Balietti, Stefano

Helbing, Dirk

Maes, Michael

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On Fragmentation and Scientiﬁc Progress1 IntroductionWhy are the social sciences so fragmented as compared to the natural sciences, for example physics orbiology? What consequences has fragmentation for the overall progress of a ﬁeld?The focus of this work is the question why disciplinary fragmentation and scientiﬁc progress arecorrelated. Potential explanations are abound. First, there might be a direct causal relationship betweenfragmentation and scientiﬁc progress. For instance, it could be that the natural sciences are less fragmentedinto opposing schools because they have developed a scientiﬁc consensus very early in their history (Cole,2001, Chap. 6). Likewise, a high degree of fragmentation might slow down scientiﬁc progress, because ithampers the diﬀusion of ideas and insights (Cole, 2001, Chap. 6). Second, fragmentation and progressmight not inﬂuence each other, but there might be third variables that aﬀect both outcomes. These factorsmight be rooted in the nature of the disciplines. For instance, many concepts of social scientiﬁc theoriesare diﬃcult to deﬁne, leading to disagreement about their appropriate interpretation and measurement(Cole, 2001, Chap. 1). Unclear deﬁnitions of concepts also slow down the process of scientiﬁc discovery.Furthermore, institutional factors might aﬀect the degree of fragmentation and progress in the diﬀerentdisciplines (Cole, 2001, Chap. 14). For instance, scarcity in public funding does not only slow downprogress but might also further increase competition between scientist and hamper the willingness tointeract with competing research teams, which in turn fosters the formation of distinct clusters.2 Model SpeciﬁcationWe assume a population of N = 100 scientists exploring a continuous epistemic space under the eﬀect ofsocial inﬂuence of related opinions. The position ?xi(t) that scientist i occupies in the epistemic space attime t represents his or her current view. At time t+ 1, scientist i can either update or not his position.Such a movement in space then represents the theoretical approach that the agent follows in his or herinvestigation. We specify the exploration of the epistemic landscape by the scientist in search for thecorrect theory as follows:d?xidt= ?vi(t)????Exploration velocity+ ?Ch(t)? ?? ?Convergence+ ?ξi(t)????Noise. (1)The exploration velocity term is speciﬁed as in Vicsek et al. (1995) model for collective motion ofself-propelled particles:?vi(t+ 1) = α?vi(t) + (1− α)??vj(t)?R , (2)where 0 < α ≤ 1 and ?.?R means an averaging over all scientists within the radius R. This speciﬁcationof the exploration speed reﬂects the desire to produce scientiﬁc progress along with one’s peers, but alsosome persistence in the research path taken.However, unlike the original Vicsek’s model, the velocity is not a constant, but varies over time. Infact, each scientist is initially assigned a velocity ?vi(t0) drawn from a uniform random distribution. Theaveraging over neighbors eventually produces an alignment of the velocities vectors of both components          Stefano Balietti, Michael Maes and Dirk Helbing                         ETH Zurich, Switzerland<sbalietti@ethz.ch> <mmaes@ethz.ch> <dhelbing@ethz.ch>Miguel, Amblard, Barceló & Madella (eds.) Advances in Computational Social Science and Social SimulationBarcelona: Autònoma University of Barcelona, 2014, DDD repository <http://ddd.uab.cat/record/125597>of Eq. 2, e.g. the direction and the strength of the vector. Given that agents that meets at a certainposition can follow completely antithetical approaches, the size of the velocity vector is usually reducedby the averaging procedure. This represents frictional eﬀects in social interactions.The convergence term ?Ch(t) reﬂects the attraction to the ground truth. As mentioned also by Hegsel-mann and Krause (2006), it is not to be interpreted literally, but rather as the feedback that individualsreceive from the results of their experiments and continued investigation. The force is suppose to give aweak hint regarding the research direction to follow, but never the exact answer, because otherwise everyindividual could jump directly to the true value, and this is simply not how scientiﬁc research typicallydevelops. Formally ?Ch(t) is modeled as:?Ch(t) =?xh − ?xi(t)τh, (3)where ?xh − ?xi(t) is the distance between the agent’s position and the location of the ground truth,and τh is a parameter representing the strength of the attractive force. It implies that initially, when stillfar away from the ground truth, scientists receive a clear signal of the research direction they should taketo approach the truth. However, the closer they get to the true value, the harder it gets to actually makeprogress.The noise term ?ξi(t) plays a crucial role in our model in a twofold manner. On the one side, we assume(i) Gaussian position noise on the approach hold by a scientist at time t, and on the other (ii) we assumeGaussian angular noise on the research direction followed by each individual scientist at time t+ 1. Theposition noise, whose standard deviation is denoted by ?, acts as white noise, while the angular noise,whose standard deviation is denoted by σ, introduces stocasticity and path dependence in the trajectoryfollowed by the scientist. The former can be interpreted as an measurement error, which can be reducedbut never completely eliminated. The latter can instead be interpreted as the inevitable diﬀerence betweenplanned and actual research path, or as well as the degree to which a scientist is voluntarily ready deviatefrom the approach of his or her peers, if he or she is making research in a group.Figure 1: Ideal typical run showing diﬀerent patterns of consensus and level of scientiﬁc progress atfour time steps: 1, 200, 1000, 2000. The ﬁgure shows the emergence of diﬀerent schools of thought, thatgradually merge together in proximity of the truth.3 Preliminary ResultsWe devised the following computational experiment. At the beginning of each simulation we have ran-domly preassigned agents to n = (1, . . . , 30) clusters. Each group of agents was then placed on a radius of0.4 units away from truth, and equidistant from neighboring groups. Afterward, we have then measuredMiguel, Amblard, Barceló & Madella (eds.) Advances in Computational Social Science and Social SimulationBarcelona: Autònoma University of Barcelona, 2014, DDD repository <http://ddd.uab.cat/record/125597>the time necessary to achieve a stable consensus on truth, deﬁned as 75% of the agents within a radiusof 0.05 units from truth. The results are shown in Fig. 2 A. Unequivocally, we observe two diﬀerentconsensus regimes, determined by the value of the interaction radius R. In the case of small R, thereis a signiﬁcant positive relationship between the number of clusters and the time necessary for reachingconsensus. In the case of large R, the number of cluster has a very limited eﬀect. Surprisingly, however,the coeﬃcient even takes the opposite sign: the more clusters the faster the consensus is built up. Theresults from the linear regression of time to consensus over initial number of clusters are shown in Table1.We then investigated, the eﬀect of the other social inﬂuence variable of our model, i.e. the strength ofsocial inﬂuence α. In case of a large radius R, as expected, manipulating α played no major role. However,in case of a small radius R, the results are striking. When social inﬂuence is very strong (α = 0.01), the R2value of the regression is 0.51. On the contrary, if social inﬂuence is very weak (α = 0.99), no simulationreached consensus within 20.000 iterations!Figure 2: At the beginning of the simulation agents were randomly preassigned to n = (1, . . . , 30) clusters.Each group of agent was then placed on a radius of 0.4 units away from truth, and equidistant from theirneighboring groups. The graph shows the time necessary to 75% of the agents to end up in a radius of0.05 units from truth. Clusters are a hurdle to consensus if and only if the interaction radius is small.On top of this, if also social inﬂuence is also weak, e.g. α = 0.99, reaching the truth can be extremelyunlikely.Clustering per se is not a factor that slows down scientiﬁc progress. It is rather the nature of socialinteractions that completely determines how consensus is built up and how long it takes to reach theground truth. A small interaction radius, and highly individualistic agents represent the worst environ-mental conditions to form a consensus, but also to ﬁnd the truth.Even if clustering does not directly retard scientiﬁc progress, it is in fact a proxy for identifying thereal cause: the small radius of inﬂuence used by the agents in the ﬁeld. Large radius, even in connectionMiguel, Amblard, Barceló & Madella (eds.) Advances in Computational Social Science and Social SimulationBarcelona: Autònoma University of Barcelona, 2014, DDD repository <http://ddd.uab.cat/record/125597>Model 1 Model 2 Model 3 Model 4(Intercept) 3735.33∗∗∗ 2037.75∗∗∗ 3406.91∗∗∗ 2142.94∗∗∗(364.17) (176.41) (482.20) (250.77)Clusters 428.33∗∗∗ −25.31∗ 418.27∗∗∗ −41.39∗∗(22.37) (9.94) (32.95) (14.13)R2 0.46 0.01 0.51 0.03Num. obs. 435 900 155 300***p < 0.001,**p < 0.01,*p < 0.05Table 1: Model 1: alpha = [0.01; 0.5; 0.99], and R = 0.03. Model 2: alpha = [0.01; 0.5; 0.99], and R = 0.3.Model 3: alpha = 0.01, and R = 0.03; Model 4: alpha = 0.01, and R = 0.3;with low social inﬂuence, do not generally lead to a clustered ﬁeld. The confounding nature of clusteringand social inﬂuence has is such that fragmentation has often been erroneously seen as the primary causeof the slow rate of progress of disciplines like sociology. 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In: ed. by D. Cartwright. Univer. Michigan. Chap. ACriterion for Unanimity in French’s Theory of Social Power, pp. 168–182.Hegselmann, R. and U. Krause (2002). “Opinion Dynamics and Bounded Conﬁdence Models. Analysisand Simulation”. In: Journal of Artiﬁcial Societies and Social Simulation 5, pp. 1–24.— (2006). “Truth and Cognitive Division of Labour: First Steps Towards a Computer Aided SocialEpistemology”. In: Journal of Artiﬁcial Societies and Social Simulation 9.3, pp. 1–28.Kitts, J.A. and P. T. Trowbridge (2007). “Shape Up Or Ship Out: Social Networks, Social Inﬂuence, andOrganizational Demography”. In: Computational and Mathematical Organization Theory 13, pp. 333–353.Lehrer, K. (1975). “Social Consensus and Rational Agnoiology”. In: Synthese 31.1, pp. 141–160.Maes, M., A. Flache, and D. Helbing (2010). “Individualization as Driving Force of Clustering Phenomenain Humans”. In: PLoS Comput Biol 6.10, e1000959+.March, J.G. 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On fragmentation and scientific progress

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On fragmentation and scientific progress

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