsliving in different parts of the city – as indicated bythe decrease of S/S0 –, an effect that could not bederived from the rewiring constraints alone (αS = 1).The increase of spatial mixing is the consequence of in-dividual shopping trips more evenly distributed in thecity space, required to homogenize the income amongneighborhoods. The behavior of S is non trivial, no-tably because one could imagine unrealistic solutionsto this problem that would simultaneously even thebusiness income distribution among neighborhoodsand decrease the total distance traveled, by rewiringmost of the shopping trips to the closest neighbor-hood containing businesses of the relevant category.The spatial mixing of individuals in this case woulddecrease dramatically, and S the distance to an ho-mogeneous spatial mixing would increase. Here thedecrease of S/S0 guarantees that it is not the case.

Preservation of human mobility properties

We wish to control further the likelihood of therewired shopping mobility networks, and ensure thatthey preserve the spatial properties of individual hu-man mobility. A small set of indicators are useful todescribe the statistical and spatial properties of hu-man mobility [20]. These include the jump length be-tween consecutive locations ∆r, the radius of gyrationrg and the tendency to return to already visited placesρ. In our case, for each individual ρ is simply definedas the ratio between the number of unique businessesvisited and the total number of transactions.

Figure 3 shows their empirical and simulated values,plus the average distance d traveled by each individ-ual for each shopping trip (see the Methods sectionfor details on the calculation of shopping trips dis-tances). On each panel both curves overlap almostperfectly, indicating that the rewiring has no signifi-cant effect on the key mobility properties. Simulateddistributions of d and rg are slightly more peaked thanthe empirical ones. Finally, we showed in a previousstudy that young adults tend to spend their moneyfurther from their neighborhood of residence [28], andcoherently their shopping trips are those that are themost affected in the simulated scenarios (see FigureS5 in Appendix).

Multi-objective improvement

We now perform multi-criteria rewiring experi-ments, to measure to what extent redistribution can

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Figure 3. Observed and simulated distributions of humanmobility indicators. The distribution of jump lengths ∆r,the radius of gyration rg, the tendency to return to alreadyvisited places (ρ) and the individual average distance traveled(d) are considered. Values measured on the empirical dataare in blue, while those obtained after rewiring are in red.The calculation of ∆r and rg is based on the business’ exactgeographical coordinates. The simulated distributions plottedhere correspond to one particular replication, see the FigureS4 for the robustness of the results and Figure S8 in Appendixfor the same curves for Madrid.

be achieved while improving simultaneously other im-portant aspects of urban mobility. To this end weperform the series of experiments summarized in Ta-ble 1. The objective is to even the wealth distributionamong neighborhoods (αW = 0) and simultaneouslyimprove either S, D or ρ without worsening the othertwo. Figure 4 gives the relative gains and losses uponthe four indicators, and the last two columns of Ta-ble 1 contain the asymptotic values obtained for thereduction rate of wealth inequality, for Barcelona (B)and Madrid (M).

Table 1. Experiments performed. Column W indicatesthe relative gain of (W0 −W )/W0. The first value is forBarcelona (B) and the second for Madrid (M).

Experiment αW αS αD αρ W (B/M)

(a) Reference 0 1 1 1 96.4%/99.5%

(b) Spatial mixing ↑ 0 0.75 1 1 85.9%/78.1%

(c) 50% energy savings 0 1 0.5 1 87.4%/84.8%

(d) 25% energy savings 0 1 0.75 1 94.7%/98.8%

(e) Exploration rate ↑ 0 1 1 1.25 96.8%/99.9%

(f) Exploration rate ↑↑ 0 1 1 1.5 97.3%/100%

Experiments prove that it is possible to combinesignificant improvements on several dimensions simul-taneously. This is not an issue with the method butrather with the objectives set, which are somewhat op-posite. Most individuals perform their shopping trips

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Figure 4. Multi-criteria improvement of shopping mobil-ity. Each group of bars gives the relative gains or losses forthe four indicators W , S, D and ρ. Experiments are describedin Table 1. See Figure S11 in Appendix for Madrid.

near their residence – as highlighted by the empiricaldistributions in Figure 3 – and consequently it is notfeasible to simultaneously diversify the neighborhoodswhere an individual regularly travels to – in order toimprove spatial mixing S – and at the same time de-crease the total travel distance D. More surprisingly,experiment (b) indicates that it is also not possible tosimultaneously improve the wealth redistribution andthe spatial mixing of individuals. The two indicatorsare based on different metrics (the amount of moneyspent per business for W and the number of trips forS), which imply different reference egalitarian situa-tions (see Figure S6 in Appendix for more details).Optimization is thus a trade-off between the variousconsequences of shopping mobility at the city scale.However, experiments (c) and (d) prove that it is pos-sible to significantly decrease the total distance trav-eled and in the same time to strongly reduce wealthinequality among neighborhoods, but not as much asin the reference experiment. Still, it is remarkablethat experiment (d) results in an alternative mobilitynetwork such that the spatial inequality of the aver-age business income is reduced by 95%, while the totaldistance associated to shopping mobility is reduced by25%, the level of spatial mixing is preserved, as well asthe individual mobility routines. Finally experiments(e) and (f) show that even if residents deeply restruc-tured their mobility routines, and typically started go-ing to a new business each time they perform a newshopping trip, keeping control of the total distancetraveled in the city would prevent from increasing themixing of individuals coming from different neighbor-hoods beyond 25%. The gains in terms of wealth re-distribution would not be significant when comparedto the reference experiment (a).

DISCUSSION

Reducing urban segregation and increasing spatialjustice are some of the major challenges faced by cities

worldwide, and the digital footprints passively pro-duced by their residents constitute a promising re-source to help addressing these issues from the bot-tom. This study is a first attempt to quantify the re-lation between shopping mobility and the spatial dis-tribution of economic activity in the city. The alter-native shopping trips resulting from our experimentsoffer an interesting trade-off between the preservationof essential aspects – the effective purchases of individ-uals and households, and their mobility properties –and some reasonable changes in the places where theyspend their money. The addition of small changes inthe shopping destinations of individuals can dramat-ically impact the spatial distribution of money flowsin the city, and the frequency of encounters betweenresidents of different neighborhoods, even if the totalnumber of changes remains small. These results haveimportant consequences, and they lead in particularto the decisive question of the effective implementa-tion of alternative shopping travels, like those drawnby our experiments. While the decision process be-hind each individual redirection may appear intricatefor a single person, one could easily imagine dedicatedmobile applications, querying databases very similarto the one used in this paper. Their purpose wouldbe to assist their users in a transition toward a moresocially and spatially concerned shopping mobility.

Limitations of the study

However one should keep in mind that individu-als do not guide most of their travel decisions byphilanthropy, but instead by balancing accessibility,price and business characteristics. Individuals firstchoose their casual shopping destinations with regardof transport facilities and travel time budget [29].Here as accessibility information we considered theEuclidean distance between neighborhoods. Howeverin urban environments the Euclidean distance is rarelya direct proxy for travel time [30], and some of therewired shopping trips are unlikely to be performed inthe real world. We also assumed that every shoppingtrip follows the simple pattern A → B → A, and wedid not consider the more complicated case of chainedtrips (e.g. A→ B → C → A) during which individualsjoin several trips associated with different purposes[31]. People also tend to choose the places where theyspend money according to several other key factors,the price of products in the first place, but also accord-ing to some more personal appreciations, such as the”ambiance” of neighborhoods and the feeling of well-being they provide. In large cities, the neighborhoodsstrongly differ in the quality of their planning and ar-chitecture, in their public spaces, in their amenitiesand leisure opportunities, commercial fabric, in theirsafety. Additionally, the changes might be consideredas problematic, since a profound spatial reorganiza-tion of shopping mobility in the city could have con-sequences on the spatial structure of employment inthe first place (see Figure S7 in Appendix), and then

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on residences. For the sake of simplicity we considerednone of these factors, but they could be implementedin more involved frameworks derived from our work.

Concluding remarks

There are recent, encouraging examples of fast andwide adoptions of new daily practices, whose benefitsare essentially collective. Examples include garbagedifferentiation [32], the increasing role of bicycle inurban transport and the development of bicycle shar-ing systems [33], or the open-source movement andthe dedication of a growing number of individualsto collectively build free knowledge databases (e.g.Wikipedia, StackExchange, the free software move-ment). In these cases, the remuneration of partici-pants, if any, is essentially symbolic. The success of aspatial counterpart to these altruistic behaviors couldrejuvenate the meaning of the so-called sharing econ-omy [21]. As citizens produce the data that documenttheir location and activity patterns, in return thesedata could serve not only the specific interest of theinstitution collecting them, but also support fair socio-economic initiatives. This study brings evidence thatthese geographical footprints we passively produce cansupport bottom-up responses to big societal issues, anexpected feature of truly smart cities.

METHODS

Estimation of shopping trips distances.

We made the assumption that to each transaction isimplicitly associated a trip originating from either themain activity neighborhood during working time, orthe neighborhood of residence, depending on the hourof the day and day of the week (see the Appendix formore details). The shopping trip distance is then theEuclidean distance between the centroids of the originand destination neighborhoods.

Variables considered when redirecting theshopping trips

The primary objective when rewiring the shoppingmobility networks is to even the distribution of com-mercial income among the neighborhoods (here zip-codes), while respecting a set of constraints to en-sure that the alternative networks produced are rea-sonable, and possess interesting properties.

We denote by W the wealth inequality among acity’s neighborhoods. It is defined as the distance to areference egalitarian situation, where the commercialincome resulting from individual purchases would beequally shared among all neighborhoods in average.More specifically, the level Wk of wealth inequality af-ter k rewiring operations is

Wk =

N

∑

i=1

(wik −w∗)2, (1)

where N is the number of neighborhoods, wik is theaverage income of businesses located in neighborhoodi after k rewiring operations, and w∗ represents thewealth per neighborhood in the reference configura-tion where commercial income is evenly distributedacross neighborhoods, such that

w∗=

1

N

N

∑

i=1

wik. (2)

An important aspect of individuals mobility in thecity is to prevent some neighborhoods from ghettoiza-tion. To measure to what extent individuals residingin various neighborhoods mix in the city space as aresult of their displacements, for each neighborhood iwe count the number of times (si1k , ..., s

iNk ) the resi-

dents of i traveled to each of the N neighborhoods (iincluded), after k rewiring operations. Then, by av-eraging the vector of trips over all the neighborhoods,we compute the geographical diversity index Sk ob-tained after k rewiring operations,

Sk =1

N

N

∑

i=1

N

∑

j=1

(sijk − s∗i )2, (3)

where s∗i represents the homogeneous distributionof visits originating from i and in direction to all neigh-borhoods,

s∗i =1

N

N

∑

j=1

sijk . (4)

The third aspect we want to control is the distancetraveled by individuals. For obvious reasons it is de-sirable that the total travel distance does not increase.Summing the distances traveled by individuals for alltheir shopping trips, we can compute Dk the total dis-tance measured on the network after rewiring k trans-actions.

Finally, in order to preserve individual mobility rou-tines and the tendency of individuals to return to al-ready visited places, for each individual we calculatedthe exploration rate ρk. It is defined as the num-ber of unique businesses he/she has visited divided byhis/her total number of transactions, after k rewiringoperations. Considering the empirical peaked distri-bution of ρk among the population of customers, inthe following we consider the mean value ρk.

Rewiring constraints

The rewiring experiments can be formalized as aconstraint satisfaction problem (CSP) over a spatial

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bipartite network. We consider four constraints, eachof them concerns one of the variables mentionned inthe previous section, and quantifying an importantaspect of shopping mobility:

• Constraint CW applies on the wealth distribu-tion; it ensures that each destination changecontributes to homogenize the distribution ofcommercial income across neighborhoods.

• CS , a constraint on the spatial mixing of indi-viduals, resulting from their shopping trips. Tobe accepted, a rewiring operation has to preservethe diversity of neighborhoods visited, hence thedegree of spatial mixing of individuals residingin different neighborhoods.

• CD, a constraint on the total distance traveled,to guarantee that each destination change doesnot result in increasing the total distance trav-eled. The distance associated to each individualtransaction is calculated with regard to the in-dividual’s main activity place at this moment ofthe day (see section above for details).

• Cρ, a constraint on the spatial exploration rateof individuals, to preserve the behavioral mobil-ity routines measured in the population.

All constrains have the same form: constraint CXis satisfied if the following condition holds

Xk+1 ≤

⎧⎪⎪⎨⎪⎪⎩

Xk if Xk+1 ≥ αX0,

αX0 otherwise,(5)

where k denotes the number of rewiring operation,and α is a parameter positive or equal to zero. Equa-tion 5 allows to fix the objective upper bound foreach variable X with respect to its empirical valueX0. While X is greater than αX0, each rewiring op-eration must decrease X. Once X is smaller thanαX0, Equation 5 ensures that none of the followingrewiring operations will increase X above this value.An experiment is then defined by a set of four val-ues (αW , αS , αD, αρ) that specify the desired maximalvalue for each of the four dimensions of interest.

We favored a numerical approach because of thelarge number of transactions (∼ 107) and because ofthe constraints imposed to guarantee that the simu-lated networks possess realistic and interesting prop-erties.

ACKNOWLEDGEMENTS

We wish to thank Julie Vallee and Suma Desufor providing feedback on an early version of themanuscript. We also thank Jean-Loup Guillaumefor fruitful discussions on the rewiring problem.Partial financial support has been received fromthe Spanish Ministry of Economy (MINECO) andFEDER (EU) under the project INTENSE@COSYP(FIS2012-30634), and from the EU Commissionthrough projects EUNOIA and INSIGHT. The workof TL has been funded under the PD/004/2015, fromthe Conselleria de Educacion, Cultura y Universidadesof the Government of the Balearic Islands and fromthe European Social Fund through the Balearic Is-lands ESF operational program for 2013-2017. JJRacknowledges funding from the Ramon y Cajal pro-gram of MINECO.

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9

APPENDIX

Data preprocessing

The dataset contains information about 14 mil-lion bank card transactions made by customers ofthe Banco Bilbao Vizcaya Argentaria (BBVA) in themetropolitan areas of Barcelona and Madrid in 2011.For both case studies, we only consider the creditcard payments whose amount was inferior to 1000 eu-ros, and which were made inside the metropolitan ar-eas, by bank customers that lived and worked in themetropolitan area in 2011. Each transaction is charac-terized by its amount (in euro currency) and the timewhen the transaction has occurred. Each transactionis also linked to a customer and a business. Customersare identified with an anonymized customer ID, con-nected with sociodemographic characteristics (gender,age and occupation) and their postcode of residence.In the same way, businesses are identified throughan anonymized business ID, a business category id,and the geographical coordinates of the credit cardterminal. Since we are primarily interested in dailyshopping mobility, we chose to consider the businesscategories that account for the top 90% of the dailyshopping trips (see Figure S1). The proportions ofshopping trips associated to each of the 20 businesscategories we selected are available in Table S1.

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Number of Categories

Cum

ulat

ive

% o

f sho

ppin

g tr

ips

●

●

BarcelonaMadrid

Figure S1. Cumulative proportion of shopping tripsas a function of the number of categories. In blue themetropolitan area of Barcelona; In red the one of Madrid

Formal description of the rewiring process

From the data we extract G(R,B,T ) the bipartitenetwork of all credit card transactions performed bythe city residents in businesses located in the city, dur-ing the entire year. R is the set of residents, B the setof businesses and T the set of transactions. Table S2contains the characteristic attributes of the networkin the two cities studied. Each city is partitioned in

Table S1. Proportion of shopping trips associated to each ofthe 20 business categories selected.

Category Barcelona Madrid

Supermarket 17.71 14.84

Hypermarket 10.25 12.09

Gas Stations 8.41 9.49

Restaurants 8.20 6.73

Retail store 5.84 2.82

Clothing store chain 5.48 4.67

Clothing store 5.16 7.33

Pharmacy, optical and orthopedics 4.52 3.81

Department store 3.14 5.73

Hair and beauty 2.88 2.72

Electronics, computers and appliances 1.97 1.44

Bars and cafe 1.85 1.60

Shoe store 1.71 1.43

Toys and sports articles 1.43 1.33

Bookshop, music shop and stationery 1.42 1.04

Fast food restaurants and chains 1.13 2.38

Car dealership and garage 1.02 1.01

Bazaar 1.01 1.06

DIY store 0.99 1.08

Hospitals, clinics and doctors 0.91 0.88

N spatial units/neighborhoods (here the units corre-spond to zip codes) and the network G is spatial: eachresident and each business is located in one neighbor-hood. We denote Ri (resp. Bi) the set of residents(resp. businesses) located in the neighborhood i. Thesets are disjointed and we have R = ⊍Ri and B = ⊍Bi,with i ∈ 1..N . Additionally the businesses are alsopartitioned in C categories according to the productsthey sell, and we have B = ⊍Bc, c ∈ 1..C. The edgesof the network represent the card transactions, henceimplicitly the shopping trips. We note tkr,b the k-thtransaction performed by resident r in business b, andby w(tkr,b) its amount.

Table S2. Summary statistics of the two metropolitanareas and of the two transactions networks.

Statistics Barcelona Madrid

Number of neighborhoods 97 123

Number of inhabitants (2009) 3,218,071 5,512,495

Area (km2) 634 1,935

Number of customers 42,023 118,447

Number of businesses 40,618 55,148

Number of transactions 3,640,961 10,025,642

The rewiring methods we implemented operate di-rectly at the micro scale of the individual transactions,and each rewiring operation tr,b → tr,b′ consists in se-

10

Residents Businessest1,1

1

t1,1

2

k-th transaction/shopping tripperformed by resident rin business b

Neighbourhoodsdelimitations

Various categoriesof businesses

tr,bk

Figure S2. The bipartite network of transactions.

lecting a business b′ ≠ b, such than b′ and b are of thesame category c but are located in different neighbor-hoods. The rewiring occurs only if b′ fulfills a numberof additional constraints (namely CW , CD, CS andCρ) which are expressed at the macro-scale of the en-tire city.

The network is rewired iteratively, i.e. transactionper transaction. A transaction tr,b is picked up ran-domly (uniform or weighted sampling, as describedin the main text). A neighborhood is chosen amongthe set of all neighborhoods that contain some busi-nesses b′ of the same category than b. Both the trans-action and the candidate business can be picked upthrough a uniform or weighted random sampling. Fi-nally, if the neighborhood change j → j′ matches thefour constraints, then the transaction/edge is rewired.The process stops when the rewiring rate falls below0.001.

Estimation of shopping trips distances andidentification of the users’ main daytime activity

location

We made the assumption that to each transactionis implicitly associated a trip originating from eitherthe main activity neighborhood during working time,or the neighborhood of residence, depending on thehour of the day and day of the week. The shoppingtrip distance is then defined as the Euclidean distancebetween the centroids of the origin and destinationneighborhoods.

We already know the neighborhood of residencethat we can assign as the place of main activity duringnight time (i.e between 7pm and 8am) on week daysand Saturday and Sunday. In addition to the neigh-borhood of residence, for each individual we can deter-mine the neighborhood in which he/she was the mostfrequently located during the typical working hours of

working days, i.e. from 8pm to 7am, from Monday toFriday.

To do so, for each individual we count the num-ber of unique couples (day, hour) during which he/shewas located in each neighborhood. For our study wekeep only the individuals for which credit card is acasual mode of payment, and for which we can thenreasonably assume that their card purchases and cor-responding shopping trips are representative of theirshopping mobility in general. Regarding the avail-able statistics for Spain on the share of credit cardpayments among all payments, we decided to keep in-dividuals whose data displayed at least N = 20 uniquecouples (day, hour) during the entire year. For eachof these individuals, we then determine the neighbor-hood in which they were the most frequently locatedduring typical working hours. If this neighborhoodaccounted for less than one third of the time δ = 1/3in his/her entire set of locations, then the individualis discarded. As it can be seen in Figure S3a and Fig-ure S3c, the couple of value (N, δ) = (20,1/3) allow usto keep enough users and discard the users not show-ing enough regularity to estimate their main daytimeactivity location.

Finally, we can estimate the commuting flows be-tween neighborhoods and assess the accuracy of theresults by comparing these flows with those ob-tained from the 2011 Spanish census in Barcelona andMadrid [34]. The census data is at the municipal level,which implies that the neighborhoods must be aggre-gated at the municipality scale to be able to performthe comparative analysis. Figure S3b and Figure S3dshow a scattered plot with the comparison betweenthe flows obtained with the two matrices. A goodagreement between the two ODs is obtained.

The source code of this method is availableat https://github.com/maximelenormand/Most-frequented-locations.

11

0.2 0.4 0.6 0.80

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ber

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sers

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103 ) N > 5

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(d)

Figure S3. Identification of the users’ main daytime activity location in Barcelona ((a)-(b)) and Madrid ((c)-(d)).(a) and (c) Number of users according to N and δ. (b) and (d) Comparison between the non-zero flows obtained with thecredit card dataset ((N, δ) = (20,1/3)) and the census data. The values have been aggregated at the municipality scale. Thevalues have been normalized by the total number of commuters for both OD tables. Blue points are scatter plot for each pairof municipalities. The red line represents the x = y line.

12

SUPPLEMENTARY FIGURES

1

2

3

4

1 2 3 4 5 6 7 8 9 10

Replication

d (k

m)

(a)

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ρ

(b)

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∆ r (

km)

(c)

2

3

4

5

1 2 3 4 5 6 7 8 9 10

Replication

r g (

km)

(d)

Figure S4. Individual human mobility indicators’ distributions obtained with ten replications of the algorithm. (a)Individual average distance traveled d. (b) Exploration rate ρ. (c) Jump length distribution ∆r. (d) Radius of gyration rg.The boxplot is composed of the first decile, the lower hinge, the median, the upper hinge and the 9th decile.

13

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]15,30]]30,45]]45,60]]60,75]>75

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0.035

Percentage of Transactions

PD

F

(d)

StudentUnemployedEmployedHomemakerRetired

Figure S5. Probability density functions of the individual percentage of rewired transactions. (a) Total. (b) By Gender.(c) By age. (d) By occupation.

14

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Xk

X0

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W S D ρ

Figure S6. Evolution of W, S, D and ρ as a function of the number of rewiring transactions. (a)(αW , αS , αD, αρ) = (0,+∞,+∞,+∞). (b) (αW , αS , αD, αρ) = (+∞,0,+∞,+∞). (c) (αW , αS , αD, αρ) = (+∞,+∞,0,+∞).(d) (αW , αS , αD, αρ) = (+∞,+∞,+∞,0).

15

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2e−04

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2000

3000

4000

5000

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Replication

Am

ount

of m

oney

spe

nt (

euro

)

(b)

Figure S7. Probability density functions of the total amount of money spent by business in 2011, in Barcelona. (a)Comparison between the original distribution and the one obtained after applying the rewiring algorithm. (b) Distributionsobtained with ten replications of the algorithm. The boxplot is composed of the first decile, the lower hinge, the median, theupper hinge and the 9th decile.

16

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)

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100

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Figure S8. Observed and simulated distributions of human mobility indicators in Madrid. The distribution of jumplengths ∆r, the radius of gyration rg, the tendency to return to already visited places (ρ) and the individual average distancetraveled (d) are considered. Values measured on the empirical data are in blue, while those obtained after rewiring are in red.The calculation of ∆r and rg is based on the business’ exact geographical coordinates.

17

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0.4

0.6

0.8

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Percentage of rewired transactions

WW

0

Uniform−UniformUniform−WeightedWeighted−UniformWeighted−Weighted

Figure S9. Decrease of wealth inequality among neighborhoods as a function of the fraction of transactions rewired, forvarious heuristics (Madrid). Four heuristics are considered, ”Uniform-Uniform”, ”Uniform-Weighted”, ”Weighted-Uniform”and ”Weighted-Weighted”.

18

0 50 100 150 200

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0.4

0.6

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Xk

X0

WSDρ

Figure S10. Decrease of wealth inequality (W /W0) while preserving the spatial mixing index (S/S0), the distancetraveled (D/D0) and the exploration rate (ρ/ρ0) as a function of the number of rewiring operations (Madrid case).Values have been averaged over hundreds of replications. The bars represent the minimum and the maximum values obtainedbut in most cases they are too close to the average to be seen.

19

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0.75

1

(a) (b) (c) (d) (e) (f)

(X0

−X

∞)

X0

W S D ρ

Figure S11. Multi-criteria improvement of shopping mobility in the city of Madrid. Each group of bars gives the relativegains or losses for the four indicators W , S, D and ρ.