论文标题
政治单极化与两极化之间竞争的模型
A model for the competition between political mono-polarization and bi-polarization
论文作者
论文摘要
我们通过在E 101，012101（2020）中引入的互动代理的人群中进行了政治双极化的现象，以进行投票意图的动态。每个代理商的倾向$ p $ in $ [0,1] $投票给两个政治候选人之一。在迭代步骤中，两个代理$ i $和$ j $，具有相应的倾向$ p_i $和$ p_j $互动，然后$ p_i $要么增加$ h> 0 $，概率是$ p_i $和$ p_i $和$ p_j $或$ h $ a $ h $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。我们研究了在衡量倾向更新规则的非线性的参数$ q \ ge 0 $的变化下系统的行为。我们专注于两个不同固定状态的稳定性：单极化，其中所有代理具有相同的极端倾向（$ 0 $或$ 1 $），而两极化则分为两组，分为两组，相反和极端的倾向。我们发现，对$ q <q_c $的两极化状态是稳定的，而单偏态化状态对于$ q>> q_c $稳定，其中$ q_c $是过渡值降低，$ h $降低。我们开发了一种速率方程方法，其稳定性分析表明，$ q_c $当$ h $变得无限时会消失。该结果得到了对连续$ h \至0 $限制中得出的传输方程的分析。我们还通过蒙特卡洛模拟显示，在$ n $ scales系统中，$τ\ sim n^α$在$ q_c $上达到单极化的平均时间$τ$，其中$α（h）$是非宇宙指数。
We investigate the phenomena of political bi-polarization in a population of interacting agents by means of a generalized version of the model introduced in PRE E 101, 012101 (2020) for the dynamics of voting intention. Each agent has a propensity $p$ in $[0,1]$ to vote for one of two political candidates. In an iteration step, two agents $i$ and $j$ with respective propensities $p_i$ and $p_j$ interact, and then $p_i$ either increases by an amount $h>0$ with a probability that is a nonlinear function of $p_i$ and $p_j$ or decreases by $h$ with the complementary probability. We study the behavior of the system under variations of a parameter $q \ge 0$ that measures the nonlinearity of the propensity update rule. We focus on the stability properties of the two distinct stationary states: mono-polarization in which all agents share the same extreme propensity ($0$ or $1$), and bi-polarization where the population is divided into two groups with opposite and extreme propensities. We find that the bi-polarized state is stable for $q<q_c$, while the mono-polarized state is stable for $q>q_c$, where $q_c$ is a transition value that decreases as $h$ decreases. We develop a rate equation approach whose stability analysis reveals that $q_c$ vanishes when $h$ becomes infinitesimally small. This result is supported by the analysis of a transport equation derived in the continuum $h \to 0$ limit. We also show by Monte Carlo simulations that the mean time $τ$ to reach mono-polarization in a system of size $N$ scales as $τ\sim N^α$ at $q_c$ , where $α(h)$ is a non-universal exponent.
