Victory Tax: A Holistic Income Tax System

How can an income tax system be designed to exploit human nature and a free market to create a poverty free society, while balancing budgets without disproportional tax burdens? Such a tax system, with universal character, is deduced from the following guiding principles: (1) a single tax rate applies to all income types and levels; (2) the tax rate adjusts to satisfy budget projections; (3) government transfer only supplements the income of households with self-generated income below the poverty line; (4) deductions for basic living expenses, itemized investments and capital losses are allowed; (5) deductions cannot be applied to government transfer. A general framework emerges with three parameters that determine a minimum allowed tax deduction, a maximum allowed itemized deduction, and a maximum deduction defined by income percentage. An income distribution that mimics the United States, and a series of log-normal distributions are considered to quantitatively compare detailed characteristics of this tax system to progressive and flat tax systems. To minimize government dependency while maximizing after-tax income, the effective tax rate (ETR) as a function of income percentile takes the shape of the letter, V, inspiring the name victory tax, where the middle class has the lowest ETR.     

Role of parties in the vote distribution of proportional elections

We analyze proportional election data to show the influence of parties on the results of this kind of election. The study compiles data from different countries and dates to show that depending on how the candidate’s votes are counted, one can find that these votes have different distributions. When considering the fraction of votes received by the candidates, the vote distribution has a power law behavior with exponent α=1 for all cases studied. However, this universal behavior is modified when we normalize the fraction of votes by the mean number of votes of the candidate’s party. Considering this normalization, the Brazilian and the Finnish results are now different. The former follows an exponential while the latter a log-normal distribution.     

Simulations of large acoustic scintillations in the straits of Florida

Using a full-wave acoustic model, Monte Carlo numerical studies of intensity fluctuations in a realistic shallow water environment that simulates the Straits of Florida, including internal wave fluctuations and bottom roughness, have been performed. Results show that the sound intensity at distant receivers scintillates dramatically. The acoustic scintillation index SI increases rapidly with propagation range and is significantly greater than unity at ranges beyond about 10 km. This result supports a theoretical prediction by one of the authors. Statistical analyses show that the distribution of intensity of the random wave field saturates to the expected Rayleigh distribution with SI= 1 at short range due to multipath interference effects, and then SI continues to increase to large values. This effect, which is denoted supersaturation, is universal at long ranges in waveguides having lossy boundaries (where there is differential mode attenuation). The intensity distribution approaches a log-normal distribution to an excellent approximation; it may not be a universal distribution and comparison is also made to a K distribution. The long tails of the log-normal distribution cause "acoustic intermittency" in which very high, but rare, intensities occur.     

Income distribution dependence of poverty measure: A theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the ‘global’ mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy.     

Properties of wealth distribution in multi-agent systems of a complex network

We present a simple model for examining the wealth distribution with agents playing evolutionary games (the Prisoners’ Dilemma and the Snowdrift Game) on complex networks. Pareto’s power law distribution of wealth (from 1897) is reproduced on a scale-free network, and the Gibbs or log-normal distribution for a low income population is reproduced on a random graph. The Pareto exponents of a scale-free network are in agreement with empirical observations. The Gini coefficient of an ER random graph shows a sudden increment with game parameters. We suggest that the social network of a high income group is scale-free, whereas it is more like a random graph for a low income group.     

Stock market return distributions: From past to present

We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index α>3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on high-frequency recordings of the S&P500, DAX and WIG20 indices over the interval May 2004-May 2006. Our findings suggest that dynamics of the contemporary market may differ from the one observed in the past. This effect indicates a constantly increasing efficiency of world markets.     

Financial Return Distributions: Past,Present, and COVID-19

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.     

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L ^d–1 × L _z , characterizing by parameters L/ξ and L _z /L (ξ is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d = 2 + ? obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g = 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for d = 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio L/ξ.     

Universality in the tail of musical note rank distribution

Although power laws have been used to fit rank distributions in many different contexts, they usually fail at the tails. Languages as sequences of symbols have been a popular subject for ranking distributions, and for this purpose, music can be treated as such. Here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution, which arises in the ranking of multiplicative stochastic processes. The parameters a and b are obtained for classical, jazz and rock music, revealing interesting features. Specially, we have obtained a clear trend in the values of the parameters for major and minor tonal modes. Finally, we discuss the distribution of notes for each octave and its connection with the ranking of the notes.     

Anomalous wave function statistics on a one-dimensional lattice with power-law disorder

Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.     

Nonextensive statistical features of the Polish stock market fluctuations

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here, we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999–31.10.2005 for the time lags ranging from 1min$1\min$ up to 1 h. This market is commonly classified as emerging. Still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power law, as identified previously for majority of the mature markets. Within the time scales studied, a quick and considerable departure from this law towards a Gaussian can however be traced. Interestingly, all the forms of the distributions observed can be comprised by the single q-Gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation. The corresponding nonextensivity parameter q was found to systematically decrease when increasing the time scales. The temporal correlations quantified here in terms of multifractality provide further arguments in favor of nonextensivity.     

Runaway events dominate the heavy tail of citation distributions

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have unproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or power-law fit. The goal of our study is to solve this debate by measuring citation distribution for a very large and homogeneous data. We measured citation distribution for 418, 438 Physics papers published in 1980–1989 and cited by 2008. While the log-normal fit deviates too strong from the data, the discrete power-law function with the exponent γ = 3.15 does better and fits 99.955% of the data. However, the extreme tail of the distribution deviates upward even from the power-law fit and exhibits a dramatic “runaway” behavior. The onset of the runaway regime is revealed macroscopically as the paper garners 1000-1500 citations, however the microscopic measurements of autocorrelation in citation rates are able to predict this behavior in advance.     

How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products

We have considered the statistical distributions of the volumes of 1131 products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries’ economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramér-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy.     

A Gibbs-Like Measure for Single-Time, Multi-Scale Energy Transfer in Stochastic Signals and Shell Model of Turbulence

A Gibbs-like approach for simultaneous multi-scale correlation functions in random, time-dependent, multiplicative processes for the turbulent energy cascade is investigated. We study the optimal log-normal Gibbs-like distribution able to describe the subtle effects induced by non-trivial time dependency on both single-scale (structure functions) and multi-scale correlation functions. We provide analytical expression for the general multi-scale correlation functions in terms of the two-point correlations between multipliers and we show that the log-normal distribution is already accurate enough to reproduce quantitatively many of the observed behavior. The main result is that non-trivial time effects renormalize the Gibbs-like effective potential necessary to describe single-time statistics. We also present a generalization of this approach to more general, non log-normal, potentials. In the latter case one obtains a formal expansion of both structure functions and multi-scale correlations in terms of cumulants of all orders.     

On the origin of bursts and heavy tails in animal dynamics

Over recent years there has been an accumulation of evidence that many animal behaviours are characterised by common scale-invariant patterns of switching between two contrasting activities over a period of time. This is evidenced in mammalian wake-sleep patterns, in the intermittent stop-start locomotion of Drosophila fruit flies, and in the Lévy walk movement patterns of a diverse range of animals in which straight-line movements are punctuated by occasional turns. Here it is shown that these dynamics can be modelled by a stochastic variant of Barabási’s model [A.-L. Barabási, The origin of bursts and heavy tails in human dynamics, Nature 435 (2005) 207-211] for bursts and heavy tails in human dynamics. The new model captures a tension between two competing and conflicting activities. The durations of one type of activity are distributed according to an inverse-square power-law, mirroring the ubiquity of inverse-square power-law scaling seen in empirical data. The durations of the second type of activity follow exponential distributions with characteristic timescales that depend on species and metabolic rates. This again is a common feature of animal behaviour. Bursty human dynamics, on the other hand, are characterised by power-law distributions with scaling exponents close to −1 and −3/2.     

Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost∕benefit model

Probability distributions of human displacements have been fit with exponentially truncated Le?vy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the city of residence), but with a non-vanishing frequency they visit nearby or far locations too. Herein, we show that an important empirical distribution of human displacements (range: from 1 to 1000 km) can be well fit by three consecutive Pareto distributions with simple integer exponents equal to 1, 2, and (>) 3. These three exponents correspond to three displacement range zones of about 1 km ?Δr?10 km, 10 km ?Δr?300 km, and 300 km ?Δr?1000 km, respectively. These three zones can be geographically and physically well determined as displacements within a city, visits to nearby cities that may occur within just one-day trips, and visit to far locations that may require multi-days trips. The incremental integer values of the three exponents can be easily explained with a three-scale mobility cost∕benefit model for human displacements based on simple geometrical constrains. Essentially, people would divide the space into three major regions (close, medium, and far distances) and would assume that the travel benefits are randomly∕uniformly distributed mostly only within specific urban-like areas. The three displacement distribution zones appear to be characterized by an integer (1, 2, or >3) inverse power exponent because of the specific number (1, 2, or >3) of cost mechanisms (each of which is proportional to the displacement length). The distributions in the first two zones would be associated to Pareto distributions with exponent β?=?1 and β?=?2 because of simple geometrical statistical considerations due to the a priori assumption that most benefits are searched in the urban area of the city of residence or in the urban area of specific nearby cities. We also show, by using independent records of human mobility, that the proposed model predicts the statistical properties of human mobility below 1 km ranges, where people just walk. In the latter case, the threshold between zone 1 and zone 2 may be around 100-200 m and, perhaps, may have been evolutionary determined by the natural human high resolution visual range, which characterizes an area of interest where the benefits are assumed to be randomly and uniformly distributed. This rich and suggestive interpretation of human mobility may characterize other complex random walk phenomena that may also be described by a N-piece fit Pareto distributions with increasing integer exponents. This study also suggests that distribution functions used to fit experimental probability distributions must be carefully chosen for not improperly obscuring the physics underlying a phenomenon.     

Multiplicative processes and power laws in human reaction times derived from hyperbolic functions

In sensory psychophysics reaction time is a measure of the stochastic latency elapsed from stimulus presentation until a sensory response occurs as soon as possible. A random multiplicative model of reaction time variability is investigated for generating the reaction time probability density functions. The model describes a generic class of hyperbolic functions by Piéron?s law. The results demonstrate that reaction time distributions are the combination of log-normal with power law density functions. A transition from log-normal to power law behavior is found and depends on the transfer of information in neurons. The conditions to obtain Zipf?s law are analyzed.     

A mechanism to derive multi-power law functions: An application in the econophysics framework

It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a two-power law distribution starting from a single power law function recently obtained, in the frameworks of the generalized statistical mechanics based on the Sharma-Taneja-Mittal information measure. In order to test the method, we fit the cumulative distribution of personal income and gross domestic production of several countries, obtaining a good agreement for a wide range of data.