Jan Lorenz

How social influence can undermine the wisdom of crowd effect

Social groups can be remarkably smart and knowledgeable when their averaged judgements are compared with the judgements of individuals. Already Galton [Galton F (1907) Nature 75:7] found evidence that the median estimate of a group can be more accurate than estimates of experts. This wisdom of crowd effect was recently supported by examples from stock markets, political elections, and quiz shows [Surowiecki J (2004) The Wisdom of Crowds]. In contrast, we demonstrate by experimental evidence (N = 144) that even mild social influence can undermine the wisdom of crowd effect in simple estimation tasks. In the experiment, subjects could reconsider their response to factual questions after having received average or full information of the responses of other subjects. We compare subjects’ convergence of estimates and improvements in accuracy over five consecutive estimation periods with a control condition, in which no information about others’ responses was provided. Although groups are initially “wise,” knowledge about estimates of others narrows the diversity of opinions to such an extent that it undermines the wisdom of crowd effect in three different ways. The “social influence effect” diminishes the diversity of the crowd without improvements of its collective error. The “range reduction effect” moves the position of the truth to peripheral regions of the range of estimates so that the crowd becomes less reliable in providing expertise for external observers. The “confidence effect” boosts individuals’ confidence after convergence of their estimates despite lack of improved accuracy. Examples of the revealed mechanism range from misled elites to the recent global financial crisis.

CONTINUOUS OPINION DYNAMICS UNDER BOUNDED CONFIDENCE: A SURVEY

Models of continuous opinion dynamics under bounded confidence have been presented independently by Krause and Hegselmann and by Deffuant et al. in 2000. They have raised a fair amount of attention in the communities of social simulation, sociophysics and complexity science. The researchers working on it come from disciplines such as physics, mathematics, computer science, social psychology and philosophy. In these models agents hold continuous opinions which they can gradually adjust if they hear the opinions of others. The idea of bounded confidence is that agents only interact if they are close in opinion to each other. Usually, the models are analyzed with agent-based simulations in a Monte Carlo style, but they can also be reformulated on the agents density in the opinion space in a master equation style. The contribution of this survey is fourfold. First, it will present the agent-based and density-based modeling frameworks including the cases of multidimensional opinions and heterogeneous bounds o...

A stabilization theorem for dynamics of continuous opinions

A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann–Krause and Weisbuch–Deffuant). The analysis detects self-confidence as a driving force of stabilization.

Systemic risk in a unifying framework for cascading processes on networks

AbstractWe introduce a general framework for models of cascade andn contagion processes on networks, to identify their commonalities andn differences. In particular, models of social and financial cascades, asn well as the fiber bundle model, the voter model, and models of epidemicn spreading are recovered as special cases. To unify their description,n we define the net fragility of a node, which is the difference betweenn its fragility and the threshold that determines its failure. Nodes failn if their net fragility grows above zero and their failure increases then fragility of neighbouring nodes, thus possibly triggering a cascade. Inn this framework, we identify three classes depending on the way then fragility of a node is increased by the failure of a neighbour. At then microscopic level, we illustrate with specific examples how the failuren spreading pattern varies with the node triggering the cascade,n depending on its position in the network and its degree. At then macroscopic level, systemic risk is measured as the final fraction ofn failed nodes, X*, and for each of the three classes we derive an recursive equation to compute its value.n The phase diagram of X* as a function of the initial conditions,n thus allows for a prediction of the systemic risk as well as an comparison of the three different model classes. We could identifyn which model class leads to a first-order phase transition in systemicn risk, i.e. situations where small changes in the initial conditions n determine a global failure. Eventually, we generalize our framework ton encompass stochastic contagion models. This indicates the potential forn further generalizations.

On Conditions for Convergence to Consensus

A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau [6] (IEEE TRANSACTIONS ON AUTOMATIC CONTROL, vol. 50, no. 2, 2005) about set-valued Lyapunov theory and convergence under switching communication topologies. We give examples that point out differences of approaches including examples where Moreaus theorem is not applicable but ours is. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.

Innovation vs. imitation and the evolution of productivity distributions

We develop a tractable dynamic model of productivity growth and technology spillovers that is consistent with the emergence of real world empirical productivity distributions. Firms can improve productivity by engaging in in-house R&D, or alternatively, by trying to imitate other firms’ technologies subject to limits to their absorptive capacities. The outcome of both strategies is stochastic. The choice between in-house R&D and imitation is endogenous, and based on firms’ profit maximization motive. Firms closer to the technological frontier have less imitation opportunities, and tend to choose more often in-house R&D, consistent with the empirical evidence. The equilibrium choice leads to balanced growth featuring persistent productivity differences even when starting from ex-ante identical firms. The long run productivity distribution can be described as a traveling wave with tails following Zipf’s law as it can be observed in the empirical data. Idiosyncratic shocks to firms’ productivities of R&D reduce inequality, but also lead to lower aggregate productivity and industry performance.

Fostering Consensus in Multidimensional Continuous Opinion Dynamics under Bounded Confidence

Social consensus is important for society. Sometimes the success of society depends on a consensus (e.g. the decision to pay taxes or to commit to the constitution). Examples for continuous opinion dynamics are discussions about tax rates or budget plan proposals for governments investments. Another example is a commission of experts which should reach a estimate about a certain issue, e.g. the tax revenues of the next year. In all these situations we got a group of agents which should reach a common agreement either for reaching a good approximation to the truth but on the other hand for the reason, that reaching consensus is a good in itself. nFrom social judgment theory and experiments we know that humans either tend to agreement with others for normative and informational reasons but on the other hand have bounded confidence against others with differing opinions. nIn a framework of models of continuous opinion dynamics we ask, which structural conditions foster the achievement of consensus? We present evidence by simulation that bringing more issues in does, but only if the issues are under budget constraints. Further, the installation of meetings where everyone hears all opinions has a better impact than relying on gossip.

Universality in movie rating distributions

AbstractnIn this paper histograms of user ratings for moviesn(1

About the Power to Enforce and Prevent Consensus by Manipulating Communication Rules

bigstar

Systemic risk in a network fragility model analyzed with probability density evolution of persistent random walks

,...,10