A model for the probabilistic function followed in Wikipedia edition is presented and compared with simulations and real data. It is argued that the probability to edit is proportional to the editors number of previous editions (preferential attachme
nt), to the editors fitness and to an ageing factor. Using these simple ingredients, it is possible to reproduce the results obtained for Wikipedia edition dynamics for a collection of single pages as well as the averaged results. Using a stochastic process framework, a recursive equation was obtained for the average of the number of editions per editor that seems to describe the editing behaviour in Wikipedia.
We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytica
lly calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T = 0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.
We study the Axelrods cultural adaptation model using the concept of cluster size entropy, $S_{c}$ that gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to r
andom, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is unambiguously given by the maximum of the $S_{c}(q)$ distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first- or second-order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait $q_c$ and the number $F$ of cultural features in regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a new partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a new $q-B$ phase diagram for the Axelrod model in regular networks.
In the compromise model of continuous opinions proposed by Deffuant et al, the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolera
nce $epsilon$. In directed networks, if agent i is a neighbor of agent j, j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions $<F>$ and their distribution as a function of $epsilon$ and of the network structural disorder. In directed networks $<F>$ exhibits a rich structure, being larger than in undirected networks for higher values of $epsilon$, and smaller for lower values of $epsilon$.
