Timing Interactions in Social Simulations: The Voter Model
The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to
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tract The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.
1 Introduction Individual based models of collective social behavior include traditionally two basic ingredients: the mechanism of interaction and the network of interactions [1]. The idea of choosing a mechanism of interaction, such as random imitation [2–4] or threshold behavior under social pressure [5–7], is to isolate this mechanism and to determine its consequences at the collective level of emergent properties. The network of interactions determines who interacts with whom. The topology
J. Fern´andez-Gracia V.M. Egu´ıluz () M.S. Miguel IFISC, Instituto de F´ısica Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain e-mail: [email protected] P. Holme and J. Saram¨aki (eds.), Temporal Networks, Understanding Complex Systems, DOI 10.1007/978-3-642-36461-7 17, © Springer-Verlag Berlin Heidelberg 2013
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of the network incorporates among other things the heterogeneity of ties among individuals. In addition ties can be non persistent, so that the network structure changes with time. In particular, the network and the state of the individuals can evolve in similar time scales (co-evolution). Such entangled process of dynamics of the network and the dynamics on the network can describe how to go from interacting with neighbors to choosing neighbors [8–12]. A third ingredient of individual based models, which was not considered in detail in the past, is the timing of interactions: When do individuals interact? The usual assumption in simulation models was that of a constant rate of interaction. In this paper we revise this assumption addressing the consequences of the heterogeneity in the timing of interactions. Addressing this question is timely due to the availability of massive and high resolution data on h
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