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Register a new userTax evasion study in a society realized as a diluted Ising model with competing interactions
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Added by
Julian Giraldo-Barreto
Publication date
2021
fields
Physics
and research's language is
English
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In this research, the tax evasion percentage, as order parameter, of a system of individuals or agents inscribed in a $N = L times L$ 2D square grid is computed. The influence of local environment over each agent is quantified both through competitive exchange integrals (ferromagnetic and antiferromagnetic bonds) and dangling bonds randomly distributed, which allows to identify the system with disordered ternary alloys of the type $mathrm{A_textit{p}B_textit{x}C_textit{q}}$ with a certain stoichiometry $(p,x,q)$ particular of each society. Our proposal is based on the so-called spin glass phase present in magnetic systems characterized by disorder, dilution and competitive interactions where magnetic frustration can take place, resembling the way as an individual or agent in a society is able to face a decision. In this sense, agents are identified as Ising spins, which can take two possible values ($sigma = pm 1$), in correspondence with a two-state system where agents can be tax compliant or not. Such an identification between social and physical variables, as well as parameters like an external applied magnetic field or temperature, are topic of discussion in this investigation. Thermalization of the observables is carried out by means of the heat bath algorithm. Other social variables, such as the audit period, and its effects over the percentage of evasion, are used to analyze the behavior of tax evasion in Colombia, however the model can be applied to any country.
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We develop a model of tax evasion based on the Ising model. We augment the model using an appropriate enforcement mechanism that may allow policy makers to curb tax evasion. With a certain probability tax evaders are subject to an audit. If they get caught they behave honestly for a certain number of periods. Simulating the model for a range of parameter combinations, we show that tax evasion may be controlled effectively by using punishment as an enforcement mechanism.
Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on Stauffer-Hohnisch-Pittnauer (SHP) networks. To control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhood of the critical noise $q_{c}$ to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied besides using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.
Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erdos-Renyi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical $q_{c}$. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust and can be reproduced also through the nonequilibrium MVM on various topologies.
By tempered Monte Carlo simulations, we study 2D site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L^2 sites in a square lattice, and point along a common crystalline axis. For x_c< x<=1, where x_c = 0.79(5), we find an antiferromagnetic phase below a temperature which vanishes as x approaches x_c from above. At lower values of x, we study (i) distributions of the spin--glass (SG) overlap q, (ii) their relative mean square deviation Delta_q^2 and kurtosis and (iii) xi_L/L, where xi_L is a SG correlation length. From their variation with temperature and system size, we find that the paramagnetic phase covers the entire T>0 range. Our results enable us to obtain an estimate of the critical exponent associated to the correlation length at T=0, 1/nu=0.35(10).
We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be developed. We illustrate our approach through a particular social network model: the rise and fall of a networked society [1]: we implement our low-dimensional description computationally using the equation-free approach and show how it can be used to (a) accelerate simulations and (b) extract system-level stability/bifurcation information from the detailed dynamic model. We discuss other system-level tasks that can be enabled through such a computer-assisted coarse graining approach.
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