Conditional dichotomy, the contrast between two outputs conditioned on the same context, is vital for applications such as debate, defeasible inference, and causal reasoning. Existing methods that rely on semantic similarity often fail to capture the nuanced oppositional dynamics essential for these applications. Motivated by these limitations, we introduce a novel task, Conditional Dichotomy Quantification (ConDQ), which formalizes the direct measurement of conditional dichotomy and provides carefully constructed datasets covering debate, defeasible natural language inference, and causal reasoning scenarios. To address this task, we develop the Dichotomy-oriented Geometric Embedding (DoGE) framework, which leverages complex-valued embeddings and a dichotomous objective to model and quantify these oppositional relationships effectively. Extensive experiments validate the effectiveness and versatility of DoGE, demonstrating its potential in understanding and quantifying conditional dichotomy across diverse NLP applications. Our code and datasets are available at https://github.com/cui-shaobo/conditional-dichotomy-quantification.