A note on the consensus time of mean-field majority-rule dynamics

In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups that, at each evolution step, gather to reach agreement. When the group size distribution has a finite mean value, the previously known logarithmic dependence on the population size holds. On the other hand, when the mean group size diverges, the consensus time and the population size are related through a power law. Numerical simulations validate this semi-quantitative analytical prediction.Comment: 4 pages, 3 figures, Commentary and Reply available in Papers in Physic

Modelization of the EOS

This article summarizes theoretical predictions for the density and isospin dependence of the nuclear mean field and the corresponding nuclear equation of state. We compare predictions from microscopic and phenomenological approaches. An application to heavy ion reactions requires to incorporate these forces into the framework of dynamical transport models. Constraints on the nuclear equation of state derived from finite nuclei and from heavy ion reactions are discussed.Comment: 17 pages, 13 figures, contributed paper to the World Consensus Initiative (WCI) book "Dynamics and Thermodynamics with Nucleonic Degrees of Freedom

Consensus Formation in Multi-state Majority and Plurality Models

We study consensus formation in interacting systems that evolve by multi-state majority rule and by plurality rule. In an update event, a group of G agents (with G odd), each endowed with an s-state spin variable, is specified. For majority rule, all group members adopt the local majority state; for plurality rule the group adopts the local plurality state. This update is repeated until a final consensus state is generally reached. In the mean field limit, the consensus time for an N-spin system increases as ln N for both majority and plurality rule, with an amplitude that depends on s and G. For finite spatial dimensions, domains undergo diffusive coarsening in majority rule when s or G is small. For larger s and G, opinions spread ballistically from the few groups with an initial local majority. For plurality rule, there is always diffusive domain coarsening toward consensus.Comment: 8 pages, 11 figures, 2-column revtex4 format. Updated version: small changes in response to referee comments. For publication in J Phys

Dynamics of Majority Rule

We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly-selected agents, consensus is reached in a time that scales ln N, where N is the number of agents. On finite-dimensional lattices, where a group is a contiguous cluster, the consensus time fluctuates strongly between realizations and grows as a dimension-dependent power of N. The upper critical dimension appears to be larger than 4. The final opinion always equals that of the initial majority except in one dimension.Comment: 4 pages, 3 figures, 2-column revtex4 format; annoying typo fixed in Eq.(1); a similar typo fixed in Eq.(6) and some references update