A mere hyperbolic law, like the Zipf’s law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the “best (or optimal) distribution”, is provided through an entropy argument. The ranking of areas through the number of cities in various countries and some sport competition ranking serves for the present illustrations.

We propose an evolutionary game to analyse the dynamics of tolerance among heterogeneous economic agents. We show that: (i) intolerance is much more persistent than tolerance; (ii) a fully tolerant society assures prosperity; (iii) cultural integration should precede economic integration

This paper discusses the size distribution, -in economic terms -of the Italian municipalities over the period 2007-2011. Yearly data are rather well fitted by a modified Lavalette law, while Zipf-Mandelbrot-Pareto law seems to fail in this doing. The analysis is performed either at a national as well as at a local (regional and provincial) level. Deviations are discussed as originating in so called king and vice-roy effects. Results confirm that Italy is shared among very different regional realities. The case of Lazio is puzzling.

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In this paper, we explore tax revenues in a regime of widespread corruption in a growth model. We develop a Ramsey model of economic growth with a rival but non-excludable public good which is financed by taxes which can be evaded via corrupt tax inspectors. We prove that the relationship between the tax rate and tax collection, in a dynamic framework, is not unique, but is different depending on the relevance of the “shame effect”. We show that in all three cases — “low, middle and high shame” countries, the growth rate increases as the tax rate increases up to a threshold value, after which the growth rate begins to decrease as the tax rate increases. But, for intermediate tax rates, the rate of growth for “low shame” countries is lower than that of “uniform shame” countries which is, in turn, lower than that of “high shame” countries. This happens because the growth rate is more sensitive to variations of t in an honest country rather than in a corrupt country

This paper analyzes the existing relationship between ethnic fractionalization, corruption and the growth rate of a country. We provide a simple theoretical model. We show that a nonlinear relationship between fractionalization and corruption exists: corruption is high in homogeneous or very fragmented countries, but low where fractionalization is intermediate. In fact, when ethnic diversity is intermediate, constituencies act as a check and balance device to limit ethnically-based corruption. Consequently, the relationship between fractionalization and growth rate is also non-linear: growth is high in the middle range of ethnic diversity, low in homogeneous or very fragmented countries.

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This work presents a text mining context and its use for a deep analysis of the messages delivered by the politicians. Specifically, we deal with an expert systems-based exploration of the rhetoric dynamics of a large collection of US Presidents' speeches, ranging from Washington to Trump. In particular, speeches are viewed as complex expert systems whose structures can be effectively analyzed through rank-size laws. The methodological contribution of the paper is twofold. First, we develop a text mining-based procedure for the construction of the dataset by using a web scraping routine on the Miller Center website -the repository collecting the speeches. Second, we explore the implicit structure of the discourse data by implementing a rank-size procedure over the individual speeches, being the words of each speech ranked in terms of their frequencies. The scientific significance of the proposed combination of text-mining and rank-size approaches can be found in its flexibility and generality, which let it be reproducible to a wide set of expert systems and text mining contexts. The usefulness of the proposed method and the speech subsequent analysis is demonstrated by the findings themselves. Indeed, in terms of impact, it is worth noting that interesting conclusions of social, political and linguistic nature on how 45 United States Presidents, from April 30, 1789 till February 28, 2017 delivered political messages can be carried out. Indeed, the proposed analysis shows some remarkable regularities, not only inside a given speech, but also among different speeches. Moreover, under a purely methodological perspective, the presented contribution suggests possible ways of generating a linguistic decision-making algorithm.