Opinion polarization is on the rise, causing concerns for the openness of public debates. Additionally, extreme opinions on different topics often show significant correlations. The dynamics leading to these polarized ideological opinions pose a challenge: How can such correlations emerge, without assuming them a priori in individual preferences or in a preexisting social structure? Here, we propose a simple model that qualitatively reproduces ideological opinion states found in survey data, even between rather unrelated, but sufficiently controversial, topics. Inspired by skew coordinate systems recently proposed in natural language processing models, we solidify these intuitions in a formalism of opinions unfolding in a multidimensional space where topics form a nonorthogonal basis. Opinions evolve according to the social interactions among the agents, which are ruled by homophily: Two agents sharing similar opinions are more likely to interact. The model features phase transitions between a global consensus, opinion polarization, and ideological states. Interestingly, the ideological phase emerges by relaxing the assumption of an orthogonal basis of the topic space, i.e., if topics thematically overlap. Furthermore, we analytically and numerically show that these transitions are driven by the controversialness of the topics discussed; the more controversial the topics, the more likely are opinions to be correlated. Our findings shed light upon the mechanisms driving the emergence of ideology in the formation of opinions.

中文翻译：

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多维主题空间中两极分化的意识形态的出现

舆论两极化正在上升，引起公众辩论公开的担忧。此外，对不同主题的极端看法通常显示出显着的相关性。导致这些两极分化的意识形态观点的动力提出了一个挑战：如何在没有先验假设的情况下出现这种相关关系是个人喜好还是已有的社会结构？在这里，我们提出了一个简单的模型，该模型定性地再现了在调查数据中发现的意识形态观点状态，即使是在不相关但有足够争议的主题之间。受自然语言处理模型中最近提出的偏斜坐标系的启发，我们在多维空间中展开的观点形式化中巩固了这些直觉，在这些多维空间中主题构成了非正交的基础。意见根据代理之间的社会互动而演变，这由同质性决定：具有相似观点的两个代理更可能互动。该模型的特征在于全球共识，意见分歧和意识形态状态之间的相变。有趣的是 通过放宽对主题空间的正交基础的假设（即主题在主题上重叠），意识形态阶段就出现了。此外，我们通过分析和数字分析表明，这些转变是由所讨论主题的争议性驱动的。主题越有争议，意见就越有可能相关。我们的发现揭示了推动思想形成中的意识形态出现的机制。