Generalized Zipf's law in proportional voting processes

Lyra, M. L.; Costa, U. M. S.; Filho, R. N. Costa; Andrade, José S.

doi:10.1209/epl/i2003-00371-6

Cited by 43 publications

(44 citation statements)

References 19 publications

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“…q-exponential distributions have also been applied in the empirical study of stock markets [39][40][41][42], DNA sequences [43], family names [44], human behavior [45][46][47], geomagnetic records [48,49], train delays [50], reaction kinetics [51], air networks [52], hydrological phenomena [53], fossil register [54], basketball [55], earthquakes [56][57][58], world track records [59], voting processes [60], internet [61], individual success [62], citations of scientific papers [63,64], football [65], linguistics [66,67] and solar neutrinos [68,69].…”

Section: Q-exponential Distributionmentioning

confidence: 99%

q-distributions in complex systems: a brief review

Picoli¹,

Mendes²,

Malacarne³

et al. 2009

Braz. J. Phys.

104

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The nonextensive statistical mechanics proposed by Tsallis is today an intense and growing research field. Probability distributions which emerges from the nonextensive formalism (q-distributions) have been applied to an impressive variety of problems. In particular, the role of q-distributions in the interdisciplinary field of complex systems has been expanding. Here, we make a brief review of q-exponential, q-Gaussian and q-Weibull distributions focusing some of their basic properties and recent applications. The richness of systems analyzed may indicate future directions in this field.

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Section: Q-exponential Distributionmentioning

confidence: 99%

q-distributions in complex systems: a brief review

Picoli¹,

Mendes²,

Malacarne³

et al. 2009

Braz. J. Phys.

104

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“…In particular, several approximate statistical laws of how vote and turnout are distributed have been identified (20)(21)(22), and some of them are shown to be valid across several countries (23,24). It is tempting to think of deviations from these approximate statistical laws as potential indicators for election irregularities, which are valid cross-nationally.…”

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confidence: 99%

Statistical detection of systematic election irregularities

Klimek

Yegorov

Hanel

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

117

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Democratic societies are built around the principle of free and fair elections, and that each citizen's vote should count equally. National elections can be regarded as large-scale social experiments, where people are grouped into usually large numbers of electoral districts and vote according to their preferences. The large number of samples implies statistical consequences for the polling results, which can be used to identify election irregularities. Using a suitable data representation, we find that vote distributions of elections with alleged fraud show a kurtosis substantially exceeding the kurtosis of normal elections, depending on the level of data aggregation. As an example, we show that reported irregularities in recent Russian elections are, indeed, well-explained by systematic ballot stuffing. We develop a parametric model quantifying the extent to which fraudulent mechanisms are present. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces robust outcomes with respect to the resolution of the data and therefore, allows for cross-country comparisons.

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“…The first empirical study was done in the case of the Federal elections of 1998 in Brazil [17], where was reported a power law distribution of the fraction of votes obtained by candidates according to Zipf law . This result was reconfirmed in the elections of 2002 [18]. This result is reproduced if the fraction of votes is treated as a product of n independent "persuasive" subprocesses with the electors, each of which succeeds with probability p i .…”

Section: Introductionmentioning

confidence: 66%

Distribution of Votes and a Model of Political Opinion Formation for Majority Elections

Prenga

Ifti

2012

Int. J. Mod. Phys. Conf. Ser.

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We study the behavior of the number of votes cast for different electoral subjects in majority elections, and in particular, the Albanian elections of the last 10 years, as well as the British, Russian, and Canadian elections. We report the frequency of obtaining a certain percentage (fraction) of votes versus this fraction for the parliamentary elections. In the distribution of votes cast in majority elections we identify two regimes. In the low percentiles we see a power law distribution, with exponent about −1.7. In the power law regime we find over 80% of the data points, while they relate to 20% of the votes cast. Votes of the small electoral subjects are found in this regime. The other regime includes percentiles above 20%, and has Gaussian distribution. It corresponds to large electoral subjects. A similar pattern is observed in other first past the post (FPP) elections, such as British and Canadian, but here the Gaussian is reduced to an exponential. Finally we show that this distribution can not be reproduced by a modified "word of mouth" model of opinion formation. This behavior can be reproduced by a model that comprises different number of zealots, as well as different campaign strengths for different electoral subjects, in presence of preferential attachment of voters to candidates.

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Generalized Zipf's law in proportional voting processes

Cited by 43 publications

References 19 publications

q-distributions in complex systems: a brief review

q-distributions in complex systems: a brief review

Statistical detection of systematic election irregularities

Distribution of Votes and a Model of Political Opinion Formation for Majority Elections

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