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In this paper, we introduce a novel flexible Gini index, referred to as the extended Gini index, which is defined through ordered differences between the $j$th and $k$th order statistics within subsamples of size $m$, for indices satisfying…
Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior. We analyze datasets of household income from 67…
We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or…
We consider the problem of dividing items between individuals in a way that is fair both in the sense of distributional fairness and in the sense of not having disparate impact across protected classes. An important existing mechanism for…
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete…
This paper presents an empirical application of the Gause-Witt model of population ecology and ecosystems to the income distribution competitive dynamics of social classes in economic systems. The Gause-Witt mathematical system of coupled…
Fairness is an important performance criterion in all resource allocation schemes, including those in distributed computer systems. However, it is often specified only qualitatively. The quantitative measures proposed in the literature are…
In this paper, we obtain an upper bound for the Gini mean difference based on mean, variance and correlation for the case when the variables are correlated. We also derive some closed-form expressions for the Gini mean difference when the…
We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to\infty$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each…
The analysis of the USA 2001 income distribution shows that it can be described by at least two main components, which obey the generalized Tsallis statistics with different values of the q parameter. Theoretical calculations using the gas…
We propose a stochastic map model of economic dynamics. In the last decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of…
In this paper we explore the dynamic relationship between income inequality and economic mobility through a pairing of a population-scale partial differential equation (PDE) model and an associated individual-based stochastic differential…
Measuring inequalities in a multidimensional framework is a challenging problem which is common to most field of science and engineering. Nevertheless, despite the enormous amount of researches illustrating the fields of application of…
Families form the basis of society, and anthropologists have characterised various family systems. This study developed a multi-level evolutionary model of pre-industrial agricultural societies to simulate the evolution of family systems…
Wealth inequality is an important matter for economic theory and policy. Ongoing debates have been discussing recent rise in wealth inequality in connection with recent development of active financial markets around the world. Existing…
I develop a revealed preference framework to test whether an aggregate allocation of indivisible objects satisfies Pareto efficiency and individual rationality (PI) without observing individual preferences. Exploiting the type-based…
This paper develops a geometric diagnostic framework for classical inequality decomposability. Representing the simplest nontrivial setting of three-person income distributions as points on the two-dimensional income-share simplex, we…
The classical Lorenz curve is often used to depict inequality in a population of incomes, and the associated Gini coefficient is relied upon to make comparisons between different countries and other groups. The sample estimates of these…
I measure the uncertainty affecting estimates of economic inequality in the US and investigate how accounting for properly estimated standard errors can affect the results of empirical and structural macroeconomic studies. In my analysis, I…
Empirical welfare analyses often impose stringent parametric assumptions on individuals' preferences and neglect unobserved preference heterogeneity. We develop a framework to conduct individual and social welfare analysis for discrete…