We propose a new version of the spatial model of voting. Platforms of five parties are evolving in a two-dimensional landscape of political issues so as to get maximal numbers of voters. For a Gaussian landscape the evolution leads to a spatially symmetric state, where the platform centers form a pentagon around the Gaussian peak. For a bimodal landscape the platforms located at different peaks get different numbers of voters.
Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported before. We first show this correlation in results from recent elections in Germany, France and republican primaries in the USA. However the mechanism generating such feature remains so far unexplained. We develop a mathematical model of voter grouping that is only based on the word of mouth and not on political contents. The model is close to the infinite allele …
The median-voter hypothesis (MVH) predicts convergence of two party platforms across a one-dimensional political spectrum during majoritarian elections. From the viewpoint of the MVH, an explanation of polarization is that each election has a different median voter so that a party cannot please all the median voters at the same time. We consider two parties competing to win voters along a one-dimensional spectrum and assume that each party nominates one candidate out of two in the primary election, for which the electorates represent only one side of the whole population. We argue that all the…
Recent political campaigns have demonstrated how technologies are used to boost election outcomes by microtargeting voters. We propose and analyze a framework which analyzes how political activists use technologies to target voters. Voters are represented as nodes of a network. Political activists reach out locally to voters and try to convince them. Depending on their technological advantage and budget, political activists target certain regions in the network where their activities are able to generate the largest vote-share gains. Analytically and numerically, we quantify vote-share gains a…
Recent empirical findings suggest that societies have become more polarized in various countries. That is, the median voter of today represents a smaller fraction of society compared to two decades ago and yet, the mechanisms underlying this phenomenon are not fully understood. Since interactions between influential actors ("activists") and voters play a major role in opinion formation, e.g. through social media, we develop a macroscopic opinion model in which competing activists spread their political ideas in specific groups of society. These ideas spread further to other groups in declining…
The binomial system is an electoral system unique in the world. It was used to elect the senators and deputies of Chile during 27 years, from the return of democracy in 1990 until 2017. In this paper we study the real voting power of the different political parties in the Senate of Chile during the whole binomial period. We not only consider the different legislative periods, but also any party changes between one period and the next. The real voting power is measured by considering power indices from cooperative game theory, which are based on the capability of the political parties to form w…
We study the opinion dynamics in a generalized voter model in which voters are additionally influenced by two antagonistic news sources, whose effect is to promote political polarization. We show that, as the influence of the news sources is increased, the mean time to reach consensus is anomalously long, the time to reach a politically polarized state is quite short, and the steady-state opinion distribution exhibits a transition from a near consensus state to a politically polarized state.
A simple model, suitable to describe the dynamics of a political system consisting of three macro--groups affected by turncoat--like behaviors and the influence of the opportunistic attitudes of politicians on voters' opinion, is presented. The model is based on raising and lowering fermionic operators whose dynamics is ruled by a suitable quadratic Hamiltonian operator with the addition of specific rules (depending on the variations of the mean values of the observables) able to adjust periodically the model to the political environment, \emph{i.e.}, we move in the framework of the so called …
The median-voter hypothesis predicts convergence of party platforms across a one-dimensional political spectrum during majoritarian elections. Assuming that the convergence is reflected in legislative activity, we study the time evolution of political polarization in the National Assembly of the Republic of Korea for the past 70 years. By projecting the correlation of lawmakers onto the first principal axis, we observe a high degree of polarization from the early 1960's to the late 1980's before democratization. As predicted by the hypothesis, it showed a sharp decrease when party politics wer…
We introduce the Multiscale Voter Model (MVM) to investigate clan influence at multiple scale -- family, neighborhood, political party... -- in opinion formation on real complex networks. Clans, consisting of similar nodes, are constructed using a coarse-graining procedure on network embeddings that allows us to control for the length scale of interactions. We ran numerical simulations to monitor the evolution of MVM dynamics in real and synthetic networks, and identified a transition between a final stage of full consensus and one with mixed binary opinions. The transition depends on the scal…
