Power-law distributions from additive preferential redistributions

We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary random interactions with a simple additive preferential rule, while the sum of quantities is conserved. The situation described by this model is similar to those of closed $N$-particle systems when conservative two-body collisions are only allowed. We obtain stationary distributions of these quantities both analytically and numerically while varying parameters of the model, and find that the model exhibits the scaling behavior for some parameter ranges. Unlike well-known growth models, this alternative mechanism generates the power-law distribution when the growth is not expected and the dynamics of the system is based on interactions between elements. This model can be applied to some examples such as personal wealths, city sizes, and the generation of scale-free networks when only rewiring is allowed.Comment: 12 pages, 4 figures; Changed some expressions and notations; Added more explanations and changed the order of presentation in Sec.III while results are the sam

Typical properties of optimal growth in the Von Neumann expanding model for large random economies

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ increases beyond $P$. The solution is characterized by a universal behavior, independent of the parameters of the disorder statistics. Associating technological innovation to an increase of $N$, we find that while such an increase has a large positive impact on long term growth when $N\ll P$, its effect on technologically advanced economies ($N\gg P$) is very weak.Comment: 8 pages, 1 figur

Power Law Distribution of Wealth in a Money-Based Model

A money-based model for the power law distribution (PLD) of wealth in an economically interacting population is introduced. The basic feature of our model is concentrating on the capital movements and avoiding the complexity of micro behaviors of individuals. It is proposed as an extension of the Equiluz and Zimmermann's (EZ) model for crowding and information transmission in financial markets. Still, we must emphasize that in EZ model the PLD without exponential correction is obtained only for a particular parameter, while our pattern will give it within a wide range. The Zipf exponent depends on the parameters in a nontrivial way and is exactly calculated in this paper.Comment: 5 pages and 4 figure

Asymptotic analysis of the model for distribution of high-tax payers

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent -5/2 when a total ``mass'' has a certain critical value. Below the critical value, the system exhibits an ordinary critical behavior, and scaling relations hold. Above the threshold, numerical simulations show that a power-law distribution coexists with a huge ``monopolized'' member. It is argued that these behaviors are observed universally in conserved aggregation processes, by analizing an extended model.Comment: 5pages, 3figure

Implementation of the Combined--Nonlinear Condensation Transformation

We discuss several applications of the recently proposed combined nonlinear-condensation transformation (CNCT) for the evaluation of slowly convergent, nonalternating series. These include certain statistical distributions which are of importance in linguistics, statistical-mechanics theory, and biophysics (statistical analysis of DNA sequences). We also discuss applications of the transformation in experimental mathematics, and we briefly expand on further applications in theoretical physics. Finally, we discuss a related Mathematica program for the computation of Lerch's transcendent.Comment: 23 pages, 1 table, 1 figure (Comput. Phys. Commun., in press

Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them focuses on one feature of randomness, leading authors to have to use multiple measures. Here we describe and advocate for the use of the accepted universal measure for randomness based on algorithmic complexity, by means of a novel previously presented technique using the the definition of algorithmic probability. A re-analysis of the classical Radio Zenith data in the light of the proposed measure and methodology is provided as a study case of an application.Comment: To appear in Behavior Research Method

Dynamics of conflicts in Wikipedia

In this work we study the dynamical features of editorial wars in Wikipedia (WP). Based on our previously established algorithm, we build up samples of controversial and peaceful articles and analyze the temporal characteristics of the activity in these samples. On short time scales, we show that there is a clear correspondence between conflict and burstiness of activity patterns, and that memory effects play an important role in controversies. On long time scales, we identify three distinct developmental patterns for the overall behavior of the articles. We are able to distinguish cases eventually leading to consensus from those cases where a compromise is far from achievable. Finally, we analyze discussion networks and conclude that edit wars are mainly fought by few editors only.Comment: Supporting information adde

Colloquium: Statistical mechanics of money, wealth, and income

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio

Are public and private social expenditures complementary?

Most analyses of social protection are focussed on public arrangements. However, social effort is not restricted to the public domain; all kinds of private arrangements can be substitutes to public programs. OECD-data indicate that accounting for private social benefits and the impact of the tax system on social expenditure has an equalising effect on levels of social effort across a number of countries. This suggests complementarity between public and private social expenditures. Changes in the public/private mix in social protection will, however, have distributional effects. We expect that private schemes will generate less income redistribution than public programs. In this paper we will perform an empirical analysis. Using comparative international data we analyse whether there is a relationship between public and private social expenditures, and the distribution of income. We find a negative relationship between net public social expenditures and income inequality, but a positive relationship between net private social expenditures and income inequality across countries. In fact, when we incorporate private social security expenditures, the impact of total social expenditure on the income distribution becomes statistically trivial. We conclude that changes in the public/private mix in the provision of social protection may affect the redistributive impact of the welfare state