We introduce the confident voter model, in which each voter can be in one of two opinions and can additionally have two levels of commitment to an opinion --- confident and unsure. Upon interacting with an agent of a different opinion, a confident voter becomes less committed, or unsure, but does not change opinion. However, an unsure agent changes opinion by interacting with an agent of a different opinion. In the mean-field limit, a population of size N is quickly driven to a mixed state and remains close to this state before consensus is eventually achieved in a time of the order of ln N. In two dimensions, the distribution of consensus times is characterized by two distinct times --- one that scales linearly with N and another that appears to scale as N^{3/2}. The longer time arises from configurations that fall into long-lived states that consist of two (or more) single-opinion stripes before consensus is reached. These stripe states arise from an effective surface tension between domains of different opinions.
We introduce the reputational voter model (RVM) to account for the time-varying abilities of individuals to influence their neighbors. To understand of the RVM, we first discuss the fitness voter model (FVM), in which each voter has a fixed and distinct fitness. In a voting event where voter $i$ is fitter than voter $j$, only $j$ changes opinion. We show that the dynamics of the FVM and the voter model are identical. We next discuss the adaptive voter model (AVM), in which the influencing voter in a voting event increases its fitness by a fixed amount. The dynamics of the AVM is non-stationary…
We analyse the structure and behaviour of a specific voting network using a dynamic structure-based methodology which draws on Q-Analysis and social network theory. Our empirical focus is on the Eurovision Song Contest over a period of 20 years. For a multicultural contest of this kind, one of the key questions is how the quality of a song is judged and how voting groups emerge. We investigate structures that may identify the winner based purely on the topology of the network. This provides a basic framework to identify what the characteristics associated with becoming a winner are, and may he…
In certain parliamentary democracies, there are two major parties that move in and out of power every few elections, and a third minority party that essentially never governs. We present a simple model to account for this phenomenon, in which minority party supporters sometimes vote ideologically (for their party) and sometimes strategically (against the party they like the least). The competition between these disparate tendencies reproduces the empirical observation of two parties that frequently exchange majority status and a third party that is almost always in the minority.
Election results are determined by numerous social factors that affect the formation of opinion of the voters, including the network of interactions between them and the dynamics of opinion influence. In this work we study the result of proportional elections using an opinion dynamics model similar to simple opinion spreading over a complex network. Erdos-Renyi, Barabasi-Albert, regular lattices and randomly augmented lattices are considered as models of the underlying social networks. The model reproduces the power law behavior of number of candidates with a given number of votes found in rea…
Motivated by the problem of partisan gerrymandering, we introduce an electoral system for a representative democracy called democratic cellular voting, designed to make modern packing and cracking strategies irrelevant by allowing districts to be influenced directly by voters through elections. We introduce an example of a democratic cellular voting system, called CV0, that is suitable for dynamic modelling. We develop a modification of the theory of discrete Markov chains using the algebraic structure of the semiring $[0,\infty]$, which is used as a space of correlation coefficients. We use t…
We generalize a binary majority-vote model on adaptive networks to its plurality-vote counterpart and analyze the time scale to consensus when voters are given more than two options. When opinions are uniformly distributed in the population of voters in the initial state, we find that the time scale to consensus is shorter than the binary vote model from both numerical simulations and mathematical analysis using the master equation for the three-state plurality-vote model. When intervention such as opinion conversion is allowed, as in the case of sudden change of mind of voter for any reason, …
A sociophysical model for opinion dynamics is shown to embody a series of recent western hung national votes all set at the unexpected and very improbable edge of a fifty-fifty score. It started with the Bush-Gore 2000 American presidential election, followed by the 2002 Stoiber-Schrőder, then the 2005 Schrőder-Merkel German elections, and finally the 2006 Prodi-Berlusconi Italian elections. In each case, the country was facing drastic choices, the running competing parties were advocating very different programs and millions of voters were involved. Moreover, polls were given a substantial ma…
Influence among individuals is at the core of collective social phenomena such as the dissemination of ideas, beliefs or behaviors, social learning and the diffusion of innovations. Different mechanisms have been proposed to implement inter-agent influence in social models from the voter model, to majority rules, to the Granoveter model. Here we advance in this direction by confronting the recently introduced Social Influence and Recurrent Mobility (SIRM) model, that reproduces generic features of vote-shares at different geographical levels, with data in the US presidential elections. Our app…
Formation of consensus, in binary yes/no type of voting, is a well defined process. However, even in presence of clear incentives, the dynamics involved can be incredibly complex. Specifically, formations of large groups of similarly opinionated individuals could create a condition of `support-bubbles' or spontaneous polarization that renders consensus virtually unattainable (e.g., the question of the UK exiting the EU). There have been earlier attempts in capturing the dynamics of consensus formation in societies through simple $Z_2$-symmetric models hoping to capture the essential dynamics o…
Non-linear voter models assume that the opinion of an agent depends on the opinions of its neighbors in a non-linear manner. This allows for voting rules different from majority voting. While the linear voter model is known to reach consensus, non-linear voter models can result in the coexistence of opposite opinions. Our aim is to derive approximations to correctly predict the time dependent dynamics, or at least the asymptotic outcome, of such local interactions. Emphasis is on a probabilistic approach to decompose the opinion distribution in a second-order neighborhood into lower-order prob…
We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the two alternatives, represented by a variable $p \in [0,1]$. When an agent $i$ interacts with another agent $j$ with propensity $p_j$, then $i$ either increases its propensity $p_i$ by $h$ with probability $P_{ij}=ωp_i+(1-ω)p_j$, or decreases $p_i$ by $h$ with probability $1-P_{ij}$, where $h$ is a fixed step. We analyze the system by a rate equation approach an…
We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many ``competing'' inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a nontrivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particle…
We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model unde…
It is known that individual opinions on different policy issues often align to a dominant ideological dimension (e.g. "left" vs. "right") and become increasingly polarized. We provide an agent-based model that reproduces these two stylized facts as emergent properties of an opinion dynamics in a multi-dimensional space of continuous opinions. The mechanisms for the change of agents' opinions in this multi-dimensional space are derived from cognitive dissonance theory and structural balance theory. We test assumptions from proximity voting and from directional voting regarding their ability to …
Merit based promotion & tenure decision have always been controversial. This paper suggests an agent based model of the decision making processs using spectral graph theory, where the voting agents are the vertices of the graph, and edge weights are determined based on the extent of collaborative research between the agents, as well as their estimated levels of social interactions. The model assumes that agents with lower research productivities tend to interact more often with one another. Using the graph theoretic spectrum, the paper proposes a 2-dimensional influence diagram that maps the v…
This paper investigates the detection of communication outbreaks among a small team of actors in time-varying networks. We propose monitoring plans for known and unknown teams based on generalizations of the exponentially weighted moving average (EWMA) statistic. For unknown teams, we propose an efficient neighborhood-based search to estimate a collection of candidate teams. This procedure dramatically reduces the computational complexity of an exhaustive search. Our procedure consists of two steps: communication counts between actors are first smoothed using a multivariate EWMA strategy. Dens…
Opinion polls mediated through a social network can give us, in addition to usual demographics data like age, gender and geographic location, a friendship structure between voters and the temporal dynamics of their activity during the voting process. Using a Facebook application we collected friendship relationships, demographics and votes of over ten thousand users on the referendum on the definition of marriage in Croatia held on 1st of December 2013. We also collected data on online news articles mentioning our application. Publication of these articles align closely with large peaks of vot…
