We assume a community whose members adopt one of two opinions [Formula: see text] or [Formula: see text]. Each member appears as an inflexible, or as a non-contrarian or contrarian floater. An inflexible sticks to its opinion, whereas a floater may change into a floater of the alternative opinion. The occurrence of this change is governed by the local majority rule: members meet in groups of a fixed size, and a floater then changes its opinion provided it is a minority in the group. Subsequently, a non-contrarian floater keeps the opinion as adopted under the local majority rule, whereas a contrarian floater adopts the alternative opinion. Whereas the effects of on the one hand inflexibles and on the other hand non-contrarians and contrarians have previously been studied separately, the current approach allows us to gain insight in the effect of their combined presence in a community. Given fixed proportions of inflexibles [Formula: see text] for the two opinions, and fixed fractions of contrarians [Formula: see text] among the [Formula: see text] and [Formula: see text] floaters, we derive the update equation [Formula: see text] for the overall support for opinion [Formula: see text] at time [Formula: see text], given [Formula: see text]. The update equation is derived respectively for local group sizes 1, 2 and 3. The associated dynamics generated by repeated local updates is then determined to identify its asymptotic steady configuration. The full opinion flow diagram is thus obtained, showing conditions in terms of the parameters for each opinion to eventually win the competing dynamics. Various dynamical scenarios are thus exhibited, and it is derived that relatively small densities of inflexibles allow for more variation in the qualitative outcome of the dynamics than higher densities of inflexibles.

中文翻译：

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由不灵活和非逆向和逆向浮动产生的两种意见动态

我们假设一个社区，其成员采用两种意见之一 [公式：见文本] 或 [公式：见文本]。每个成员都表现为一个不灵活的人，或者一个非逆向或逆向浮动的人。不灵活的人坚持自己的意见，而浮动的人可能会变成另一种意见的浮动。这种变化的发生受当地多数规则的约束：成员以固定规模的群体开会，然后如果漂浮者是群体中的少数群体，它就会改变其意见。随后，非逆向漂浮者保持当地多数规则下采用的意见，而逆向漂浮者采用替代意见。鉴于一方面不灵活和另一方面非逆势者和逆势者的影响先前已分别研究过，当前的方法使我们能够深入了解它们在社区中的联合存在的影响。给定两种意见的固定比例[公式：参见文本]，以及 [公式：参见文本] 和 [公式：参见文本] 浮动变量中的固定比例 [公式：参见文本]，我们推导出更新方程 [公式：见文]对意见的整体支持[公式：见文]时[公式：见文]，给定[公式：见文]。更新方程分别针对局部组大小 1、2 和 3 导出。然后确定由重复局部更新产生的相关动态以识别其渐近稳定配置。因此获得了完整的意见流程图，显示了每个意见最终赢得竞争动态的参数条件。