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# O voto dos fÃ­sicos

Tactical Voting in Plurality Elections

(Submitted on 16 Sep 2010)

Abstract: How often will elections end in landslides? What is the probability for a head-to-head race? Analyzing ballot results from several large countries rather anomalous and yet unexplained distributions have been observed. We identify tactical voting as the driving ingredient for the anomalies and introduce a model to study its effect on plurality elections, characterized by the relative strength of the feedback from polls and the pairwise interaction between individuals in the society. With this model it becomes possible to explain the polarization of votes between two candidates, understand the small margin of victories frequently observed for different elections, and analyze the polls’ impact in American, Canadian, and Brazilian ballots. Moreover, the model reproduces, quantitatively, the distribution of votes obtained in the Brazilian mayor elections with two, three, and four candidates.

 Comments: 7 pages, 4 figures Subjects: Physics and Society (physics.soc-ph); Data Analysis, Statistics and Probability (physics.data-an) JournalÂ reference: PLoS One 5, e12446, 2010 DOI: 10.1371/journal.pone.0012446 CiteÂ as: arXiv:1009.3099v1 [physics.soc-ph]

Statistics of opinion domains of the majority-vote model on a square lattice

Authors: Lucas R. Peres, Jose F. Fontanari
(Submitted on 22 Aug 2010)

Abstract: The existence of juxtaposed regions of distinct cultures in spite of the fact that people’s beliefs have a tendency to become more similar to each other’s as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors’ opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only.
Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $\ln L^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model — Axelrod’s model — we found that these opinion domains are unstable to the effect of a thermal-like noise.

 Subjects: Computational Physics (physics.comp-ph); Statistical Mechanics (cond-mat.stat-mech); Physics and Society (physics.soc-ph) CiteÂ as: arXiv:1008.3697v1 [physics.comp-ph]
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