Election results and the Sznajd model on Barabasi network

Bernardes, Américo Tristão; Stauffer, Dietrich; Kertész, János

doi:10.1140/e10051-002-0013-y

Cited by 100 publications

(92 citation statements)

References 15 publications

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“…Bernardes et al [45] have shown that a similar model of 'magnetic' electoral voting on a scale-free network, in which the votes are to be distributed among a large number of candidates rather than just two, produces a power-law distribution of votes -which is precisely what has been observed for the 1998 Brazilian elections, in which over 100 million people voted for over 10,000 minor governmental offi cials [46] . The key consideration here is that these power-law statistics are not what would be expected if each voter were making his or her decision independently; in that case, the distribution of votes among candidates should be Gaussian.…”

Section: The Dynamics Of Votingmentioning

confidence: 69%

The Physical Modelling of Human Social Systems

Ball¹

2003

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One of the core assumptions in the study of complex systems is that there exist ‘universal’ features analogous to those that characterize the notion of universality in statistical physics. That is to say, sometimes the details do not matter: certain aspects of complex behaviour transcend the particularities of a given system, and are to be anticipated in any system of a multitude of simultaneously interacting components. There can be no tougher test of this idea than that posed by the nature of human social systems. Can there really be any similarities between, say, a collection of inanimate particles in a fluid interacting via simple, mathematically defined forces of attraction and repulsion, and communities of people each of whom is governed by an unfathomable wealth of psychological complexity? The traditional approach to the social sciences has tended to view these psychological factors as irreducible components of human social interactions. But attempts to model society using the methods and tools of statistical physics have now provided ample reason to suppose that, in many situations, the behaviour of large groups of people can be understood on the basis of very simple interaction rules, so that individuals act essentially as automata responding to a few key stimuli in their environment. This is clearly a challenging, perhaps even disturbing, idea. I will review some of the evidence in its favour. I will show, with examples ranging from pedestrian dynamics to social choice theory, economics, demography, and the formation of businesses and alliances, that modelling the behaviour of individuals and social and political institutions according to the viewpoint of statistical physics does seem capable of capturing some of the important features of social systems. These models reveal many of the characteristic elements displayed by other complex systems: collective dynamics that changes via abrupt shifts (phase transitions), metastability, critical phenomena and scale-free statistical variations. I will discuss what this implies for the notions of human free will and determinism.

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Section: The Dynamics Of Votingmentioning

confidence: 69%

The Physical Modelling of Human Social Systems

Ball¹

2003

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“…It has spawned many variations, including the addition of noise, independent behavior, contrarianlike agents and undecided voters, as well as generalizations to more than two states (opinions) and to arbitrary networks [2,9,10]. In all these variations, the most defining aspect of the Sznajd model is that it gives a greater convincing power to bigger groups of agreeing agents.…”

Section: Introductionmentioning

confidence: 99%

Connections between the Sznajd model with general confidence rules and graph theory

Timpanaro

Prado

2012

Phys. Rev. E

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The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

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“…Predictions on Brazilian and Indian elections has been possible by introducing more than two opinion states together with probabilistic external influences of the candidates on the individuals [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…The two dimensional version of the Sznajd-Weron model has been extensively studied on simple square lattice [11,13,[24][25][26], on triangular lattice [27], on three-dimensional cubic lattice [19] and also on the dilute [12] systems.…”

Section: Introductionmentioning

confidence: 99%