Linear threshold models have been studied extensively in structured populations; however, less attention is paid to perception differences among the individuals of the population. To focus on this effect, we exclude structure and consider a well-mixed population of heterogeneous agents, each associated with a threshold in the form of a fixed ratio within zero and one that can be unique to this agent. The agents are initialized with a choice of strategy $A$ or $B$, and at each time step, one agent becomes active to update; if the ratio of agents playing $A$ is higher (resp. lower) than her threshold, she updates to $A$ (resp. $B$). We show that for any given initial condition, after a finite number of time steps, the population reaches an equilibrium where no agent’s threshold is violated; however, the equilibrium is not necessarily uniquely determined by the initial condition but depends on the agents’ activation sequence. We find all those possible equilibria that the dynamics may reach from a given initial condition and show that, in contrast to the case of homogeneous populations, heterogeneity in the agents’ thresholds gives rise to several equilibria where both $A$-playing and $B$-playing agents coexist. Perception heterogeneity can, hence, preserve decision diversity, even in the absence of population structure. We also investigate the asymptotic stability of the equilibria and show how to calculate the contagion probability for a population with two thresholds.

线性阈值模型已在结构化人群中进行了广泛研究；但是，人们对人群个体之间的感知差异的关注较少。为了关注此效果，我们排除了结构，并考虑了异构试剂的充分混合的群体，每种试剂均与固定阈值形式的阈值相关，该阈值的范围在零以内，而该试剂对于该试剂而言是唯一的。通过选择策略初始化代理$\mathrm{一种}$ 要么 $乙$，并且在每个时间步骤中，一个代理都会处于活动状态以进行更新；如果代理商比例$\mathrm{一种}$ 高于（低于）阈值，她更新为 $\mathrm{一种}$ （分别 $乙$）。我们表明，对于任何给定的初始条件，经过有限的时间步长后，总体就会达到平衡，在此平衡下不会违反任何行为者的阈值。然而，平衡不一定由初始条件唯一决定，而是取决于试剂的活化顺序。我们发现了在给定的初始条件下动力学可能达到的所有可能的均衡，并表明与同质种群的情况相比，代理阈值的异质性引起了几种均衡，其中$\mathrm{一种}$播放和 $乙$游戏代理商并存。因此，即使没有人口结构，感知异质性也可以保留决策多样性。我们还研究了平衡点的渐近稳定性，并展示了如何计算具有两个阈值的种群的传染概率。