Understanding opinions. A cognitive and formal account

Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Adv a nces in Complex Sy stems c  W orld Scien tific Publishing Compan y Understanding opinions. A cognitiv e and formal accoun t F rancesca Giardini Dep artment of Co gnitive Scie nc e, Centr a l Eur op ea n University, Budap est , Hungary, email: Giar diniF@c eu.hu ∗ Giar diniF@c eu.hu W alter Quattrocio cchi Dep artment of Mathematics and Computer Scienc es, University Of Siena, Italy † walter.quattrio c chi@unisi.it Rosaria Con te LABSS, CNR - Institute of Co gnit ive Sciences and T e chnolo gies, R ome, Italy ‡ r osaria.c onte@istc.cnr.i t Receiv ed (received date) Revised (revised dat e) The study of opinions, their formation and change, is one of the defining topics addressed b y social psyc hology , but in recen t years other dis ciplines, as computer science and complexit y , hav e addressed this cha llenge. Despite the flourishing of differen t mo dels and theories in both fields, several ke y questions still remain unanswered. The aim of this paper is to challenge the current theo ries on opinion by putting forward a cognitiv ely grounded mo del where opinions are desc rib ed as sp ecific men tal represen tations whose main properties are put forw ar d. A comparison with reputation will be also presen ted. Keywor ds : opinion dynamics; so cial influence; gossip; media; agend a-setting 1. In tro du ctio n Opinions represent a conspicuo us part of our mental re pr esentations. A large part of our so cia l time is spent in ex changing, ev aluating, r evising and compar ing our opinions. W e also say , abo ut many different issues, that w e have o pinions and we try to co nvince others ab out the gr oundedness o f our own o pinio ns. Since the b eginning of the last centu ry , so cia l psychologists hav e b een interested in understanding the sp ecificity of opinions, as c ompared to o ther kinds of men ta l repres entations, by fo- cusing their attent ion on the multiplicit y of dimensions, including attitudes, beliefs ∗ Cen tr al Eur opean Universit y , Hungary email: GiardiniF@ceu.h u † Unive rsity of Siena, Italy email: w alter.quattrio cc hi@unisi.it ‡ Labss-ISTC-CNR, Italy email: r osaria.cont e@istc.cnr.it 1 Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 2 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte and ev aluations, that ta ke pa rt within this phenomeno n. Also p olitical science has alwa ys been v er y attentiv e to what is cons idered as a wa y to measur e p eople’s pref- erences and belie fs ab out publicly re lev ant issues. Many o f these contributions ha ve bee n directed tow a rds under standing the so-calle d public opinion a nd the pro cesses through which it is p ossible to influence it, manipula ting p eo ple’s awareness and tendencies ([1 8]). Mo re re c ent ly , other disciplines hav e shown a g reat interest re- garding suc h an issue , rang ing from computer science passing thr ough so cio-physics ([7, 13]) up to complexity science ([19]). Despite the larg e amount of s tudies on opinions, the term itself and the un- derlying concept are p o orly sp ecified and to o genera l, since there a re at least tw o classes o f mental representations that can be ter med opinions but they differ with regar d to imp or tant asp ects. Moreover, relev a nt contributions coming fro m so cial psychology and computer science tr y to mo del distinct issues , thus making the analysis of opinions quite difficult. This la ck of so und theor etical contributions is often comp ensa ted by giving more preeminence to transmissio n and c o mmun ication pro cesses, thus par tia lly putting aside the ontological iss ue. In this work we pr o- po se a theoretical acc o unt in which, star ting from a critical revie w o f a pproaches coming from so cial psychology and computer scie nc e , the necessity of a co gnitive approach is claimed. Defining the sp ecific c o gnitive features that characteriz e an opinion, thus disting uishing it from o ther mental repre s entations, and intro ducing also tw o differ ent kinds of o pinions, ev aluative and factual, we will cla im for the necessity o f inv estig ating the men tal ro ots of o pinions, in order to understand how they are transformed and manipulated within and b etw een minds. This means that an opinion is sp ecific with reg ard to other mental representations, that has sp ecial features and is transfo r med thr o ugh spe c ific mental pr o cesses. Defining an opinion in ter ms of its mental ing redients p er mits to predict opinion change, its p ersis- tence, the effects of contrasting force s a nd a lternative paths of diffusion, b ecause the different forces are endo genously determined by sp ecific rules. Unders tanding opinions, describing how they are gener ated a nd revis e d, a nd how far e opinions trav el ov er the so cial space b oth as a consequence of so cial influence and as one of the main means throug h which s o cial influence unfolds, is c r ucial for gra sping a deep e r understanding of human so cial cognition a nd behaviors. Mo r eov er , our co g- nitive analysis is supported b y a preliminary formal description, in which a new to o l called Time V arying Gr aphs [8] is presented. This fo r malism has been developed to deal with dyna mically evolving systems[24, 23], a nd it allows to ov erco me some of the limitations impo s ed b y other instruments -e.g. metrics, formalis ms that are not suited to acco un t for a) the relatio nships be tw een o pinions and other epistemic representations and b) their dynamics b oth at s o cial a nd individual level. In sec- tion 2, a c ritical intro duction to some of the main contributions a b o ut o pinions is provided. Section 3 is devoted to the description of our mo del, in whic h a definition of o pinions as sp ecific mental r epresentations and cognitively founded hypo theses ab out their diffusio n and change will b e put forward. In section 4 a preliminary formal account of how opinions are generated and ho w they can change is pr ovided. Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Understanding opinions. A c o gnitiv e and formal ac c ount 3 In section 5 some conclusions are drawn and future directions are sugg ested. 2. A critique to exis ti ng approac hes The understa nding of o pinions requir e s to take into account tw o levels o f expla- nation: the individual and the so cial lev el. As mental representations, opinio ns are created within agent s’ minds and they need to b e in tegrated with the ex isting net- work of b eliefs, data, information, memor ies a nd ev aluations . How ever, in opinion change the so cia l influence plays a ma jor role and the shar edness o f a n opinion can heavily affect its p ersistence and resis tance to change. These tw o dimensions are tightly linked and their interpla y is one of the defining feature s of opinio ns, but so cial psychology and computer science are usually int erested in tackling only one of thes e tw o a sp ects, witho ut studying them in c o mbination. W e claim tha t developing a c o gnitive theory of opinions allows us to combine the micro- and the macro-level, understa nding how macro-s o cial pheno mena emerg e, unin ten tionally , from micro-elements and their interactions. In this wa y we can s e e that opinions derive from ag ents’ cognitive r epresentations and states but they also exist in the so cial space, in which they ar e transmitted and shared, and this so cial pro cess af- fects, in turn, individuals’ opinions. This complex lo op requires a non-reductionist approach in order to deal with b o th levels, without giving preeminence to one or the other. So cial psychology mainly fo cuses on the individual side, trying to describ e how opinions ar e genera ted within the mind, devoting m uch attention to define attitudes and ev aluations, but paying little attention to the so cially interactive dimension of opinions. On the o ther hand, sc holars fr om computer science and physics ha ve tr ie d to explain how different opinions can co exist or how they are mo dified through communication, treating opinions as mere o b jects that a re ex changed and rev is ed according to certain mec ha nisms that are quite far from the reality of cognitive a nd so cial pr o cesses. In b oth cases there is a reductionist fallacy that works in different wa ys but in b oth cases re sults in a downgrading of a co mplex issue in to either a set o f unrelated sp ecific elements or a unidimensiona l ob ject that is far from the complexity of a cog nitive representation. 2.1. So cial psycholo gy: individu alistic fal lacy So cial psyc hologists hav e de voted muc h attent ion to the s tudy of o pinions’ forma tion and s preading, but a c omprehensive and definite mo del allowing for an oper ational and genera tive account is still missing. Pr oviding a compr ehensive r e view of so cial psychology litera ture is b eyond the scop e of this work, but in this se c tio n we will discuss so me of the main theo ries in or der to underline ho w par tial is the pictur e of opinions emerging from these studies. In genera l, opinio ns are trea ted as syno nyms for different ment al ob jects, a s belie fs [21], or mor e frequen tly , attitudes. Opinions are o ften conceptualized as atti- tudes [20], [16], [22] or they a re used a s in ter changeable terms that hav e in common Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 4 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte the fact of b eing a ffected b y so c ial influence and p ersua sion [26]. It is worth no tic- ing that many con tr ibutions are sp ecifically oriented to understand ”public opinion” [14], a s the in teg ration o f opinio ns a nd a ttitudes coming from differen t sources and exp osed to differ ent kinds of influencing . Another gener al feature of the so cial psy- chology approa ch to opinions is the pree minence given to measuring opinions, rather than o n conceptualizing them. As a result, man y studies (for a review, see Sc hw arz N, Sudman S, eds. 1996. Answering Questions: Metho do logy fo r Determining Cog- nitive and Communicative P ro ceses s in Sur vey Research. San F rancisco: Jossey- Bass) trie d to develop reliable and fine- tuned w ays to mea sure p eople’s approa ches to gener al questions, partially aba ndoning the is sue of defining wha t an opinion is and focusing on how it should b e measured. Allpo r t [3] recog nize s the difference b etw een attitudes and opinions but he nonetheless consider s the measurement of o pinions as o ne wa y of identifying the strength and v alue of p er sonal attitudes. An a lternative view contrasts the affective conten t o f a ttitudes with the mor e cog nitiv e quality of opinions that inv olve some kind of conscious judgmen ts [12]. In g eneral, it is p os s ible to identif y t wo main trends in the relev ant literature: one more fo cus e d on attitudes and the other more centered on conscious reaso ning a nd judgmen t. Cr e spi [9] considers individual opinions as ” judgment al outcomes o f a n individua l’s transactions with the s urrounding world” (p.19), emphasizing the interpla y b etw een wha t he calls an attitudinal system a nd the external w o rld c haracter iz ed by the pre s ence of other agen ts a nd different sub- jective per ceptions. O pinions a re the outcomes of a judging pr o cess but this do es not mean that they are necessar ily ratio nal or reasoned, although Crespi recognizes that they need to b e consistent with the individua l’s b eliefs, v alues and affective states. As other authors alrea dy po inted out [1 ], many mo dels of opinio n a nd so cia l influence do not provide car e ful definitions of what an opinio n is and how it is af- fected by so cia l influence. This ha pp e ns to b e true also for theo r ies o f p er suasion, like the so cial impact theor y [17], a static theory of how so cial pro cess es op erate at the level o f the indiv idua l at a g iven p oint in time. Part of this theory has bee n developed us ing computational mo deling b y Nowak, Szamrej and Latan [2]. In their mo del, individuals change their attitudes a s a consequence of o ther indi- viduals’ influence. In pa rallel with the idea that so cia l influence is prop ortio na l to a multiplicativ e function of the strength, immediacy , and num b er of so ur ces in a so cial force field [17], [14] suggest that each a ttitude within a cognitive structure is joint ly determined b y the strength, immediacy , and num b er of linked attitudes as individua ls seek harmony , balance, or consistency a mong them. Althoug h very int eresting, this a ccount fails to distinguish betw een attitudes and beliefs a nd do es not ex plain how inco nsistencies can be resolved. The effect o f communication o n opinion formation has been addr essed b y different disciplines from within the s o cial and the computational sciences, as w ell as complex systems science (for a review on attitude change models, see [1]). One of the first works on this topic has focused on Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Understanding opinions. A c o gnitiv e and formal ac c ount 5 po larizatio n, i.e. the concentration of o pinions by means of interaction, as one main effect of the ”socia l influence” [11], whereas the So cia l Impact Theory’ [2] prop oses a mo re dy namic account, in which the amount of influence dep ends on the dista nc e , nu mber, a nd strength (i.e., p ers uasiveness) of influence sources. As stated in ([7 ]), an imp ortant v ar iable, p o orly controlled in c ur rent studies, is structure top olog y . Int eractions ar e inv ar iably assumed as either all- to-all or bas e d on a spatial reg ula r lo cation (lattice), while more realistic scenar ios a re ignored. Although v ery interesting, these studies fail to addr ess the sp ecificity of o pinions, treating them as generic mental ob jects that change as a conseque nce of so cial influence, as it happ ens als o to b eliefs, or even g oals. The question ab out what an opinion is and what its main features ar e re ma ins unanswered, a s well a s their relationships with attitudes and their resis ta nce to influencing. 2.2. C omputer scienc e and c omplex systems: hy p er-simplific ation fal lacy T urning our attent ion to complex systems science, o ne of the most p opula r mo del applied to the aggr egation of opinions is the b ounded confidence mo del, presented in [10]. Much like previo us studies, in this work agents exchanging info r mation are mo deled as likely to adjust their opinions o nly if the prece ding and the r e- ceived infor ma tion are clo se enough to each other. Suc h an as pec t is mo deled by int ro ducing a rea l num b er ǫ , which stands for tolerance or uncertaint y ([7]) such that an agent with opinion x interacts o nly with agents who se opinions is in the int erv al ] x − ǫ , x + ǫ [. This hyper -simplification helps in mak ing this complex phe- nomenon more tracta ble using computational to ols but, at the s ame time, re duce s it to a simple e x change of v alues that stand for mental ob jects, without any kind of relationship with mental r e pr esentations. An analo gous a ttempt to mo del so cial influence has b een do ne by Axelrod (19 97), who fo cused on the spreading of given cultural features through communication. Again, agen ts do not have internal repre- sentations of what they transmit, and final results are ma inly due to initial top olo gy and to the distribution of traits, without a real exchange among age n ts. The mo del we present in this pa pe r extends the b ounded confidence mo del by providing a cognitively pla usible definition of opinion as men tal representations a nd ident ifying their constitutive elemen ts and their relationships . W e cla im that opinions ar e highly dynamical repres ent ations resulting from the int erplay of different mental ob jects and affected by the mental states o f other in- dividuals in the same netw or k. Aim o f this work is to provide an int erdisciplinary account to descr ib e how so cial influence leads to o pinion for mation, evolution and change. Moving fro m a characterizatio n of opinions as mental representations with sp ecific features, we will try to mo del how opinions are generated within the agen ts’ minds (micro-level) and ho w they spread within a net work of agents (macr o-level). When explaining the emergence of macro -so cial phenomena we need to know what happ ens at the micro-level, i.e. what drives human actions and decisio ns in order to Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 6 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte understand ho w individuals’ representations and behaviors c an g ive rise to so c ia lly complex phenomena and how those affect a gents’ actions. Without explaining how opinions a re formed and ma nipulated within the individuals’ minds, it is v er y diffi- cult to account for the wa y in which they c hange as an effect of socia l influence. Our aim is to understa nd whether and how heterogeneous age nts, endo wed with differ- ent b eliefs and goals, may co me to shar e a given viewp oint a nd wha t consequences this sha ring has o n agents’ b ehaviors. W e a re interested in pr oviding answers, at least par tially , to the following questions: What is an opinio n? What mechanisms lead people to change their opinions? Ho w ca n individuals resist to changes? What are the mechanisms of influence acting within a nd betw een individual minds? Ho w do es so cial impact affect agents’ elab o r ation of new or contrasting infor mation? 3. A Co g nitiv e Theory of Opinions This work aims at o utlining a non-reductio nist cognitive mo del o f opinions and their dynamics. Differently from the mo dels re viewed above, we first pr ovide a definition of opinions as mental repr esentations presenting sp ecific features that make their revision and updating mor e or less easy a nd enduring. Moreov er , gro unding o pinions in the minds allow us to take into account no t o nly direct pro cess es o f r evision triggere d b y the comparison with other s’ differen t opinions, i.e. socia l influence, but also revisions based up on changing in other men tal representations supp orting that opinion. The computational mo del in tro duce d in this pa pe r is intended to provide a pre- liminary unifying fra mework to define opinions and to characteriz e their dynamics in an ea sy but non- r eductionist appro ach. Opinions in several mo dels o f opinion dynamics a re c o nsidered to change according to s o cial influence, we try to outline what is so cial influence and the wa y the s o cial netw ork structure a ffects the ag e n ts’ opinions. 3.1. F acts and evaluations: two kinds of opini ons In everyday language the word opinion is often confronted with fac t, s tr essing the difference b etw een something ob jective b ecause it happ ened and there ar e pr o ofs of it, like in the latter case, and something that do es not hav e any refere nc e in the exter nal rea lity . This distinction is imp ortant, beca use it po ints to a prominen t feature of opinions, i.e. their b eing reg arded as uncertain and not gro unded in an y external pro o f. Opinions can b e debated, co mpared, discussed, argumented, but they can not b e pr ov en to b e true, co n trary to what happ ens w ith facts. How ever, individuals contin uously resort to their opinions as less stable but more versatile men tal ob jects whose relev ance is not r educed be c ause of their being uncertain. This feature is specific of opinio ns and it als o explains why opinio ns are more prone to c hang e a nd revision, esp ecially when confronted with others’ opinio ns. Moreov er, ident ifying this and other traits as sp ecific, allows us to place opinions among other Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Understanding opinions. A c o gnitiv e and formal ac c ount 7 kinds o f mental repres e ntations, describing the kinds of relatio ns hips opinions ha ve with epistemic and motiv ational men tal ob jects. Opinions can b e describ ed as config urations o f an individual’s b eliefs, v alues and feeling s that can b e conditionally activ ated. Co nditional activ atio n p oints to the flex ible and dynamic nature of these re presentations that a re no t g rounded in certaint y and that usually come out from the merging and ela b o ration of other representations and a ttitudes. Opinions ar e not only co nditional, but also comp o- sitional. This means that, for instance, starting from my feeling of aversion tow ar d mathematics and as a conseque nc e of ha ving met a rude friend of friends who hap- pene d to teach math at school, when asked a bo ut my opinion on the time kids should sp end in studying mathema tics, I ca n form or , b etter, activ ate an opinion according to whic h the less time they spe nd the b etter it is. Opinions stem from the co nditional a ctiv ation o f differen t kinds of mental repre - sentations, that can ha ve a propos itional conten t o r, as in the case of attitudes and feelings, they can b e more ev aluative. Ho wev er, there is a sp ecific featur e that dis- tinguishes an opinion from other kinds of mental ob jects. An opinion is an e pis temic representation in which the truth-v alue is deemed to b e uncertain. Opinions refer to ob jects o f the e x ternal world that ca n not b e told to b e either true or false. This impo ssibility (or irrelev ance) to say whether the conten t of a representation is true or false, but only if it makes sense acco rding to what so meone b elieves and k nows is what makes a mental representation an o pinion. This essential feature accounts for the fact that opinio ns can be easily influenced no t only by socia l influence, i.e. an external for ce, but that they ca n also b e easily revised accor ding to the change in one’s own mental r epresentations. This basic feature can be paired with the presence of an attitude, i.e. an ev alu- ative comp onent that sp ecifies whether the individual lik es or dis likes the topic. In general, attitudes are present when the topic is someho w inv olving for the sub ject, so he is pos itively or negatively inclined tow a rd it. When this is no t the case , we have ”factual opinio ns”, like in the following example. If someone is required to say when Mozart died, he can know the cor r ect answer o r not, but this is no t a moo t point. On the con trary , the causes of Mozart’s death are debatable because without knowing where he w as buried it is impo ssible to analy ze the b o nes and to ascertain wha t killed him. This means that we know that Mozar t died in 1 791 but there a r e contrasting opinions ab out the c auses of his death, and, e ven if there exist one true opinion, none can tell which is the truth. On the o ther hand, when opinions involv e also ev a luative comp onents o r facts, the opinions result from the activ ation of a pattern of related representations like b eliefs, knowledge, other opinions, but also goals. This view allows us to describ e opinions as non-sta tic patterns o f relationships in which different r epresentations a re linked through a v ar iety of different link ages . This work is meant to addres s the origin and changing of opinio ns thanks to these inter-relationships. Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 8 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte 3.2. A trip arti te mo del of opini on: tru th-value, c onfidenc e and shar e dness An opinio n is characterized by the three following features. First, the truth v alue can not b e verified (or it is not r elev ant). In genera l, opinions a re repre s entations whose truth v a lue ca n no t b e a ssessed through dir ect exp erience. The topic of the opinion can not b e exp erienced and then it is imp ossible to s ay whe ther a given ob ject is true o r false. If I ask someone ab out his opinion on the military int erven tion in Afghanista n, he can no t tell me that his opinion, whether po sitive or nega tive, is true, b ecause it is not p o s sible to tes t an alternative state of the world in which the interv ention has not ta ken place and then ass es which state was the b est. Nonetheless, he can tell me that he has a stro ng opinion or that he is very confident in it b ecause he has many supp o rting b eliefs (e.g. T alibans’ regime had to b e fighted, civilians needed the interven tion, the world is a sa fer place after the int erven tion, etc) a nd even some goals (for instance, feeling safer) related with that opinion. W e can ha ve strong or w e a k opinions , but our c onfidence do es not dep end on the fact that something is known to be true, g iven the imp os s ibilit y to assess its truth-v alue. In other cas e s, assessing the truth-v alue is not re le v ant, b ecause the attitude and the supp orting mental representations are strong er enough to support the opinion, without caring for its b eing true o r false. Going ba ck to the exa mple ab out the time sp ent in s tudying ma th, I can build upo n my negative experienc e a t school, suppo rting it with my negative attitude and reca lling my exp erience with the unfriendly friend of my friends who happ ens to b e a ma th teacher, to build up m y negative opinion. F ur thermore, notwithstanding the existence of statistics or exp erts that can suppo rt or co nfute my opinion, I do not care a b o ut them, b eca use they are not relev a n t to me. A creationis t’s opinion a b o ut Dar win and the theory of na tural selection is not a ffected by the pro ofs o f its v alidity , b ecause he do es not care fo r those pro ofs and focus his atten tion o n o ther k inds o f kno wledge (like that coming from the Bible, for instance). The second feature is the degr ee of confidence whic h is a sub jective measure of the streng th of b elief a nd it expr esses the ex e nt to which one’s opinion is resistant to change. This is to say that the lack of a n assess able truth v a lue is totally indep endent from the confidence one has in his opinions.The degree of confidence dep ends on the num b er of supp orting representations, and the hig her this n umber the s tr onger an opinion will b e. Castelfranchi, Poggi [6] made a distinction b etw een co nfidence coming fr om the source and confidence co ming fro m the degree of compa tibilit y that a g iven b elief has with pre-existing b eliefs. It is interesting to no tice that representations do not need to be a b o ut the same topic o r to b elong to the s ame set to form a co herent netw o rk. If we take the Afghanistan exa mple, we can easily imagine that a negative opinion ab out the military interven tion could be supp or ted by a genera l b elief ab o ut the right of other countries to intervene in int ernal disputes or b y negativ e ev a lua tions abo ut the US foreign policy , or ev en by k nowledge ab out the roles played by URSS and US in Afghanistan during the Cold W ar. These Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Understanding opinions. A c o gnitiv e and formal ac c ount 9 belie fs are not exclusiv ely related to the target opinion a nd they c an have stronge r or weaker connec tio ns with other opinions. The stro nger the confidence in these belie fs and the higher their num b er , the s tr onger will b e the confidence in that opinion. The degr e e of confidence can also v a ry in accorda nce with the co nfiguration activ ated by a certain opinion. Since opinions are dynamic configuratio ns emerging from the conditional a ctiv ation of other repr e sentations, the pa th follow e d to link different b eliefs, goals, data and memories can result in o pinions that hav e the s ame conten t but differen t deg rees o f confidence. I ca n be aga inst the militar y interven tion in Afghanistan b eca use I feel empathic with the civilians, thus fo cusing on the attitudinal and ev alua tive asp ects, o r b e c ause I hav e s trong belie fs ab out the US foreign p olicy . In this la tter cas e , my opinion is supp o r ted by fac ts and follows a sp ecific argumentative line, and it could lead me to be more confident. Finally , the shar ing o f an opinion, i.e. the ex ten t to which a g iven opinion is considered shared, is ano ther crucial feature. The shar ing may heavily affect the degree of confidence, making p eople feel mor e confident b ecause many other indi- viduals have the sa me opinion. The shar ing is the outco me of a pr o cess o f so cial influence, through whic h age nts’ o pinion are circulated within the so cia l spa ce and they can b ecome more or less s ha red. This dimension is crucial, but it is a lso true that it carach terizes o ther so cial beliefs, like reputation. It is worth no ticing that there are other kinds o f b eliefs tha t are rea lly c lose to opinions but, at a closer inv e s tigation, ther e are some impo rtant differences. Reputation can be one of these, because it is shared a nd it is a lso carach terize d b y a v ary ing degr e e of co nfidence. But, unlikely opinions, reputation has a truth v alue bec ause it refers to someone’s behaviors or actions tha t were actually exhibited (o r that were repo r ted as such, but we do not wan t to a ddr ess here the is s ue of lying) and rep orted to other people. Rea lit y matters in reputation, whereas it is m uch less relev ant in opinions, as witnessed also by the fact that reputatio n do es not hav e to be convincing (i.e. supp orted by some r e asoning or arguments), wherea s opinions need. 4. T o w ard a F ormal Definitio n 4.1. Pr eli mi naries 4.1.1. Time V arying Gr aphs As mentioned in previous sec tio n the temp ora l asp ects of our opinion mo del is based upo n Time-V arying Graphs (TVG ) formalism, an algo rithmic fr amework [8] designed to deal with the tempo ral dimension of net work ed data and to express their dynamics from an inter action-c entric p oint o f view [27]. Consider a set of e ntities V (or no des ), a set of relations E betw een these entities ( e dges ), and an alphab et L acco unt ing for any prop erty suc h that a relation could hav e ( lab el ); that is, E ⊆ V × V × L . L can con tain multi-v alued e le men ts. Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 10 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte The relations (interactions) among entities a re assumed to take place ov er a time dimension (cont inu os or discrete) T the lifetime o f the system whic h is generally a subset of N (discr e te- time systems) or R (cont inu ous-time systems). The dyna mics of the s y stem can subseq uent ly b e describ ed by a time- v a rying graph, or TVG , G = ( V , E , T , ρ, ζ ), wher e • ρ : E × T → { 0 , 1 } , called pr esenc e function , indicates whether a given edge or node is av ailable at a given time. • ζ : E × T → T , ca lled latency function , indicates the time it takes to cr oss a given edge if starting at a g iven da te (the latency of a n edge could v a ry in time). 4.1.2. The underlying gr aph Given a TVG G = ( V , E , T , ρ, ζ ), the gra ph G = ( V , E ) is called u n derlying g raph of G . This static graph should be seen a s a sort of fo otprint of G , whic h flattens the time dimension and indicates only the pairs of no des that hav e relatio ns at s o me time in a given time interv al T . In most studies a nd applications, G is assumed to be co nnected; in genera l, this is not necessar ily the case. Note that the connectivity of G = ( V , E ) do es not imply that G is connected at a given time instant; in fact, G could be disconnected at all times. The la ck of relatio nship, with regards to connectivity , b etw een G and its footprint G is even strong er: the fact that G = ( V , E ) is connected do es not even imply that G is “co nnected o ver time”. 4.1.3. Edge-c entric evolution F rom an edge po int o f view (relationships within epistemic represe ntations), the evolution derives from v ariations of the av ailability . TVG defines the avai lable dates of a n edge e , noted I ( e ), as the union of a ll dates at which the edge is av ailable, that is , I ( e ) = { t ∈ T : ρ ( e, t ) = 1 } . Given a multi-in terv al o f av aila bilit y I ( e ) = { [ t 1 , t 2 ) ∪ [ t 3 , t 4 ) ... } , the sequence o f dates t 1 , t 3 , ... is called app e ar anc e dates o f e , noted App ( e ), and the s equence of dates t 2 , t 4 , ... is c a lled disapp e ar anc e dates of e , no ted Dis ( e ). Finally , the sequence t 1 , t 2 , t 3 , ... is called char acteristic dates of e , noted S T ( e ). 4.1.4. Gr aph-c entric evolution F rom a globa l standpoint, the ev olution of the system can b e derived by a sequence of (static) gr aphs S G = G 1 , G 2 .. where every G i corres p o nds to a s tatic snapshot of G such that e ∈ E G i ⇐ ⇒ ρ [ t i ,t i +1) ( e ) = 1, with tw o p ossible meaning s for the t i s: either the sequence of t i s is a discr etization of time (for example t i = i ); o r it corr e s po nds to the set of par ticular da tes when top ologica l even ts o ccur in the graph, in which case this seq uence is equal to sor t ( ∪{S T ( e ) : e ∈ E } ). In the latter case, the sequence is called char acteristic dates of G , and noted S T ( G ). Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Understanding opinio ns. A c o gnitive and formal ac c ount 11 4.2. Mo deling Epistemic R epr esentations An opinion is an epistemic r epresentation of a state of the world with respect to a given ob ject p . It is defined on a three dimensio nal space defined b y: a) the obje ctive truth value T o , a subje ctive truth value , namely T s and a de gr e e of c onfidenc e d c with resp ect to the ob ject p . More formally w e can state that: Definition 1. an epistemic repres e n tation of a sta te of the world m ∈ M is a quadruplet p, T o , T s , d c defined by a prep osition p r elated to a g iven ob ject O , and t wo v ariable T o and T s defined on R . The d c ∈ R resp ectively quan tifying the “real“ truth v alue of an info r mation, namely the ob jective truth v a lue, the perceived truth v alues, and the degree of confidence, with resp ect to the prep osition p . By v arying the dimensio ns of the doma in of T o and T s , we c an define a ta xonomy of the epistemic representation of the world that can b e s ummarised as follows: Definition 2. An epistemic representation m k = { p, T o , T s , d c } is know le dge when T o = T s . Definition 3. An epistemic r epresentation m b = { p, T o , T s , d c } is a b elief when 0 < T o < 1 ∧ 0 ≤ T s ≤ 1 . Definition 4. An epistemic representation m o = { p, T o , T s , d c } is an opi ni on when 0 ≤ T o < 1 ∧ 0 ≤ T s ≤ 1. 4.3. Opi nions and Individu al s W e can define an epistemic repr esentation graph as a ne tw ork of epistemic repre- sentation immerged in a dynamic netw ork in a given time interv a l and the links state the correla tion among them. Let us consider a s et V of men ta l representation (or nodes ), in ter acting with one another o ver time. Each r elation among the ment al representation can b e formalized by a q ua druplet c = { u , v , t 1 , t 2 } , where u and v are the involv ed men tal repres e n tations (either b eliefs, or knowledge or an o pinion), t 1 is the time at which the corr elation oc c urs, and t 2 the time a t which the relatio n terminates. A g iven pair of no des can natur a lly b e sub ject to se veral s uch interac- tions o ver time (and for generality , w e allow these interactions to o verlap). Given a time in ter v al T = [ t a , t b ) ⊆ T (wher e t a and t b may b e either t wo dates, or one date and one infinity , o r b oth infinities), the se t C ( T ) (or simply C ) of all interactions o ccurring during that time interv al defines a se t of intermitten tly-av aila ble edges E ( T ) ⊆ V × V , such that: ∀ u, v ∈ V , ( u, v ) ∈ E ( T ) ⇐ ⇒ ∃ t ′ ∈ [ t a , t b ) , ( u, v , t 1 , t 2 ) ∈ C ( T ) : t 1 ≤ t ′ < t 2 (1) that is, an edge ( u , v ) exists iff a t least one interaction b etw ee n u and v o c c urs, or ter mina tes, b etw een t a and t b . The intermitten t av ailability of an edg e e = Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 12 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte ( u, v ) ∈ E ( T ) is describ ed by the pr esenc e function ρ : E ( T ) × T → { 0 , 1 } such that ∀ t ∈ T , e ∈ E ( T ): ρ ( e, t ) = 1 ⇐ ⇒ ∃ ( u , v , t 1 , t 2 ) ∈ C : t 1 ≤ t < t 2 (2) The triplet G = ( V , E , ρ ) is called an epistemic r epr esent ation gr aph , and the tempo ral domain T = [ t a , t b ) o f the function ρ , is the lifetime of G . W e denote by G [ t,t ′ ) the mental r epr esentation sub gr aph of G covering the per io d [ t a , t b ) ∩ [ t, t ′ ) Hence, a se quence of co uples J = { ( e 1 , t 1 ) , ( e 2 , t 2 ) , ... } , with e i ∈ E a nd t i ∈ T for all i , is calle d a jo urney in G iff { e 1 , e 2 , ... } is a walk in G and fo r all i , ρ ( e i , t i ) = 1 and t i +1 ≥ t i . Jo urneys can be thought of as p aths over time fro m a source no de to a destination node (if the jour ne y is finite). Let us denote by J ∗ G the set of all p ossible jour neys in an epistemic representation system G . W e will say that G admits a journey from a node u to a no de v , and note ∃J ( u,v ) ∈ J ∗ G , if there exists at least one poss ible journey from u to v in G . 4.4. Opinion Dynamics and So ciety One of the most famous forma lis ms aimed a t desc ribing the pro cess of p ersua s ion is the “Bo unded Co nfidence Mo del” (BCM) where a gents exchanging informatio n are mo deled as likely to adjust their opinions o nly if the preceding a nd the received information are clo se enough to each other. Suc h an aspec t is modeled by introduc- ing a rea l num b er ǫ , which s tands for toler ance or uncertaint y such that an agent with o pinio n x interacts only with agents who se opinio ns is in the int erv al ]x ǫ , x + ǫ [. Neverthless the wide, massive and cross - disciplinary use of the BCM ([19, 15]) ranging fro m “viral marketing” to to the Italians’ opinions distortion pla yed b y controlled mass media ([25 , 4, 5 , 15]). Such a mo del do es no t pr ovide an expla na- tion of the phenomena yielding to the tolerance v alue, it is just assumed as a static v alue. In this w o rk w e will outline whic h are the facto rs affecting the a cceptance or the refuse of one another opinion. In pa rticular, how can we formalize compariso n of tw o or more opinions? Recalling that a mental representation is a pr ep osition with the truth v alue defined by t w o v ariable T o , T s ∈ R and d c ∈ R resp ectively qua nt ifying the “real” and the p erceived truth v alue and the degr ee of confidence with resp ect to a given o b ject or prop ositio n. And considering that suc h mental representations are modeled as set of time connected entities of the form G = ( V , E , ρ ) we can now provide some definitions aimed at descr ibing the pro cess o f per suasion. Assuming that an epistemic re presentation system, which is by nature adaptive, when facing with external even ts, reacts to the stimulus b y ac tiv a ting o nly a subset of its comp onents. F or instance, consider the e xample where an age nt x is q uestioned by an agent y ab out his opinion on a given targ et. What do es happ en in the x ’s men tal r epresentation system? How can we quant ify x ’s attitudes to c hange or not is opinions regarding a giv en matter of fact? Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV Understanding opinio ns. A c o gnitive and formal ac c ount 13 According to our model the epistemic repr e s entation system of x , as reaction to the external stimulus p osed b y the y ’s questio n, will pe r form j our n ey within the elements that in its mind a re rela ted with the tar get of the question and on this base will be able to compare its opinion with the one o wned b y y . Definition 5. (r elational-)c onne cte d c omp onent induc e d by an external event in G x is defined as a s et of no des V ′ ⊆ V such that ∀ u, v ∈ V ′ , ∃J ( u,v ) ∈ J ∗ G . Then G is said connected if it is itself a connected comp onent ( V ′ = V ). Since all no des in V ′ are defined by an ob jectiv e tr uth v alue T and a degr ee of confidence (p erceived tr uth v alue) d g it is obvious that the r esistence to an opinio n to change is denoted by these v alues in all the nodes in V ′ . 5. Conclusions In this preliminary work w e tried to s ketc h a cognitively g r ounded dynamic mo del of o pinions, in which we defined these men tal representations as cara ch terized b y the pr esence of thre e sp ecific features. Differently than psy chologica l theorie s of opinions that usually provide ric h definitions that are too c o mplex to be r educed to measurable v aria bles, we isolated three ma in constitutive elemen ts that characterize this k ind of mental representations. O n the other hand, we tr ied to ov ercome the reductionist appro ach of opinion dyna mic mo dels, in which the richness o f human cognitive pro cesses is substituted by easy-to -compute factors po orly related to a c- tual human behaviors. F or this reason, we pr op osed to apply time-v ar y ing-gra ph to develop a for mal mo del able to account for the wa y in whic h opinions ar e gener- ated and change a s a function of the presence and opinions o f o ther agents in the net work. W e are p erfectly aware of the complexity o f this issue and this work represent s a preliminary attempt to merge the cognitive complexity of opinions with a rigor ous formal appro ach, but there are ma ny pr oblems that we need to a ddress. First, the cognitive mo de l should b e refined and sp ecific hypo theses ab out o pinion rev is ion and diffusion should b e put forw a rd. Mor eov er , the robustness of the forma l mo del will b e tested and such a model will be implemen ted in cognitive multi-agent system in order to explore the parameter space up o n which our mo del ha s b een defined. Our ultimate aim is to build up a sim ula tion en vironment in which a gents e ndowed with heterogeneous representations of the external world interact and this leads to the creation of new opinions , the disapp e aring of some of the previous ones and, in general, to different distributions o f representations in the p opulation. 6. Ac knowledgemen ts This w o rk w a s s uppo rted b y the Europ ea n Communit y under the FP6 pr ogramme (eRep pro ject CIT5-028 575). A particula r thanks to Ilvo Diamanti, F eder ica Mattei, Mario P aolucci, F ederico Cecconi, Stefano Picascia, Gero nimo Stilton and the Hyp- Septem ber 21, 2018 7:14 WSPC/INSTR UCTION FILE OpinionsECCS˙Arx iV 14 F r anc esc a Giar dini, Walter Quattr o cio c chi, R osaria Conte notoad. In a ddition we are g rateful to the biggest Italian anoma ly and the Italian media for the inspirations and insight s. References [1] E. Smith A. Mason, F.Conrey . Situating social influence p rocesses: Dy namic, m u ltidi- rectional flo ws of infl u ence within social netw orks. Personality and So cial Psycholo gy R eview , 11(279-300), 2007. [2] B. Latan´ e A. No wak, J. Szamrej . F rom priv ate attitude to pu blic opinion: A dynamic theory of social impact. Psycholo gic al Re view , 97:3 62–376 , 1990. [3] G.W. Allport. 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