Institutions and Cultural Diversity: Effects of Democratic and Propaganda Processes on Local Convergence and Global Diversity

RESEARCH ARTICLE Ins i u ions and Cul u al Di e si y: E ec s o Democ a ic and P opaganda P ocesses on Local Con e gence and Global Di e si y Robe o Ulloa 1 *, Celina Kacpe ski 2 , Fe nando Sancho 3 1Depa men o Mode n Languages and Li e a u es, Uni e si y o Wes e n On a io, London, Canada, 2Spo and Exe cise Psychology Lab, Uni e si y o Wes e n On a io, London, Canada, 3Depa amen o de Ciencias de la Compu ación e In eligencia A i icial, Uni e sidad de Se illa, Se illa, Spain * obe o.u @p o onmail.com Abs ac In a connec ed wo ld whe e people in luence each o he , wha can cause a globalized mono- cul u e, and which measu es help o p ese e he coexis ence o cul u es? P e ious esea ch has shown ha ac o s such as homophily, popula ion size, geog aphy, mass media, and ype o social in luence play impo an oles. In he p esen pape , we in es iga e o he i s ime he impac ha ins i u ions ha e on cul u al di e si y. In ou i s h ee s udies, we ex end exis ing agen -based models and explo e he e ec s o ins i u ional in luence and agen loyal y. We ind ha highe ins i u ional in luence inc eases cul u al di e si y, while indi- iduals' loyal y o hei ins i u ions has a small, p ese ing e ec . In h ee u he s udies, we es how bo om-up and op-down p ocesses o ins i u ional in luence impac ou model. We ind ha bo om-up democ a ic p ac ices, such as e e enda, end o p oduce con e gence owa ds homogenei y, while op-down in o ma ion dissemina ion p ac ices, such as p opa- ganda, u he inc ease di e si y. In ou las model—an in eg a ion o bo om-up and op- down p ocesses in o a eedback loop o in o ma ion—we ind ha when democ a ic p o- cesses a e a e, he e ec s o p opaganda a e ampli ied, i.e., mo e di e si y eme ges; how- e e , when democ a ic p ocesses a e common, hey a e able o neu alize o e e se his p opaganda e ec . Impo an ly, ou models allow o con ol o e he ull spec um o di e - si y, so ha a manipula ion o ou pa ame e s can esul in p e e ed le els o di e si y, which will be use ul o he s udy o o he ac o s in he u u e. We discuss possible mechanisms behind ou esul s, applica ions, and implica ions o poli ical and social sciences. In oduc ion Models o cul u e and social in luence In ligh o inhe en ensions in in e na ional in eg a ion [1] and a con empo a y end owa ds cul u al policy [2,3], ac o s ha impac cul u al globaliza ion and he p ese a ion o di e si y ha e been a ecen ocus in compu a ional modeling. The ques ion how di e si y, i.e. he co- PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 1/26 OPEN ACCESS Ci a ion: Ulloa R, Kacpe ski C, Sancho F (2016) Ins i u ions and Cul u al Di e si y: E ec s o Democ a ic and P opaganda P ocesses on Local Con e gence and Global Di e si y. PLoS ONE 11(4): e0153334. doi:10.1371/jou nal.pone.0153334 Edi o : Bo is Podobnik, Uni e si y o Rijeka, CROATIA Recei ed: Sep embe 19, 2015 Accep ed: Ma ch 28, 2016 Published: Ap il 8, 2016 Copy igh : © 2016 Ulloa e al. This is an open access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed. Da a A ailabili y S a emen : All da a iles a e a ailable om h ps://zenodo.o g/ eco d/31133 and h p://dx.doi.o g/10.5281/zenodo.31133. All code is a ailable om h ps://gi hub.com/ obe ou /cul u al- simula ions/ eleases/ ag/1.0 and h p://dx.doi.o g/10. 5281/zenodo.31186. Funding: The au ho s ha e no suppo o unding o epo . Compe ing In e es s: The au ho s ha e decla ed ha no compe ing in e es s exis . exis ence o many a ied cul u es, can be sus ained in he ace o a g owing endency owa ds globaliza ion has been explo ed wi h a ious app oaches [4–8]. Cul u e is he e cons ued as he in o ma ion which is ansmi ed be ween indi iduals in a social manne (such as music, cus oms, and language). The p ocess o ansmission is also known as social in luence [9]. Fo mal ma hema ical models o social in luence illus a ed ha , when e e yone in a ne - wo k is connec ed, a global monocul u e is ine i able—all cul u es con e ge o a global consen- sus and become homogenous [4,10,11]. Cul u al simula ions, among hem a i icial socie ies [5,12], ha e since hen been adop ed o acili a e he s udy o pa e ns o cul u al ansmission. They ha e enhanced ou unde s anding o how di e si y and global consensus eme ge in socie- ies, and how socie ies can luc ua e be ween one and he o he , explo ing hese dynamics by in oducing a ious ac o s o social in luence o ind ways by which di e si y can be p ese ed. One example o a social p ocess ha has yielded aluable insigh s is homophily, he p inci- ple o "like a ac s like": he highe he simila i y be ween wo indi iduals, he mo e likely hey a e o in luence each o he [13,14]. Schelling used his idea o show ha a small "dislike" o a dissimila neighbo could lead o comple e seg ega ion in an agen -based model [15,16]. Fol- lowing his, Axel od's seminal pape [5] in oduced an agen -based model ha in eg a ed bo h, he p oposed ne wo k s uc u e o p e ious models [4] and homophily [13], bu ins ead o looking a seg ega ion by mo emen like Schelling [16], he s udied seg ega ion by a i ude change, in pa icula he ques ion: when indi iduals change hei alues and opinions based on simila i ies wi h each o he , do cul u es become mo e alike o mo e di e se? He ound ha cul u al di e si y eme ges and pe sis s unde homophily, because g oups o agen s wi h simila cha ac e is ics g ow mo e simila inside each g oup, un il he g oups don' sha e any common cha ac e is ics. Once comple e dissimila i y be ween wo g oups is eached, hey no longe in e ac . Ini ial pa ame e s, such as popula ion size, neighbou hood in e ac ion size, and numbe o cul u al ea u es and ai s, impac ed he eme gence o cul u al di e si y, o example, a smalle popula ion size was conduci e o di e si y, while an inc ease in neigh- bou hood size inc eased cul u al homogenei y [5,17]. In ecen esea ch, mass media has been shown o inc ease cul u al di e si y when he mass media messages a e s ong enough, whe eas weake messages we e mo e likely o lead o global homogenei y [18,19]. A change in geog aphy, such as modelling moun ains ha minimize con- ac be ween g oups o agen s, inc eased le els o di e si y as well [20]. The ypes o in e ac ion be ween agen s ha e been also explo ed: while in Axel od’s o iginal model, in e ac ions we e o dyadic na u e, i.e. indi iduals in e ac ed wi h and in luenced each o he on one-on-one basis, Pa isi e al [20] and Flache e al [21] implemen ed mul ila e al social in luence models based on Richa dson e al [22], in which agen s conside opinions o mul iple neighbo s a ound hem (ins ead o jus one), be o e changing hei ai s. Finally, Axel od’s o iginal idea o es ing he model agains andom noise was implemen ed, in he o m o "mu a ion a es" [20,23], and la e , “selec ion e o ”[21]. Klemm e al [23,24] in oduced a ious a es o noise in o Axel od's model and ound ha e en a he smalles a e o pe u ba ions, he model quickly des abilized and con e ged in o a monocul u e wi hou any di e si y, while a a la ge a e o pe u ba ion, i de ol ed in o anomie, he comple e cul u al isola ion o each indi idual om hei neighbo s [25,26]. The “selec ion e o ”, which is based on he assump ion o an occasional pe cep ion e o o a neighbou ’s simila i y (o dissimila - i y), was added o cul u al d i as ano he le el o noise, and p oduced a simila ins abili y [21]. By in eg a ing mul ila e al social in luence wi h Axel od’s o iginal pos ula ion o homo- phily, Flache e al [21] p oposed, o he bes o ou knowledge, he hus a mos success ul model, acili a ing he eme gence o cul u al di e si y and s abilizing Axel od’s o iginal model [5] agains he wo sou ces o noise. I will he e o e se e, along wi h Axel od's model, as a compa ison poin in ou esul s. Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 2/26 Models o ins i u ions Following cul u al d i , limi ed communica ion, e ain e ec s, echnology and b oadcas ing, wi h he p esen pape , we would like o in oduce a no el ques ion o ex end Axel od’s o iginal model: wha ole do ins i u ions play in he eme gence and esilience o di e si y? Fi s analyses o ins i u ional in luence supposed ha a diminishing impac o social ins i u- ions on alues and beha io would inc ease indi idualis ic endencies and could, in ex eme cases, lead o anomie [26]. Since hen, much esea ch in o social ins i u ions has in es iga ed hei e ec s in e ms o social ne wo ks [27,28] and heo y o games app oaches, such as p is- one ’s dilemma and coo dina ion games [29–31]. Ve y li le esea ch has looked a he impac o ins i u ions on cul u e and i s unde lying p ocesses o social in luence. To ou knowledge, only h ee majo p ojec s ha e used agen -based models in his con ex : (1) one s udy show- cases how indi iduals hide hei ue belie s in au ho i a ian egimes (ins i u ions), and how he egimes a e a ec ed by his [32]; (2) one pla o m exis s ha allows an in eg a ion o in o - ma ion eposi o ies, and le s esea che s analyze pa e ns o cul u al dynamics [33], and (3) a line o esea ch exis s ha in es iga es mass media in luence [18,19,34], which can be in e - p e ed as ins i u ional in luence and shows se e al me hodological simila i ies o ou s. The addi ion o ins i u ions o an agen -based model o cul u al pa e ns, as we p opose, can add insigh in o p ocesses o cul u al di e si y eme gence and esilience by o example analyz- ing he impac o a ying le els o ins i u ional in luence and ins i u ional loyal y on cul u e. Fu he mo e, we can analyze he way in which indi iduals and ins i u ions in e ac wi h each o he inside di e en poli ical sys ems, o example h ough means o democ a ic p ocesses (like e e enda), o o ganized dissemina ion o in o ma ion (like p opaganda), and hen explo e how his impac s he sys em’s composi ion. In agen based models, he idea o "cen al au ho i ies" has been mos ly excluded om he me hodology so a . This migh be due o he assump ion ha hey can only play he pa o cen al coo dina ing agen s [5,12]. To he con a y, we would like o es ablish ha cen al au ho i ies and ins i u ions do no deno e he same concep . A he cen e o ins i u ional esea ch lies he exchange be ween human au onomy (i.e. he agency in human beha io ), and social s uc u e (i.e. in luences de i ed by ins i u ions in socie y) [35]. Axel od [5] explici ly excludes powe ul au ho i ies om his model because o hei absolu e coo dina ing impac on cul u e (whe e an au ho i y in luences indi iduals’belie s and alues, bu is no in u n in lu- enced in any way). An example o a p e ious implemen a ion o cen al au ho i y is he inclu- sion o geog aphy, such as a moun ain ange [20]. I impac s agen s’beha iou (by p e en ing in e ac ion be ween neighbou hoods o agen s), bu canno be impac ed by agen s i sel . Howe e , au ho i ies a e no necessa ily absolu e. Wi h ou p esen wo k, we aim a a use o ins i u ions which exe in luence on indi iduals and go e n people's beha io and a e in u n in luenced by indi iduals, especially in hei c ea ion [36]. We speak o ins i u ions in e ms o in o ma ion cen e s, i.e. mechanisms o poli ical, economic o social in e ac ions [37]. They can be mo e o mal, such as go e nmen s, ma iage, o ganized eligion, o in o mal ag ee- men s, such as ege a ianism o spi i ual belie s. In gene al, space in which sha ed in o ma ion is s o ed does no need o be angible, bu in a i icial ep esen a ions, he e is a need o concep ualize a second le el o in o ma ion ha lies beyond i s le el indi idual in e ac ion pa e ns. This idea has been p e iously applied in cul u al algo i hms (a b anch o e olu iona y algo i hms) in he way o “belie spaces”[38]. Belie spaces inhe i cul u al knowledge; hey a e he s o age o agen s’sha ed belie s, and a e upda ed as hose belie s change. A he same ime, belie spaces ha e an impac on how he agen s e ol e alongside each o he ; hey impac who in e ac s wi h who and who is in luenced in wha way. In agen - based models, his pa icula kind o belie space has been e med a "cul u al eposi o y" [33]. Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 3/26 In o de o illus a e he ela ionship o hese wo le els o in o ma ion s o age, le us assume, o example, ha Romeo in e ac s wi h Julie , discussing he alue o ce ain ypes o music. In Axel od’s model [5], he e is only one le el: h ough homophily and social in luence, Romeo can be con inced by Julie ha salsa music is be e han ha d ock, and Romeo and Julie would hen sha e a common " ai ". In ou model, bo h Romeo and Julie s ill in e ac on an indi idual le el, bu hey also ha e a belie space ha ep esen s he wo di e en ins i u- ions ha hey belong o, o example hei espec i e amilial uni s, House Mon ague and House Capule (Fig 1). When Romeo in e ac s wi h Julie , he is no only awa e o hei in e - pe sonal simila i y and hei own ai s, he is also p essu ed by how ep esen a i e his ins i u- ion (i.e. his amily) is o him, and how much in luence his has on him. The le el o ins i u ional in luence ha Romeo pe cei es can p e en him om liking salsa music. He needs o check whe he his amily app o es o salsa music, and i i doesn’ , whe he his homophily wi h Julie is s ong enough o igno e his amily. I Romeo does change his ai , because he likes Julie be e han his amily, he can hen also choose o change his ins i u ion, i.e. see i becoming a Capule will sui him be e han being a Mon ague, as Julie ’s amily, he Capule s, migh be mo e ep esen a i e o who he is han his own amily. This choice will depend on Romeo's loyal y owa ds his amily, i.e. how willing he is o gi e up his amily name and connec ions. The di e en le els o ins i u ional in luence and agen loyal y can be exempli ied by di e - en ypes o ins i u ions. Fo example he e a e ins i u ions ha p omo e s ong iden i ica ion and exe a lo o in luence, such as amilies o na ionali ies, o hose ha do less so, such he school one wen o, o he TV channels one wa ches. Indi iduals can eel a ying le els o loy- al y o hei ins i u ions as well, o example when someone is pa o a poli ical pa y because i has always been his way in hei amily (conse a ism), o when social punishmen is no - ma i e (e.g. some amilial s uc u es o eligious o ganiza ions). Wi h all hese conside a ions in mind, we would like o p opose ou ini ial esea ch ques- ions: How is he di e si y o a sys em impac ed by a ying amoun s o in luence ha ins i u- ions exe on indi iduals? How is he sys em impac ed by a ying amoun s o loyal y ha ins i u ions demand om hei ollowe s? And how does he inclusion o ins i u ional in lu- ence and agen loyal y o an agen -based cul u al dissemina ion model compa e wi h esul s ob ained by Axel od [5] and Flache e al [21]? Fig 1. Model o ins i u ions, Romeo and Julie example. "R" ep esen s agen Romeo, "J" ep esen s agen Julie , "M" and "C" hei espec i e houses, Mon ague and Capule . Agen s om one cul u al egion (e.g. yellow, blue) a e connec ed o he ins i u ion ha hey belong o (also colo ed yellow and blue). doi:10.1371/jou nal.pone.0153334.g001 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 4/26 Re e endum and p opaganda Ou p e ious esea ch ques ions look a he impac o a ious le els o in luence and loyal y on cul u al di e si y in a way in which ins i u ions only p e en possible cul u al changes ( he in luence is indi ec ). An addi ional ocus o ou wo k a e he wo di ec ions in which social in luence can unc ion be ween low le el in e ac ions (indi iduals) and high le el in e ac ions (ins i u ions) [35,36], and how his impac s cul u al dissemina ion; on one hand, in luence can be exe ed in a bo om-up end, on he o he hand, i can be exe cised in a op-down manne . Thus, concep ually, he p ocesses o ins i u ional in luence we p opose can be unde s ood as a eedback loop o in o ma ion. These wo o ms o di ec in luence ha e ound ansla ion in o o ms o go e nance employed in poli ical sys ems. Common bo om-up in luences upon ins i u ions a e o ing, and mechanisms o di ec democ acy such as e e enda o plebisci es [39], while a common o m o op-down in luence by ins i u ions is he use o in o ma ion dissemina ion, such as campaign ad e ising o p opaganda [40]. Some p e ious agen -based models ha e looked a he impac o a eedback loop o in luence on cul u al di e si y and ha e ela ed his p ocedu e o mass media co e age on a global popula ion le el [18] o di e en ia ed by p ede e mined local neighbo hoods [19]. Howe e , hose models do no di e en ia e be ween op-down and bo om-up p ocesses, and hey lack a alida ion agains noise le els, which ha e been shown o g ea ly impac sys em s abili y [23]. By eason o his, we would like o p opose ano he line o in es iga ion, subdi ided in o h ee speci ic esea ch ques ions. We will i s indi idually explo e a bo om-up p ocess, in which he ins i u ions adap hei ai s owa ds popula ion majo i y belie s, simila o he exe- cu ion o e e enda, and see how his p ocess impac s he composi ion o ins i u ions, hei in luence, and he e o e, he eme gence and pe sis ence o di e si y wi hin he sys em. Then we will explo e a op-down p ocess in he same manne , in which indi iduals adap hei ai s due o ins i u ional p essu es, simila o he employmen o p opaganda. Las ly, we will combine he wo in one sys em o show he e ec s o he eedback loop o social in luence. We will also see how a a ie y o equencies o occu ence o hese p ocesses a ec sys em s abili y unde noise. Me hods Agen -based models Agen based models a e a popula ool o empi ical es ing o ealis ic concep s in complex sys ems. Ini ial models we e common in economy and biology [41–43] and ha e since hen pe mea ed many knowledge ields anging om psychology o physics. In he social sciences, Eps ein & Ax ell popula ized hei use wi h hei suga space model [12]. Models commonly include a wo-dimensional g id, which se es as he “wo ld”. I is inhab- i ed by agen s, which can be in e p e ed as indi iduals, ibes o illages/ owns. How agen s in e ac wi h each o he and hei wo ld en i onmen is based on he ules o any gi en model. This ype o abs ac ion allows a ep esen a ion o a a ie y o pa e ns and ideas, such as cul- u al pa e ns, while no applying i o any speci ic, named cul u e. In ou model, we ollow and expand he a angemen o Axel od’s o iginal con e ging di e si y model [5] wi h he ollowing uni s: 1. Indi idual agen s: Each indi idual agen is an au onomous en i y ha holds a ce ain amoun o in o ma ion, i s cul u e. In he simula ion, his cul u e is ep esen ed by a s ing o ea u es, such as o example music, cuisine, language, e c. Each agen exhibi s a p e e - ence on each ea u e, which is called a ai ; an agen migh like salsa music, Mexican ood and Spanish language. In simula ions, hese ai s a e ep esen ed by in ege alues. Based Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 5/26 on Flache e al [21], we used 5 ea u es and 15 possible ai s pe ea u e. An agen acan be ep esen ed as ollows: [2,4,12,9,14], in which a e e s o he ai on ea u e o agen a. 2. Ins i u ional eposi o ies: Each ins i u ion is a second laye "agen " ha ep esen s a belie space. I is deno ed by a s ing o ea u es and hei ai exhibi s a e based on in ege alues, exac ly as indi idual agen s. Howe e , unlike indi idual agen s, ins i u ions a e no a ached o a g id and hey also can ha e emp y ea u es ( ea u es wi hou an assigned ai ), in e nally ep esen ed wi h -1. An agen acan only belong o one ins i u ion a a ime, deno ed i a , and i ollows ha i a will ep esen he ai o ea u e o a's ins i u ion. E e y indi idual agen is ini ially associa ed wi h an ins i u ion wi h all emp y ea u es. The agen can hen, in in e - ac ion and ag eemen wi h ano he agen , o e w i e one ea u e. An agen can also swi ch hei ins i u ional associa ion o be associa ed wi h a di e en ins i u ion ins ead. 3. G id en i onmen : Agen s a e a anged on a wo-dimensional la ice. We ollow Flache e al [21] in selec ing h ee a ying sizes o he la ice, 10x10, 32x32, and 100x100, making up wo ld popula ions o 100, 1024 and 10000 agen s. Al hough human popula ions a e gene - ally much bigge , 10000 agen s can be a ep esen a ion o a own, o , acco ding o Axel od [5], each one agen can be ep esen a i e o one illage. By s udying di e en sizes, we can obse e whe he ou pa e ns will s ay consis en ac oss a ious popula ion sizes (bigge popula ions han 10000 agen s we e di icul o s udy due o high compu a ional demands). Neighbo hoods a e de ined as he a eas wi hin which agen s can in e ac . We de ine a Von Neumann neighbo hood wi hin a dis ance o 6, meaning each agen can in e ac wi h a maximum o 84 agen s (Fig 2). The en i onmen is ep esen ed as a non- o oidal wo ld, so agen s ha e ewe neighbo s when hey a e close o he bo de s. Agen s ha sha e he exac same ai combina ion on all hei ea u es and a e loca ed nex o each o he in he g id a e conside ed o be o he same cul u e. All agen s ha belong o he same cul u e de e mine a "cul u al egion". Di e - si y is de ined as a leas wo exis ing ai a ia ions, e.g. cul u al egions, exis ing a he same ime. Anomie indica es ha he e a e as many cul u al egions as he e a e agen s; con e sely, comple e globaliza ion deno es ha he e is only one cul u al egion. Fig 2. Two possible on Neumann neighbou hoods wi h dis ance 6. Two example neighbou hoods on a 15x15 g id. Le : cen al agen (da k blue) wi h 84 neighbou ing agen s (ligh blue) ha i can in e ac wi h. Righ : bo de agen (da k blue) wi h 27 neighbou ing agen s (ligh blue). doi:10.1371/jou nal.pone.0153334.g002 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 6/26 4. Rules: The model in eg a es dynamical ules which allow agen s o in e ac based on p oba- bili ies associa ed o cul u al simila i y. Cul u al simila i y is he numbe o cul u al ai s ha a e equi alen on wo ec o s o agen s o ins i u ions. The e a e h ee ypes o p obabili ies wo king in he model: (1) agen simila i y, which is he simila i y be ween wo agen s (i.e. homophily); (2) in e nal ins i u ional simila i y, which exis s be ween an agen and i s own ins i u ion, and (3) ex e nal ins i u ion simila i y, which exis s be ween an agen and he ins i u ion o a neighbo . Ins i u ions impac agen in e ac ions based on hese cul u al simila i ies, and based on wo ac o s: ins i u ional in luence and agen loyal y. Agen s impac ins i u ions when hey c ea e ins i u ions, o when hey join an exis ing ins i u ion and he ins i u ion’s "ac i e ea u e" is emp y. An "ac i e ea u e" deno es he one pa icula ea u e ha is being discussed when wo agen s in e ac . Table 1 p esen s an o e iew o e he mos impo an ules ha we a e including in ou simula ions, and he combina ions in which hey we e implemen ed in p e ious esea ch. Fi s ly, Axel od's o iginal model [5] gene a ed cul u al di e si y by using homophily o eg- ula e dyadic social in luence. Secondly, Klemm e al [24] showed ha a ious a es o mu a- ions des abilize Axel od's cul u al di e si y, wi h low a es con e ging he model in o monocul u e while highe a es led o anomie. Finally, Flache e al [21] in oduced mul ila e al social in luence o Axel od's homophily (based on wo k by Pa isi e al [20]). We a e adop ing he same concep ualiza ion o social in luence (di ec ed by homophily) as Axel od [5]. Homophily o agen s aand nde e mines whe he an in e ac ion occu s o no , based on he numbe o equi alen ai s in bo h agen s, so we can use he ollowing unc ion o simila i y (Sim(a,n)) o calcula e he homophily be ween agen s: Simða;nÞ¼1 FX F ¼1 dða ;n Þð1Þ He e, Fis he o al amoun o ea u es and he δ(i,j) unc ion e e s o he K ockene del a: dði;jÞ¼ 1i¼j 0i6¼ j (ð2Þ We will concep ualize noise in he same way Flache e al [21] did: an ins ance o mu a ion [23] occu s when he ai o an agen , a e a possible in e ac ion, is andomly selec ed and se o a new ea u e. A mu a ion occu s wi h p obabili y m. An ins ance o selec ion e o [21] occu s a e he ini ial in e ac ion ou come has been decided based on homophily, and i e e ses he ini ial decision o in e ac (o no ). A selec ion e o occu s wi h p obabili y s.In o de o simpli y he s udy we will keep m=sac oss all he expe imen s, as Flache e al [21] did. Table 1. O e iew o e p e ious models and hei included pa ame e s, and ou model. Model Homophily Pe u ba ion Mu a ion Pe u ba ion Selec ion E o Mul ila e al Social Influence Ins i u ions Axel od 1997 Yes No No No No Klemm 2003 Yes Yes No No No Flache 2011 Yes Yes Yes Yes No Ou s Yes Yes Yes No Yes The fi s column iden ifies models by au ho . The second o six h column indica e di e en ules ha ha e been es ed in he di e en models. doi:10.1371/jou nal.pone.0153334. 001 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 7/26 We also decided o in eg a e he selec ion e o in o he homophily ule, esul ing in one o mula, which we call Pe cei ed Homophily (PH(a,n)): PHða;nÞ¼ð1sÞSimða;nÞþsð1Simða;nÞð3Þ Ou Pe cei ed Homophily ule is equi alen o Flache e al's app oach o applying homo- phily i s , and selec ion e o second [21]. Finally, ou esponse a iable will be he numbe o cul u al egions emaining a e he inal agen in e ac ion i e a ion. We decided on a di e en esponse a iable han Flache e al [21] due o he di e en ou comes ha we a e analyzing. Flache e al used he "no malized size o he la ges egion" in o de o obse e how noise a ec s he endency owa ds a monocul u e o globaliza ion in a sys em, wi h he assump ion ha his measu e does e lec di e si y, wi h- ou he need o explici ly s a e he numbe o cul u es. We ha e chosen o examine he numbe o cul u es, since we a e in e es ed in cul u al di e si y pe se as i eme ges and is p ese ed by manipula ion o di e en ins i u ional ac o s, so ou measu e is mo e i ing and exp essi e o ou pu poses. I will be no malized h ough di ision by he o al numbe o agen s (deno ed N) in he gi en simula ion, o bes showcase simila i ies ac oss di e en popula ion sizes. esponse a iable ¼ o al numbe o cul u al egions Nð4Þ Fo a compa ison o he wo esponse a iables in ques ion and how hey a ec ou esul s, please e e o S6 File. Baseline: Models o ins i u ional in luence and loyal y The main pu pose o ou in es iga ion o ins i u ions is hei impac on cul u al pa e ns e lec ed in Axel od’s model o dyadic social in luence. Fo ou baseline model we in eg a e ins i u ional in luence in o ou combina ion o dyadic social in luence wi h homophily [5], mu a ion [23,24], and selec ion e o [21]. Fo his in en , we use he ins i u ional in luence unc ion (In (a,n)): In ða;nÞ¼ aSimða;iaÞ ð1aÞSimða;nÞþ aSimða;iaÞ;whe e a½0;1ð5Þ Ins i u ional in luence is exe ed as a combina ion o agen simila i y, (Sim(a,n)) and ins i- u ional simila i y Sim(a,i a ),. We de ine ins i u ional simila i y in he same way as he o iginal homophily o mula o simila i y. As he o mula exp esses, he p obabili y o ai change dec eases as he agen ’s simila i y o i s own ins i u ion inc eases. Mo eo e , he alpha pa ame- e (α) con ols he amoun o ins i u ional in luence. This same alue is applied o all he agen s in he simula ion. The bigge he α, he mo e impo ance agen s gi e o hei ins i u- ions, and he e o e he less likely i is ha a ai change will occu . Ins i u ional in luence, In (a,n), is applied only when he e is an ins i u ional con lic , i.e. a si ua ion in which he agen acu en ly holds he same ai as i s own ins i u ion, i a , bu he "ac i e ai " (i.e. he agen ’s o-be-adop ed ai by social in luence) is di e en om he ai ha he ins i u ion i a holds. The agen is "being emp ed" in o dissimila i y om i s own ins i- u ion, and he ins i u ion is exe ing i s in luence o s op his om happening. In he case whe e he e is no ins i u ional con lic , he o mula o Pe cei ed Homophily PH(a,n) is used ins ead, and no ins i u ional in luence is exe ed. Because o cons an in e ac ions wi h neighbo s, an agen ’s cul u al ec o can u n ou o be mo e simila o i s neighbo ’s ins i u ion han i s own. In his case, a e he in e ac ion wi h i s neighbo , he agen checks i a change o ins i u ions is a ou able. We de e mine whe he Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 8/26 an agen awill emain loyal o i s own ins i u ion i a when con on ed wi h he ins i u ion i a o he neighbo nby applying he agen loyal y unc ion Loy(a,n): Loyða;nÞ¼ a0Simða;iaÞ ð1a0ÞSimða;inÞþ a0Simða;iaÞ;whe e a0½0;1ð6Þ The α'pa ame e con ols he agen 's loyal y o i s cu en ins i u ion and applies iden ically o all agen s: he highe he α'pa ame e , he highe he agen 's loyal y owa ds i s o iginal ins i- u ion, and he less likely an ins i u ional change. We in oduce he agen ’s simila i y o he neighbo ’s ins i u ion, Sim(a,i n ), in o he denomina o 's unc ion, so ha he p obabili y o ins i u ional change inc eases as he agen ’s simila i y o i s neighbou ’s ins i u ion inc eases. Ex ensions: Models o e e enda and p opaganda A e in es iga ing he s abili y and di e si y alues o ou baseline model, we will in es iga e he in luence p ocesses be ween agen s and ins i u ions in wo ways. The i s ex ension is a bo om-up p ocess ha esembles a democ a ic p ocess, e.g. a e e - endum. Agen s can in luence hei ins i u ions wi h he in en ion o aligning he ins i u ion owa ds he agen s' ai s. When many indi iduals in a popula ion mani es disag eemen wi h hei ins i u ion’s cu en s ance on a pa icula issue, hey can o ce he ins i u ion o change owa ds he popula opinion. In ou model, we adop his ex ension by selec ing one ins i u- ional ai ha is he leas popula among he gi en popula ion a he ime; hen we allow agen s o “ o e” o change i o ha ai which he majo i y app o es. We can con ol he p e - alence o democ acy by speci ying he numbe (X) o in e ac ion oppo uni ies ha each agen has wi h ano he agen be o e hey a e allowed o ac oge he in a o ing p ocess. This is called he equency o democ acy, d, and i is he ecip ocal o X, i.e. 1/X. The second ex ension is a op-down p ocess ha esembles a p opaganda campaign o an ins i u ion, by way o dissemina ion o i s cul u al ai s wi h he in en ion o aligning mo e o he agen s' ai s owa ds i sel . In ou model, we adop his ex ension by allowing he ins i u- ion o y and push i s ai s on o each o i s a ilia ed agen s. Whe he an agen allows he p o- paganda o change i s ai depends on how simila his agen aal eady is o i s own ins i u ion, i.e. Sim(a,i a ). We con ol he p e alence o p opaganda he same way we did o democ acy, i.e. by a ce ain numbe (Y) o in e ac ion oppo uni ies be ween agen s, and de ine he e- quency o p opaganda, p,as he ecip ocal o Y, i.e. 1/Y. We will also combine he wo ex ensions in ou las model o analyze he esul s o a combi- na ion o bo h bo om-up and op-down p ocesses oge he , in he o m o a eedback loop o ins i u ional in luence. We summa ize all o mal ules which we a e adop ing o ou six model a ia ions in Table 2. Rules a e cons uc ed based on Axel od's model (A), o which we add ou baseline (B, ins i u ional in luence and agen loyal y), and which we hen ex end by adding a democ a ic p ocess (D, e.g. a e e endum), o a p opaganda p ocess (P, e.g. ad e isemen campaigns), o bo h combined. Expe imen al Design We a e explo ing he e ec s o ins i u ional in luence and agen loyal y, and compa ing some esul s wi h Axel od and Flache e al by eplica ing hei models wi h ou code. We a e also in eg a ing democ a ic p ocesses, p opaganda p ocesses, o bo h oge he in o simula ions. We a e he e o e p esen ing he esul s o six di e en expe imen s, called expe imen s A o F. Fo all six expe imen s, we hold ce ain ac o s cons an . Resul s a e p esen ed ac oss he h ee cho- sen popula ion sizes (10x10, 32x32, 100x100), and o six chosen le els o noise (10 -n , whe e e Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 9/26 suppo o his pos -hoc hypo hesis. The al e na i e hypo hesis, i.e. ha he size o he popula- ion is he explana o y ac o , is no suppo ed by Expe imen A, as ou da a shows ha popula ion size had no s ong e ec s in any o he simula ions. Howe e , expe imen s ha spe- ci ically add ess his hypo hesis will be necessa y o expand on ou indings. We ound ha , in ou models, he no malized numbe o cul u al egions was p opo ional o he popula ion (when α/α'is held cons an ) which sugges s ha ou esul s a e scalable, i.e. he esul s hold ega dless he popula ion size. Consequen ly, he e is a linea end o he absolu e numbe o cul u al egions, whe e he bigge he popula ion, he mo e cul u es eme ge. This implies ha he size o he cul u al egions (i.e. numbe o agen s pe cul u al egion on a e age) is simila ac oss popula ions, bu changes o each model h ough he gi en αand α' alues. Thus, an al e na i e in e p e a ion o ou esul s is ha he addi ion o s ong ins i u ions o he simula ion impac ed he size, no he numbe , o he cul u al egions ha eme ged in he sys em. Ou model he e eplica es he e e sal beha iou o Axel od's p e ious inding ( ha numbe o cul u es dec eases wi h inc easing popula ion size, p.219 in [5]), which had p e iously also been add essed and discussed by Flache e al (p.984 in [21]). Las ly, ou esul s in Table 4 show ha , gene ally speaking, mo e cul u es han ins i u ions eme ged in ou models. This means ha e en unde he in luence o one ins i u ion, mul iple agen s can all belong o di e en cul u es and hose cul u es can su i e. In o he wo ds, an ins i u ion can allow he simul aneous exis ence o se e al cul u es. This esul is consis en wi h Shibanai e al [18], in which mass media, as a globally ac ing en i y, was also ound o p o- mo e he eme gence o cul u al di e si y. So a , ou models suppo he idea ha ins i u ional in luence can be used o con ol cul- u al di e si y. In he ollowing expe imen s D o F, we will now ex end ou s udy o ins i u- ions o include wo mechanisms o in luence used by and on ins i u ions: democ acy and p opaganda. Sec ion 2: Expe imen D o F In his second se o expe imen s, we show how wo di ec ions o ins i u ional in luence a ec he sys em: bo om-up (democ acy) and op-down (p opaganda). We explo e how hey impac cul u al egions and ins i u ion numbe s when we apply he in luence-loyal y model om expe imen C, i.e. model alues o 10x10/0.85/0.5, 32x32/0.8/0.5 and 100x100/0.75/0.5. Expe imen D: Ra e and equen democ a ic p ocesses. In ou democ a ic model, we manipula ed he equency a which democ a ic p ocesses ( e e enda) occu in a sys em. We de ined a uni o ime as equi alen o he numbe o i e a ions necessa y o ha e one i e a ion on a e age pe agen , i.e. a uni o ime is equi alen o 100 i e a ions in 10x10; 1024 in 32x32; and 10000 in 100x100. Then, a pe iod is he du a ion o ime be ween e en s. Fo example, a pe iod o 10, i.e. a equency o 1/10, means ha he e e enda occu a e an a e age o 10 i e - a ions pe agen . We ha e se he equency in exponen ial dec emen s o 1/10 (high democ- acy), 1/100 (mode a e democ acy) and 1/1000 (low democ acy), in o de o s udy a b oad spec um o possible alues. As can be seen in Fig 6, in a model whe e democ a ic p ocesses a e allowed, cul u al di e - si y was sus ained, bu i was s ongly educed compa ed o he p e ious baseline o di e si y ha we achie ed in expe imen A. This was he case a all h ee equencies o democ acy and all popula ion sizes. Addi ionally, o he 10x10 popula ion, he lowe he democ acy, he highe he di e si y, when noise <= 0.01, wi h F(2, 735) = 48.806, p <0.0001. Fo popula ions >= 32x32 his e ec was non-mono onous. The lowes amoun o di e si y was eached by allowing mode a e democ acy (1/100). The di e ence was signi ican when compa ed o low democ acy (1/1000) when noise <= 0.01, wi h F(1, 980) = 259.595, p <0.0001, as well as Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 16 / 26 compa ed o high democ acy (1/10), wi h F(1,980) = 181.324, p <0.0001 when noise <= 0.01. We p esen he esul s wi h noise <= 0.01 o a oid he ex eme e ec wi h noise = 0.1 obse ed in he igu e, al hough ha e ec is consis en wi h ou esul s. Fo u he de ails on he pe - o med ANOVA calcula ions, please e e o S3 File. Wi h ega ds o obus ness, he sys em wi h added democ acy u ned somewha uns able om a noise le el o 0.01 onwa ds; a noise equals o 0.1, a s a e o anomie was eached o low democ acy in 100x100, o medium democ acy in 32x32 and 100x100, and o high democ acy in all popula ion sizes. Thus, an explo a ion o e en mo e equen democ a ic p ocesses was deemed unnecessa y; he esul s indica ed ha highe le els o democ acy would only u he des abilize ou model agains noise. Expe imen E: Ra e and equen p opaganda p ocesses. Jus as wi h democ acy in expe imen D, in ou model wi h p opaganda, we manipula ed he equency a which p opa- ganda p ocesses occu in a sys em. When one looks a he occu ence o hese wo poli ical ools, one inds ha e e enda a e, in eali y, a e (p.76 in [44]), whe eas ins ances o p opa- ganda a e qui e common and equen ly encoun e ed [45], so his ime, we used highe e- quencies o 1/1, 1/3 and 1/5. When we a emp ed a e equencies o p opaganda in an ea lie explo a o y analysis, aligned wi h ou p edic ions, once p opaganda becomes oo a e, e ec s become indisce nible. As can be seen in Fig 7, ou model wi h p opaganda gene a ed many co-exis ing cul u al egions, i.e. in gene al, mo e p opaganda led o mo e di e si y. The only excep ion o his e ec was ound a he highes alue o noise (0.1). A his le el o noise, i was he a e le el o p o- paganda (1/5) which yielded mo e di e si y han he mode a e le el (1/3). In e ms o esilience agains noise, p opaganda was able o s abilize he sys em e en a he highes le els o noise (0.1). Howe e , we ound no iceable a ia ions o di e si y o he chosen equencies o p opaganda unde highe le els o noise. Fo example, he e was a endency o Fig 6. Cul u al di e si y o di e en equencies o democ acy. X-axis displays le els o noise; Y-axis displays no malized cul u al di e si y. Each colo ed line symbol deno es one equency o democ acy, om low (ligh blue) o high (da k blue). 95% con idence in e als a e displayed only when exceeding he size o he line symbol. Da a poin s a e a e ages o 50 epe i ions pe e i o y wi h 100,000 i e a ions pe agen . doi:10.1371/jou nal.pone.0153334.g006 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 17 / 26 monocul u e, i.e. di e si y was educed signi ican ly a noise le els = 0.01 and 0.1 and when p o- paganda was a e o medium equen . This is a clea depa u e om he beha io o ou p e i- ous models, whe e we so a ended o obse e a con e gence o anomie, which is be e subs an ia ed heo e ically (as he highes possible noise alue (1.0) can be equa ed wi h anomie). Expe imen F: Re e endum + P opaganda. Ou inal expe imen explo ed wha e ec s he combina ion o he wo s udied p ocess in expe imen s D and E, democ acy and p opa- ganda, would ha e on he di e si y in ou sys em. We combined he wo p ocesses, gene a ing a eedback loop o in o ma ion ha lows om indi idual o ins i u ions (democ acy) and ice e sa (p opaganda), so ha ins i u ional in luence could un in bo h di ec ions. This idea has been implici ly p oposed in p e ious ins i u ional esea ch [35]. We manipula ed he equency a which bo h hese p ocesses occu in a sys em wi h he same alues as we explo ed be o e, so o p opaganda, we applied i on a e age e e y 1/1, 1/3 and 1/5 o in e ac ions, while o democ acy, we chose o apply i a equency le els o 1/10, 1/100 and 1/1000; in he ollowing g aph (Fig 8), we omi ed medium democ acy (1/100) o b e i y and eadabili y, as i did no add addi ional in o ma ion, i.e. i ollowed he p e ailing end desc ibed below. Fo he g aph including medium democ acy, please e e o S8 File. In ou eedback loop o ins i u ional in luence, he main e ec s o p opaganda and democ- acy we e pa ly con i med om p e ious expe imen s: high le els o democ acy s ill p oduced less di e si y han baseline alues ha we ob ained in expe imen C (black lines in Fig 8), and also signi ican ly less han low democ acy, simila o expe imen D. Fu he mo e, when we analyzed e ec s o p opaganda in e ac ing only wi h low democ acy, p opaganda held a posi- i e ela ionship wi h di e si y, i.e. he mo e p opaganda, he mo e cul u al egions, jus as was he case in expe imen E. The e ec s a e mo e di icul o disce n o common democ a ic p ocesses (1/10). Fo noise le els <= 0.001, di e ences in di e si y a e small, and o noise le els >= 0.01, he model Fig 7. Cul u al di e si y o di e en equencies o p opaganda. X-axis displays le els o noise; Y-axis displays no malized cul u al di e si y. Each line symbol deno es one equency o p opaganda, om low (ligh ed) o high (da k ed). 95% con idence in e als a e displayed only when exceeding he size o he line symbol. Da a poin s a e a e ages o 50 epe i ions pe e i o y wi h 100,000 i e a ions pe agen . doi:10.1371/jou nal.pone.0153334.g007 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 18 / 26 u ns e y sensi i e o p opaganda. The in e ac ion o democ acy and p opaganda o noise le els <= 0.00001, howe e , signi ican ly impac s di e si y. In his si ua ion, he way p opa- ganda impac s di e si y was e e sed, i.e. a sys em wi h high p opaganda and high democ acy p oduced less di e si y, while less p opaganda in a s a e o high democ acy p oduced mo e cul- u al egions. This e ec is only ma ginally isible in Fig 8, bu s a is ically, we ound a signi i- can di e ence o popula ions >= 32x32, wi h F(2, 588) = 142.552, p <0.0001. Fu he de ails ega ding ou calcula ions can be ound unde S4 File. Finally, we would also like o p esen some da a wi h ega ds o he numbe s o ins i u ions o his las expe imen . Da a and igu es illus a ing ins i u ional numbe s om expe imen s A, C, D and E can be ound unde S7 File. We p e iously indica ed in Table 4 ha he numbe o ins i u ions is gene ally smalle han he numbe o cul u es ac oss all ou models. As illus a ed in Fig 9, in his combined model, bo h democ acy and p opaganda inc eased he numbe o ins i u ions when compa ed o he baseline. Democ acy had he s onge e ec . These e ec s we e quali a i ely simila o a sepa- a e analysis o democ acy (Figu e C in S7 File), and p opaganda (Figu e D in S7 File), bu somewha less ex eme in hei indi idual applica ions, i.e. numbe s o ins i u ions ended o be smalle han shown he e. In pa icula o high le els o democ acy, he numbe o ins i u- ions inc eased such, ha i was highe han he esul ing numbe o cul u al egions, i.e. one cul u al egion could be go e ned by mul iple di e en ins i u ions. Discussion Expe imen D o F. Al hough he goal o democ acy and p opaganda is he same; i.e. o inc ease simila i y be ween agen s and ins i u ions in o de o each o exe mo e in luence on he o he , he impac o he wo p ocesses on cul u al di e si y was ound o be opposi e. Gene ally speaking, equen democ a ic p ocesses led o ewe , la ge cul u al egions (as shown in expe imen D), while equen p opaganda led o mo e, smalle cul u al egions (as shown in expe imen E). Ou esul s also e lec in ui i e assump ions abou hese Fig 8. Cul u al di e si y o combina ions o democ acy and p opaganda equencies. X-axis displays le els o noise; Y-axis displays no malized cul u al di e si y. Each line symbol deno es one combina ion o democ acy and p opaganda. 95% con idence in e als a e displayed only when exceeding he size o he line symbol. Da a poin s a e a e ages o 50 epe i ions pe e i o y wi h 100,000 i e a ions pe agen . doi:10.1371/jou nal.pone.0153334.g008 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 19 / 26 p ocesses: p opaganda needs o be common o succeed, so a e equencies did no p oduce any ele an esul s; e e enda a e a e , and we ound ha he sys em des abilized mo e quickly when hey we e pe mi ed oo equen ly. When bo h ins i u ional in luence p ocesses a e combined, we ound ha he esul s obse ed in expe imen s D and E we e ein o ced, excep in a s a e o high democ acy, whe e highe equencies o p opaganda induced a mo e homogenous s a e in he popula ion. Wi h ega ds o ins i u ional numbe s, we ound ha ha hey inc eased in he p esence o democ acy and p opaganda. One possible explana ion o his inc ease is ha he eedback loop o ins i u ional in luence ha exis s in ou model allows o a mo e consis en exchange o in o ma ion be ween agen s and ins i u ions, so ha he numbe s o cul u es and ins i u ions con e ge mo e. Addi ionally, we ound ha equen democ a ic p ocesses inc eased he num- be o ins i u ions e en mo e; in ac , o models wi h high democ acy we ound ha he e we e mo e ins i u ions han cul u es. This is he case when one cul u e is spli in o egions ha each ha e i s own ins i u ion, bu a e cul u ally iden ical. In his si ua ion, a numbe o agen s who belong o he same cul u e each subsc ibe o a di e en ins i u ion. I is impo an o highligh ha by using di e en combina ions o p opaganda and democ- acy, we a e able o con ol mos o he cul u al di e si y spec um. Se e al combina ions p o e e y success ul a p ese ing di e si y wi hou des abilizing he sys em (i.e. no esul ing in ex emes such as anomie o global con e gence), e en when he noise is se a i s highes le el. Gene al Discussion O e he cou se o six expe imen s, we explo ed he e ec s o ins i u ions on cul u al di e si y. We ound ha ou model o ins i u ional in luence and agen loyal y compa e well agains p e- ious models p oposed by Axel od [5] and Flache e al [21]: high le els o ins i u ional in lu- ence success ully p omo ed di e si y and sus ained i agains pe u ba ions in ou sys em, and Fig 9. Numbe o ins i u ions o combina ions o democ acy and p opaganda equencies. X-axis displays le els o noise; Y-axis displays no malized numbe s o ins i u ions. Each line symbol deno es one combina ion o democ acy and p opaganda. 95% con idence in e als a e displayed only when exceeding he size o he line symbol. Da a poin s a e a e ages o 50 epe i ions pe e i o y wi h 100,000 i e a ions pe agen . doi:10.1371/jou nal.pone.0153334.g009 Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 20 / 26 he agen s' loyal y helped p ese e his di e si y, hough i did no u he inc ease o impac i in any signi ican way. The p omo ion o di e si y can be unde s ood i we look a he mechanism o ins i u ional in luence. The mo e an ins i u ion a ec s indi iduals' li es, he mo e i con ols in e ac ions be ween people, hei ai s and alues, and how hey socially in luence each o he . S ong ins i- u ions can keep people o one cul u al belie sys em om associa ing wi h people om o he cul u es, which leads o isola ion and educes assimila ion. This becomes pa icula ly e iden when we conside socie ies in which amilial uni s play a e y s ong in luencing ins i u ional ole: in cases whe e his is ue, people a e much less likely o in e ac abou cul u al belie s wi h o he " i al" amilies, o ake on he cul u al belie s o s ange s; ins ead, dis us owa ds he gene al public, poli ical and social isola ion and sel ishness owa ds ou g oups a e ound o be p edominan [46,47]. Aside om simple ins i u ional in luence, he second goal o ou esea ch was o in es iga e how indi iduals' powe o change hei ins i u ions a ec s he wo ld in which hey li e, and wha happens when ins i u ions a emp o di ec ly con ince hei membe s o e-adop mo e adi ional ai s, e en when hose membe s migh ha e been emp ed away owa ds new belie s. To s udy his, we implemen ed bo om-up and op-down ins i u ional in luence p o- cesses. He e, we ound ha democ acy (bo om-up in luence) p omo ed global con e gence, whe eas p opaganda ( op-down in luence) by i sel boos ed di e si y. A possible explana ion o his di e gen esul can be ound in he sou ce o ins i u ional ai s. In bo h cases, agen s a e he ini ia o s o ins i u ions. Howe e , in he p opaganda model, ins i u ions a e c ea ed, and hen hey p ese e hei con igu a ion, hey a e ixed. "Old" ai s a e kep in he sys em, e en when agen s change owa ds mo e popula cul u al opinion (due o in e ac ions wi h neighbou s). The ai s ha a e s o ed in he ins i u ions can be eused o in luence agen s once again h ough p opaganda. This way, many small pocke s o cul u al egions can eme ge and e-eme ge. Ins i u ions' ai s in he democ acy model do no s ay ixed. They a e modi ied when agen s a e in luenced by in e ac ions wi h hei neighbou s, i.e. ins i u ions a e upda ed wi h he mo e ecen , popula ai s as old ai s a e abandoned by hei agen s. These new ai s ha e success- ully sp ead h ough he popula ion and a e con e ging agen s' cul u es. A bo om-up p ocess gene a es he possibili y ha hese new ai s pe mea e he ins i u ions as well, and ins i u ions in u n can help o p ese e hese ai s in he u u e. This way, less di e se, la ge cul u al egions eme ge. In ou inal model, in which we in eg a ed bo h bo om-up and op-down in luence in a eedback loop o in o ma ion, we eplica ed he main e ec o democ acy, and he main e ec o p opaganda unde low democ acy. Addi ionally, we ound an in e ac ion in which he inclu- sion o high le els o democ acy led o a e e sal o p opaganda e ec s: now, lowe le els o p opaganda inc eased di e si y, while highe le els o p opaganda educed he amoun o di e si y in he sys em. Conside ing he p e ious explana ions o he o igins o ins i u ional ai s, we ound a simila logic ope a ing behind his in e ac ion: i ins i u ions can be modi ied owa ds he ai s ha a e popula ized ac oss cul u es (which hen end o con e gence), he ins i u ions' p opaganda hen does no e e se agen s' ai s back o 'olde ' alues; hey ins ead now help sp ead he new ideas ha a e g owing popula in he popula ion h ough p opa- ganda, and i hese p opaganda p ocesses a e e y equen , hey homogenize he popula ion e en mo e han be o e. Measu ing amoun s o cul u al di e si y and equencies o he men ioned ins i u ional p o- cesses (such as how much democ a ic powe people exe and how much p opaganda exis s) is e y di icul in eal socie ies. One a emp o apply ou ideas can be o look a how cul u al di e si y is commonly pe cei ed ac oss he wo ld. Fo example, we ind a highly agmen ed Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 21 / 26 landscape wi h many small, di e se cul u al pocke s ac oss he A ican con inen (i.e. Chad alone holds a ound 100 dis inc e hnic g oups), which ends o also be low in democ acy and high in p opaganda, compa ed o o example a Wes e n Eu opean poli ical landscape which is mo e democ a ic, and a guably less di e se (i.e. we commonly use he e m "Wes e n cul u e" o desc ibe many ea u es ha a e iden ical ac oss i ) [48,49]. One conc e e " ai " ha can be men ioned, which is sp eading ac oss al eady ai ly simila cul u al egions h ough democ acy and p opaganda, and which is u ning hose egions mo e simila , is ma iage equali y; he idea o ole ance owa ds sexual o ien a ions has been expand- ing ac oss he Wes e n wo ld in ecen yea s, wi h mul iple e e enda being held on he opic [50–52]. This mo emen , in u n, has been aken up by he media, is popula ized u he h ough posi i e ins i u ional po ayals o ole ance (such as in school cu iculums), and has success ully led o new, mo e inclusi e laws in some coun ies. This s ands in s a k con as o many smalle , au oc a ically go e ned a eas ac oss he wo ld whe e homosexuali y is ea ed e y di e en ly, anging om os acism o e c iminaliza ion o punishmen by dea h penal y [53]. This inding is eminiscen o Flache's hypo hesis ha maybe, i onically, con o mis cul- u es a e able o sus ain mo e di e si y han indi idualis ic ones (p.990 in [21]), and ha no all cases o pe sis en di e si y a e necessa ily posi i e, as some imes hey can be a disguise o xenophobic and os acizing, disc imina i e endencies [21,54,55]. Limi a ions and u he esea ch We ha e subs an ially ex ended he cu en line o esea ch on cul u al di e si y on a heo e i- cal le el by inco po a ing cen al au ho i ies, i.e. ins i u ions, o he i s ime, and by p o id- ing a sys em which, o u u e esea ch, will acili a e con olling he ull spec um o possible di e si y le els. Howe e , h ee o ou indings in pa icula will need o be cla i ied by u he esea ch. Fi s ly, we only ound a small e ec o agen loyal y; i was able o p ese e di e si y bu no inc ease i . We assume he main eason o he small size o he e ec is ha an agen 's change o ins i u ions is dependen on he p obabili y o i changing i s ai i s . We added his assump ion o he model because we pe cei ed ha ealis ically, i is unlikely ha a pe son will change hei ins i u ional a ilia ion o ha o hei neighbo i he neighbo did no con ince hem o hei cul u al ai in he i s place. Fu he esea ch in o he agen loyal y pa ame e when i is concep ualized as independen o ins i u ional in luence should cla i y i i will indeed s ay a small e ec o ha e a bigge impac in i s own igh . Secondly, we didn' ind a clea ela ionship be ween he numbe o ins i u ions and he numbe o cul u al egions (Expe imen F, Fig 9); in some cases hey we e mo e cul u al egions han ins i u ions, bu in o he cases, he e e se was ue. In eal li e se ings, bo h op ions a e possible: one cul u al egion can be go e ned by mul iple ins i u ions, and one ins i u ion go e n mul iple cul u es, howe e , we canno be su e how his impac s di e si y. F om ou esul s, we hypo hesize ha a i icially manipula ing he numbe o ins i u ions would no consis en ly change he esul ing di e si y (in ei he di ec ion), bu his should be cla i ied in u he s udies. Thi dly, he ques ion emains how cul u al di e si y can be sus ained e en when ins i u ions a e pe mea ed by no el ideas ha a e gaining app o al in he popula ion (i.e. unde democ- acy). We hypo hesize ha democ a ic ins i u ions s ill exe enough in luence o slow down cul u al d i pa e ns ha would o he wise lead o comple e monocul u e. Possibly, allowing in luences om o he cul u al egions o pe mea e ins i u ions is wha p omo es he he e es ab- lished le els o cul u al di e si y. Fu he esea ch should conside no only in es iga ing he Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 22 / 26 amoun o cul u al di e si y ha exis s in a sys em, bu also use a measu e o equency a which cul u al change has occu ed inside hose cul u al egions. We also conside impo an he in eg a ion o mul ila e al social in luence in o ou model o ins i u ions, which has been used p e iously o induce and main ain cul u al di e si y [20,21]. In his sense, u he esea ch can also conside he inclusion o new pa ame e s ha expands he condi ions in which he in e ac ions occu , o example he dis inc ion be ween no ma i e and in o ma ional social in luence [56], agen s' di e ing pe sonali ies (openness, desi e o con- ol [57,58]), si ua ional ac o s (such as cul u al esilience in he p esence o peace and wa , weal h and po e y [59,60]) o he possibili y o agen mobili y wi hin he sys em [15,16]. Finally, we ound ha li le esea ch has in es iga ed he pa e ns p esen ed he e in eal li e se ings as o ye . Field s udies and expe imen al esea ch on he impac s o ins i u ions on di e si y need o be ca ied ou in o de o es he p ac ical and empi ical ele ance o ou model's p edic ions. Suppo ing In o ma ion S1 File. Di e si y di e ences by popula ions. (PDF) S2 File. Di e si y di e ences by agen loyal y. (PDF) S3 File. Di e si y di e ences by democ acy. (PDF) S4 File. Di e si y di e ences by democ acy/p opaganda combined. (PDF) S5 File. S able s a es o equilib ium. (PDF) S6 File. Replica ion o Axel od/Flache's esul s. (PDF) S7 File. Numbe o ins i u ions. (PDF) S8 File. Comple e esul s Expe imen F (inclusion o democ acy 1/100). (PDF) Acknowledgmen s We would like o hank And eas Flache o his help ul explana ions o he o iginal implemen- a ion desc ibed in his a icle, on which we based ou code. We would also like o hank Liz Goldenbe g, Ca oline Kacpe ski and Isa Spi znagel, and he e iewe s o hei insigh ul com- men s on ea lie d a s o he manusc ip . Au ho Con ibu ions Concei ed and designed he expe imen s: RU CK FS. Pe o med he expe imen s: RU. Ana- lyzed he da a: RU CK. Con ibu ed eagen s/ma e ials/analysis ools: RU. W o e he pape : RU CK FS. Ins i u ions and Cul u al Di e si y PLOS ONE | DOI:10.1371/jou nal.pone.0153334 Ap il 8, 2016 23 / 26 Re e ences 1. James P. Globalism, Na ionalism, T ibalism: B inging Theo y Back in. Pine Fo ge P ess; 2006. 2. D’Angelo M, Vespe ini P, Eu ope C o . 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