Three-state modified voter model for languages--论文代写范文精选

任何试图解决现象的复杂性，在全球层面上,偶然发现一系列的理论和方法论，最近的研究表明,在给定的选择域,如果个人倾向分享相似的知识结构，目前的研究中,我们将分析地理,语言学,社会学和政治因素。下面的政治essay代写范文进行详述。

Abstract 
  The standard three-state voter model is enlarged by including the outside pressure favouring one of the three language choices and by adding some biased internal random noise. The Monte Carlo simulations are motivated by states with the population divided into three groups of various affinities to each other. We show the crucial influence of the boundaries for moderate lattice sizes like 500 × 500. By removing the fixed boundary at one side, we demonstrate that this can lead to the victory of one single choice. Noise in contrast stabilizes the choices of all three populations. In addition, we compute the persistence probability, i.e., the number of sites who have never changed their opinion during the simulation, and we consider the case of ”rigid-minded” decision makers.

 Motivation and Model 
  The political situation after the break-up of former communist powers and the emergence of new sovereign states in Europe and elsewhere, justify yet another look at linguistic practices as informed by geopolitical agendas with the ever growing asymmetric power relations and the ongoing struggle for the accumulation of linguistic and cultural capital. Pronounced language asymmetries with highly competitive behaviour have caused a situation in which no successor state can claim a one-and-only homogeneous ”national language” without serious caveats. In complex decision making, there are typically no single agreements when large numbers of decision makers are expected to choose from a large set of alternatives [1]. 

  Any attempts to tackle the intricacies of these phenomena at the more global level, stumble across a series of theoretical and methodological problems. However, more recent studies have shown that if individuals tend to share similar knowledge structures within a given choice domain, then a rather stable global choice behaviour is observed with about 90% probability [2]. In the present study, we shift the analysis of geographical [3], linguistic, sociological and political factors to another report [4], while looking here for a model which may describe a type of language competition observed in an environment populated by strong minorities facing several alternative choices and partially bordering on supporting states. 

  We do not intend to discuss whether ”dialects” would be a better name instead of ”languages”, however, we notice that recent linguistic analyses [5] could not trace any dialectal differences following national lines in many of the successor states in e.g. Southeast Europe. Instead, it has been increasingly argued [6] that all different groups in the region tend to use exactly the same idiom. However, the restructured political pictures lead to the emergence of completely new policies, such that the question of language has become a top political issue in a community which is linguistically homogeneous but politically divided [6]. We treat this problem as the one of opinion dynamics where everybody can adopt one of the three choices A, B, and C (each representing the opinion about the linguistic identity), with transitive [7] preference relations. Thus we model the evolution of the global choice behaviour in a tripartite system where due to particular economic and political alliances, languages may happen to be in a closer contact at one point in time and more divided at another. 

  As a consequence, people may start adopting linguistic features or even full languages of their neighbours, if they have sufficient gains or are in- fluenced by a set of social and/or political factors. This is especially valid for those languages which both belong to the same linguistic family and border with one another. In our model, we assume that the simulated L × L lattice is bordered on top by the population preferring the linguistic choice A and on bottom by the population preferring the choice C. 

  This we achieve through two boundary lines of only A on top and only C on bottom. Initially, in the middle of the lattice, the decision makers (DM) preferring the choice B are dominant, while on the top we have DM mostly preferring A and on the bottom mostly preferring C, with the concentrations of A, B, and C varying linearly with Opinion dynamics can be described in several different ways, by using e.g. the models of Deffuant et al. [8], Krause and Hegselmann [9], Sznajd [10], or some older approaches such as the model of Axelrod [11]. In the present paper, the basic dynamics is the traditional voter model [12], where at each iteration every site accepts the language of a randomly selected nearest neighbour. 

  Then every individual with choice A having three individuals with choice B and one with A as neighbours is likely to give up the choice A and shift to B. Instead of this voter model we also could have used a Pottstype model [14], as did Lim et al. [3] without mentioning Potts, or an Ising model with spin +1, 0, −1. The voter model, however, seems to be simpler, and is a first step towards a more complete future work on this topic. In addition, we assume that with low probability p at each iteration each individual accepts the choice B because of ”advertising campaigns” [13] from higher authority. Furthermore, we added noise to the whole process, in We further investigate the case in which one of the two fixed boundaries in the model is removed (e.g. when the neighbouring side weakens or disrupts its support), assuming that this might lead to the victory of one of the opinion alternatives within the tripartite system. （essay代写)

  We also compute the persistence probability s(k, t) for different lattice sizes, where k is the number of opinions in the original voter model, and p = q = 0.00001. We do not take into account the population size dynamics (birth vs. death rates). Of course, the question of how exactly individuals aggregate their preferences over k candidate languages involves much more fine-granularity than considered in the present model. Indeed, the opinion switching dynamics might be far more complex than described by the update rule in the present study. For instance, not only single individuals, but moreover, larger amounts of population members might drastically change their attitudes towards linguistic (and political) campaigns such that they no longer participate in the opinion switching process. Thus, they might just ”tune out” [15] at one or more points in time, thereby considerably affecting the overall evolution of preferences or choices. At such times, the individual state remains frozen, until a particular event causes the decision maker to re-enter the switching process. In order to reflect on this type of behaviour in our simulations, we included a situation in which a particular random (quenched)（essay代写)

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