The Krause-Hegselmann Consensus Model with Discrete Opinions

The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For the case of a society in which everybody can talk to everybody else, we find that the chance to reach consensus is much higher as compared to other models; if the number of possible opinions Q<=7, in fact, consensus is always reached, which might explain the stability of political coalitions with more than three or four parties. For Q>7 the number S of surviving opinions is approximately the same independently of the size N of the population, as long as Q<N. We considered as well the more realistic case of a society structured like a Barabasi-Albert network; here the consensus threshold depends on the outdegree of the nodes and we find a simple scaling law for S, as observed for the discretized Deffuant model.Comment: 12 pages, 6 figure

Monte Carlo Simulation of Deffuant opinion dynamics with quality differences

In this work the consequences of different opinion qualities in the Deffuant model were examined. If these qualities are randomly distributed, no different behavior was observed. In contrast to that, systematically assigned qualities had strong effects to the final opinion distribution. There was a high probability that the strongest opinion was one with a high quality. Furthermore, under the same conditions, this major opinion was much stronger than in the models without systematic differences. Finally, a society with systematic quality differences needed more tolerance to form a complete consensus than one without or with unsystematic ones.Comment: 8 pages including 5 space-consuming figures, fir Int. J. Mod. Phys. C 15/1

An Evaluable Theory for a Class of Migration Problems

A master equation formulation for a class of migration problems describing the spatio-temporal dynamics of a system of regions is introduced. The transition probabilities are functions of trend parameters, which characterize preferences, growth pool and saturation effects. The trend parameters can be determined by regression analysis from the empirical migration matrix. The solution of meanvalue equations yields a nonlinear migration prognosis. The relation between trend parameters and motivation factors, e.g., income per capita, infrastructure and transportation costs, is also discussed. Numerical simulations illustrate the influence of the superposition of migration trends on the evolution of the system

Opinion dynamics and decision of vote in bipolar political systems

A model of the opinion dynamics underlying the political decision is proposed. The analysis is restricted to a bipolar scheme with a possible third political area. The interaction among voters is local but the final decision strongly depends on global effects such as, for example, the rating of the governments. As in the realistic case, the individual decision making process is determined by the most relevant personal interests and problems. The phenomenological analysis of the national vote in Italy and Germany has been carried out and a prediction of the next Italian vote as a function of the government rating is presented.Comment: 8 pages, 1 figure. To be published in International Journal of Modern Physics

The Sznajd Consensus Model with Continuous Opinions

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighbouring agents with the same opinion forces all their neighbours to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here the opinion s is a real number between 0 and 1, and a parameter \epsilon is introduced such that two agents are compatible if their opinions differ from each other by less than \epsilon. If two neighbouring agents are compatible, they take the mean s_m of their opinions and try to impose this value to their neighbours. We find that if all neighbours take the average opinion s_m the system reaches complete consensus for any value of the confidence bound \epsilon. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.Comment: 11 pages, 4 figures. To appear in International Journal of Modern Physics

Simulation of Consensus Model of Deffuant et al on a Barabasi-Albert Network

In the consensus model with bounded confidence, studied by Deffuant et al. (2000), two randomly selected people who differ not too much in their opinion both shift their opinions towards each other. Now we restrict this exchange of information to people connected by a scale-free network. As a result, the number of different final opinions (when no complete consensus is formed) is proportional to the number of people.Comment: 7 pages including 3 figs; Int.J.MOd.Phys.C 15, issue 2; programming error correcte

Universality of the Threshold for Complete Consensus for the Opinion Dynamics of Deffuant et al

In the compromise model of Deffuant et al., opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. The opinions of a randomly chosen pair of compatible agents get closer to each other. We provide strong numerical evidence that the threshold value of \epsilon above which all agents share the same opinion in the final configuration is 1/2, independently of the underlying social topology.Comment: 8 pages, 4 figures, to appear in Int. J. Mod. Phys. C 15, issue

Bridging Gaps Among Scientific Disciplines. Paper Presented on IIASA's 20th Anniversary

IIASA celebrated its twentieth anniversary on May 12-13 with its fourth general conference, IIASA '92: An International Conference on the Challenges to Systems Analysis in the Nineties and Beyond. The conference focused on the relations between environment and development and on studies that integrate the methods and findings of several disciplines. The role of systems analysis, a method especially suited to taking account of the linkages between phenomena and of the hierarchical organization of the natural and social world, was also assessed, taking account of the implications this has for IIASA's research approach and activities. This paper is one of six IIASA Collaborative Papers published as part of the report on the conference, an earlier instalment of which was Science and Sustainability, published in 1992. Professor Koptyug's paper is written from the viewpoint of a chemist, but of one who has an unusual consciousness of error in estimates of some of the vital parameters affecting the environment. He finds a variation of 100 percent between the low and high estimates of absorption of carbon dioxide by the oceans, and adding that to the similar variation in estimate of emissions and related quantities he ends up with a four-fold variation between the lowest and the highest rate of accumulation of carbon dioxide in the atmosphere. Yet the paper does not argue from this that we should do nothing until we know more. We know in what directions we have to move as we try for stability, and are learning something about directions we should not try. A lesson was learned in this latter sense from the building of a dam across a bay in the Caspian Sea in order to reduce evaporation. The story is that with the agricultural and industrial development along the Volga River the level of the Caspian Sea fell by three meters between 1933 and 1977. It was hoped that the darn separating off the Black Jaws Gulf would counteract the withdrawal of water from higher up. But there seems at the same time to have been a flow of water of unknown origin into the Caspian Sea. The Gulf dried out by evaporation, while the Caspian Sea rose a wholly unanticipated 13 centimeters per year. Such a rise was disastrous for people living along the coast, and the dam is now to be destroyed. For me the lesson is not that we should never do anything about the environment, hut rather that we should look very closely and be very sure of our knowledge base before we try smart tricks with the planet in the hope of neutralizing the effects of irresponsible industrialization. One such smart trick that was fortunately checked before it started to be built was the diversion southward of four major rivers that flow into the Arctic Ocean. No one has any way of estimating what unanticipated results might come from that, what uncontrollable positive feedback loops it might initiate. These are among the things I have learned from Professor Koptyug's paper

Opinion formation models based on game theory

A way to simulate the basic interactions between two individuals with different opinions, in the context of strategic game theory, is proposed. Various games are considered, which produce different kinds of opinion formation dynamics. First, by assuming that all individuals (players) are equals, we obtain the bounded confidence model of continuous opinion dynamics proposed by Deffuant et al. In such a model a tolerance threshold is defined, such that individuals with difference in opinion larger than the threshold can not interact. Then, we consider that the individuals have different inclinations to change opinion and different abilities in convincing the others. In this way, we obtain the so-called ``Stubborn individuals and Orators'' (SO) model, a generalization of the Deffuant et al. model, in which the threshold tolerance is different for every couple of individuals. We explore, by numerical simulations, the dynamics of the SO model, and we propose further generalizations that can be implemented.Comment: 18 pages, 4 figure